Optical fiber nanowires and microwires:

fabrication and applications

Gilberto Brambilla,1,* Fei Xu,1 Peter Horak,1 Yongmin Jung,1
Fumihito Koizumi,2 Neil P. Sessions,1 Elena Koukharenko,3 Xian Feng,1
Ganapathy S. Murugan,1 James S. Wilkinson,1 and David J. Richardson1
1
Optoelectronics Research Centre, University of Southampton,
Southampton SO17 1BJ, UK
2
Asahi Glass Co. Ltd., Kanagawa-ku, Yokohama 221-8755, Japan
3
School of Electronics and Computer Science, University of Southampton,
Southampton SO17 1BJ, UK
*Corresponding author: gb2@orc.soton.ac.uk

Received August 21, 2008; revised November 17, 2008; accepted November 17, 2008;
posted November 18, 2008 (Doc. ID 100357); published January 30, 2009

Microwires and nanowires have been manufactured by using a wide range of

bottom-up techniques such as chemical or physical vapor deposition and
top-down processes such as fiber drawing. Among these techniques, the
manufacture of wires from optical fibers provides the longest, most uniform
and robust nanowires. Critically, the small surface roughness and the
high-homogeneity associated with optical fiber nanowires (OFNs) provide
low optical loss and allow the use of nanowires for a wide range of new
applications for communications, sensing, lasers, biology, and chemistry. OFNs
offer a number of outstanding optical and mechanical properties, including
(1) large evanescent fields, (2) high-nonlinearity, (3) strong confinement, and
(4) low-loss interconnection to other optical fibers and fiberized components.
OFNs are fabricated by adiabatically stretching optical fibers and thus preserve
the original optical fiber dimensions at their input and output, allowing
ready splicing to standard fibers. A review of the manufacture of OFNs is
presented, with a particular emphasis on their applications. Three different
groups of applications have been envisaged: (1) devices based on the
strong confinement or nonlinearity, (2) applications exploiting the large
evanescent field, and (3) devices involving the taper transition regions. The
first group includes supercontinuum generators, a range of nonlinear optical
devices, and optical trapping. The second group comprises knot, loop, and
coil resonators and their applications, sensing and particle propulsion by optical
pressure. Finally, mode filtering and mode conversion represent applications
based on the taper transition regions. Among these groups of applications,
devices exploiting the OFN-based resonators are possibly the most interesting;
because of the large evanescent field, when OFNs are coiled onto themselves
the mode propagating in the wire interferes with itself to give a resonator.
In contrast with the majority of high-Q resonators manufactured by other
means, the OFN microresonator does not have major issues with input–
output coupling and presents a completely integrated fiberized solution. OFNs
can be used to manufacture loop and coil resonators with Q factors that,
although still far from the predicted value of 109, are well in excess of 105.

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 The input–output pigtails play a major role in shaping the resonator response
and can be used to maximize the Q factor over a wide range of coupling
parameters. Finally, temporal stability and robustness issues are discussed, and
a solution to optical degradation issues is presented.

OCIS codes: 060.2310, 060.2370, 230.3990, 230.2285, 160.2290, 160.4236.

1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2. Manufacture of OFNs and OFMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3. Properties of OFNs and OFMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.1. Loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.2. Spot Size and Mode Confinement. . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.3. Mechanical Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.3a. The Big Issue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
3.3b. Embedding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4. Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.1. High-Q Resonators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.1a. Single-Loop Resonators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.1b. Coil Resonators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.2. Particle Manipulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.3. Sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.3a. Resonating Sensors: Schematic and Manufacture. . . . . . . . . 132
4.3b. Resonating Sensors: Theory. . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.3c. Resonating Sensors: Sensitivity. . . . . . . . . . . . . . . . . . . . . . . 136
4.3d. Resonating Sensors: Detection Limit. . . . . . . . . . . . . . . . . . . 139
4.3e. Resonating Sensors: Experimental Demonstration. . . . . . . . . 140
4.4. Supercontinuum Generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.5. Particle Trapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.6. Mode Filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.6a. Mode Filtering: Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

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Optical fiber nanowires and microwires:
fabrication and applications
Gilberto Brambilla, Fei Xu, Peter Horak, Yongmin Jung,
Fumihito Koizumi, Neil P. Sessions, Elena Koukharenko, Xian Feng,
Ganapathy S. Murugan, James S. Wilkinson, and David J. Richardson

1. Introduction

In the past decade nanowires have attracted much attention because of the
unique properties that materials display on the nanoscale [1]. A vast variety of
materials have been studied, including carbon nanotubes [2], single-element
nanowires (Si, Ge, Cu, Au, and Ag [3–7]), multicomponent structures (GaAs,
GaN, InP, CdS, SiC, Si3N4, SiO2, Al2O3, ZnO, SnO2, In2O3 [8–18]), and
even organic materials [19,20]. Nanowires have been manufactured by using a
wide range of techniques: electron beam lithography [21], laser ablation
[22], template-based methods [23], bottom-up methods such as vapor–liquid–
solid techniques [24], chemical and physical vapor deposition [8,25], solgel
methods [26], and top-down techniques such as fiber pulling [27–31] or direct
draw from bulk materials [20,32].
Prior to 2003 only two attempts to manufacture submicrometer wires by using
a top-down process were reported in the literature [33,34]. Interest in optical
fiber nanowires (OFNs) has been limited mainly because of the perceived
difficulties in manufacturing suitably low-loss structures. Although several
OFNs were fabricated by using a variety of bottom-up methods [35–42], all of
them exhibited an irregular profile and a surface roughness that appear to
have limited the loss levels that could be reliably achieved [43,44]. In 2003 a
two-step process to fabricate low-loss submicrometric silica wires was presented
[27]; it involved wrapping and drawing a pretapered section of standard
fiber around a heated sapphire tip. Although the measured loss was orders of
magnitude higher than that achieved later with flame-brushing techniques
[28–31], it was low enough to allow the use of OFNs for optical devices and
ignite interest in the technology. In the following years a spate of publications
investigated novel properties and applications of OFNs. It has become
commonly accepted to define optical fiber nanowires (or photonic nanowires)
as fiber waveguides with a submicrometric diameter. In this paper wires
with diameter bigger than 1 µm will be referred to as optical fiber microwires
(OFMs)
OFNs and OFMs are of interest for a range of emerging fiber optic applications,
since they offer a number of enabling optical and mechanical properties,
including the following:
1. Strong confinement. Light can be confined to a very small area over long
device lengths, allowing the ready observation of nonlinear interactions, such as

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supercontinuum generation [45–48], at relatively modest power levels.
2. Large evanescent fields. A considerable fraction of the power can propagate
in the evanescent field outside the OFN physical boundary [28], and this
can be exploited for atom guides [49,50], particle manipulation [51,52], sensors
[53–58], and high-Q resonators [59–66].
3. Great configurability. OFNs can be easily manipulated and bent because
of their relatively high-mechanical strength. Bend radii of the order of a few
micrometers can be readily achieved with low induced bend loss [67],
allowing for highly compact devices with complex geometries, e.g., 2D [60]
and 3D [59] resonators.
4. Low-loss connection. Low-loss connection to other optical fibers and
fiberized components is possible; since OFNs are manufactured by adiabatically
stretching optical fibers, they maintain the original fiber size at their input
and output, allowing ready splicing to standard fibers and fiberized components.
Insertion losses smaller than 0.1 dB are commonly observed.

In the next sections the properties of OFNs and OFMs will be introduced and
the fabrication methodologies discussed. Applications ranging from mode
filters to high-Q resonators and to sensors will be presented.

2. Manufacture of OFNs and OFMs

OFN and OFM tapers are made by adiabatically stretching a heated fiber,
forming a structure comprising a narrow stretched filament (the taper waist),
each end of which is linked to an unstretched fiber by a conical section (the taper
transition region), as shown in Fig. 1.
In the past few years, three different methodologies have been used to fabricate
OFNs and OFMs from optical fibers:
1. Tapering the fiber by pulling it around a sapphire rod heated by a flame,
2. The flame-brushing technique,
3. The modified flame-brushing technique.

The flame-brushing technique has been previously used for the manufacture of
fiber tapers and couplers [68]. A small flame moves under an optical fiber
that is being stretched: because of mass conservation, the heated area
experiences a diameter decrease. Controlling the flame movement and the fiber

Figure 1

Optical fiber taper.

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stretching rate lets the taper shape be defined to an extremely high-degree of
accuracy. This technique provides access to the OFN from both pigtailed ends.
Moreover, it delivers OFNs with radii as small as 30 nm [31], the longest
and most uniform OFNs–OFMs [28] and the lowest measured loss to date
[29–31].
The third fabrication method is a modified version of the flame-brushing
technique in which the flame is replaced by a different heat source. Two types
of heat source have been used: a sapphire capillary tube hit by a CO2 laser
beam [59], and a microheater [69]. This method is not limited to silica but
provides OFNs and OFMs from a range of glasses including lead silicates [69],
bismuth silicate [69], and chalcogenides [48].

3. Properties of OFNs and OFMs

3.1. Loss
For diameters ␸ of the minimum waist region comparable with the wavelength
␭ of the radiation propagating in the OFNs, light is strongly guided. When
␸
␭, the mode is strongly affected by diameter fluctuations. It has been shown
[70] that for very small ␸ the propagation loss ␣ is related to the propagation
constant k, the absolute value of the transversal component of the
propagation constant ␥ and the characteristic length of diameter fluctuations Lf
by

␣=
1
4␥
冑 冉
k
LF
exp −
␲ L f␥ 2
k
冊 . 共1兲

Experimentally, ␣ has been evaluated during and after fabrication by launching

light into the OFN pigtail from a laser diode and collecting the transmitted
signal with an InGaAs photodiode connected to the output pigtail. A summary
of recorded losses in OFNs made from telecommunication optical fibers
versus radius for ␭ = 1.55 µm is reported in Fig. 2.

The flame-brushing and modified flame-brushing

techniques provide the lowest loss across a wide range
of ␸.

3.2. Spot Size and Mode Confinement

The spot size of the light propagating in the taper is also strongly dependent on
␸ [71] through the V factor:

2␲ ␸
V= NA, 共2兲
␭ 2

where NA denotes the numerical aperture. Equation (2) provides the cladding
共Vcl兲 or core 共Vco兲 V numbers, when the cladding ␸ or the core ␸co diameters
are used, respectively. The relationship between the spot size ␻ and Vcl during

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 Figure 2

10 Method 1
Method 2
Method 3
1

Loss α (dB/mm)
0.1

0.01

0.001

100 200 300 400 500 600

Waist radius φ/2 (nm)

Summary of optical loss ␣ achieved in OFNs and OFMs for the three
manufacturing techniques presented in Section 2: 1, the two stage process
involving a sapphire rod heated by a flame [27]; 2, the flame-brushing technique
[28–31]; 3, the modified flame-brushing technique [this work, 30, 71].

tapering for a standard single-mode fiber (SMF) is shown in Fig. 3. Vcl has
been calculated from Eq. (2) for a mode confined by the silica–air interface
(NA⬃ 1 if the silica and air refractive indices are taken to be 1.444 and 1,
respectively).
A conventional optical fiber falls at the right in this figure. The label SMF in
Fig. 3 represents the value of Vco for a telecom optical fiber at 1.55 µm. When the
optical fiber diameter decreases, V decreases and ␻ initially decreases until
a minimum point (B) is reached. After that, the mode is no longer guided in the
core, and ␻ suddenly increases to a maximum associated with cladding
guiding. For even smaller diameters ␻ decreases with decreasing V until it
reaches a minimum (A) for Vcl ⬃ 2, and then it increases again. This region at
Vcl ⬍ 2 is typical of OFNs: the mode is only weakly guided by the
waveguide, ␻ can be orders of magnitude bigger than the physical diameter of
the OFN, and a larger fraction of the power resides in the evanescent field.
Figure 4 shows the evanescent field at the surface of an OFN with various waist
diameters simulated by using the beam propagation method. Simulations were
carried out by using a full 3D vectorial method, and the electric field E was
normalized to unit power. The propagating mode of untapered optical fiber is
completely confined within the physical boundary of the fiber, and when
the fiber is tapered below a certain diameter a considerable fraction of the power
propagates in the surrounding medium. The electric field at the interface
shows a maximum around the waist diameter ␸ of about 0.7 µm, below which
it sharply decreases. This can be explained by the increased ␻, which
effectively decreases the power density in the OFN. The decrease at larger ␸ is
ascribed to the increasing mode confinement into the core.
It is interesting to note that the minimum beam waist ␻ depends on the
cladding material, and the minimum beam size is ultimately limited by

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 Figure 3
Vco
0.012 0.12 1.2 SMF

ω (µm)
10

A
1
1 OFN 10 100
Vcl

Relationship between the spot size ␻ (defined as the radius where the intensity
has dropped to 1 / e2 [71]), the cladding 共Vcl兲 and core 共Vco兲 V numbers of a
tapered telecom fiber. Labeled points are the points of maximum confinement,
A, in the cladding and, B, in the core and, C, the beginning of cladding
guiding. Vcl and Vco are related to the cladding ␸ and core ␸co diameters by Eq.
(2). SMF and OFN represent the V numbers of a common telecom optical
fiber and an optical fiber nanowire with r = 500 nm in air at 1.55 µm.

Figure 4
0.8
Normalised E-field at surface

(a)

0.6

0.4

0.2

0.0
0.0 0.5 1.0 1.5 2.0

φ (μm)
SMOW diameter (μm)

Relationship between the electric field at the OFN surface and the OFN
diameter ␸. The wavelength and the refractive indices of the silica OFN were
taken to be 1.047 µm and 1.45, respectively. Water was taken as the
surrounding medium with a refractive index of 1.33.

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diffraction. Figure 5 compares the dependence of ␻ on the cladding diameter
for three different fiber glasses: silica, lead silicate (F2, Schott glass) and
bismuth silicate (Asahi glass). ␻ in bismuth silicate is nearly 40% smaller than
in silica, and the OFM diameter at which the minimum occurs is nearly
40% smaller.
In Fig. 5, it is possible to identify two regions: the high-confinement region (I)
and the large-evanescent-field region (II). In the high-confinement region ␻
is comparable with ␸, the beam has its minimum waist diameter, and the optical
nonlinearity ␥ reaches its maximum. ␥ is a figure of merit that is related to
the material nonlinear refractive index n2 and the beam size Aeff 共=␲␻2 / 4兲 by
the following equation:

2␲ n2
␥= . 共3兲
␭ ␲共␻2/4兲

A standard telecom SMF has ␥ ⬃ 1 W−1 km−1, while typical silica OFMs can
have ␥ as high as 100 W−1 km−1. OFNs made from highly nonlinear
materials such as lead silicate, bismuth silicate, and chalcogenide glasses can
be used to produce OFNs with maximum values of ␥ of the order of 1000,
6000, and 80,000 W−1 km−1 respectively. OFMs with diameters in this region
can be used for a wide range of nonlinear applications, including
supercontinuum generation, particle trapping at the nanowire end facet, and
nonlinear switching (see Subsections 4.4 and 4.5).

Figure 5
10

II I
ω (µm)

Silica
F2 (Lead-silicate)
BS (Bismuth-silicate)

0.1
0.1 1
φ (µm)

Relationship between the spot size ␻ and the OFM–OFN diameter ␸ for three
different fiber materials: silica (refractive index at ␭ = 1.55, nSiO2 = 1.444), a
lead silicate glass 共nF2 = 1.597兲, and a bismuth silicate glass 共nBS = 2.02兲. For
increasing refractive indexes, the minimum ␻ becomes smaller and occurs
at smaller diameters ␸.

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 In other words, a chalcogenide OFN at maximum
confinement has a nonlinearity that is ⬃105 times
higher than that observed in conventional telecom
fibers.

By contrast, in the evanescent field region OFMs and OFNs have diameters
smaller than the waist of the propagating modes. ␻ can be orders of magnitude
bigger than ␸, and a considerable fraction of the power propagates in the
evanescent field outside the fiber physical boundary. OFMs and OFNs with
diameters in this region can be used for high-Q resonators (knot, loop, and coil),
particle manipulation, and sensing (Subsections 4.1–4.3).

3.3. Mechanical Strength

Although they have an extremely small diameter, OFNs can be handled
relatively easily because of their exceptional mechanical strength. Their ultimate
strength ␴fract, defined as the maximum stress a material can withstand, can
be measured in a simple static experiment by adding milligram masses at the
lower extremity of the vertically held fiber pigtail until fracture occurs.
The mass m can then be measured and ␴fract can be derived from the relation

m m
␴fract = = , 共4兲
A ␲共␾2/4兲

where A is the OFN cross section.

Figure 6 shows a summary of the results carried out on OFNs with radii r
= ␸ / 2 in the range from 60 to 300 nm. The tapers were produced with the
modified flame-brushing technique by scanning a microheater (NTT-AT, Japan)
over 6 mm along the optical fiber. For OFNs with r ⬍ 200 nm ␴fract is in

Figure 6
18
16
Ultimate strength σf (GPa)

14
12
10
8
6
4
2
0
0 50 100 150 200 250 300
Radius r (nm)

Dependence of the ultimate strength of silica OFN on the radius r.

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excess of 10 GPa. Although this value is slightly smaller than that measured
for carbon nanotubes (␴fract = 21–63 GPa [72,73]), it is still considerably larger
than the values recorded for commercially available high-strength materials
like Kevlar 共␴fract = 3.88 GPa兲 [74] and the high-strength steel ASTM
A514 共␴fract = 0.76 GPa兲.
␴fract for OFNs is also higher than the measured ␴fract ⬃ 5 GPa of bare telecom
optical fibers, where the radius is up to 3 orders of magnitude larger 共r
⬃ 62.5 µm兲 [75,76]. It is interesting to note that OFNs fabricated by the modified
flame-brushing technique seem to have a considerably better mechanical
strength than those manufactured by the two-step technique, for which the
reported tensile strength was 2.5–5 GPa [27]; this can be explained by the better
surface quality. Nanowires manufactured by the modified flame-brushing
technique also provide a better mechanical performance than those
manufactured by the conventional flame-brushing technique because of the
lower water content in the nanowires. The flame produces a considerable amount
of OH groups that then diffuse in the nanowire at high temperatures, and it
is known from experiments on optical fibers that the water content in silica
reduces the overall mechanical strength.

3.3a. The Big Issue

Surfaces degrade with time, and they need protection for long-term applications.
Since OFNs have a large ratio between surface and volume, the effect of
degradation is considerably more pronounced than in bigger specimens, i.e.
optical fibers. Experiments have been conducted to quantify the long-term
degradation of optical and mechanical properties of optical fiber nanowires and
have shown a considerable difference between the nanowires preserved in a
cleanroom environment and those kept in a conventional optics laboratory; in a
conventional optics laboratory a group of OFNs manufactured by the
flame-brushing technique with r ⬃ 375 nm experienced a decay approximated
by the relation [31]

␴fract = 共10.4 − 0.172 ⫻ t兲 GPa, 共5兲

where t represents the time from fabrication in days.

The decrease in ␴fract has been related to optical properties, and it was found
that an average decrease of 1.34 GPa in ␴fract was associated with an average
induced loss of 1 dB/ mm. This connection was explained by the continuous
formation of cracks, which simultaneously degrade the optical and the
mechanical properties of the OFNs. This effect is well known to the optical
fiber industry, where optical fibers are coated immediately after their fabrication
to protect them from mechanical degradation. Some means to protect the
surface of the nanowire is therefore required.

3.3b. Embedding
The acrylic coating used to protect optical fibers has a higher refractive index
than silica because it has the additional purpose of stripping the modes
propagating in the cladding. In OFNs the propagating mode has a significant
intensity at the interface between silica and air, and the only approach to avoid
confinement losses is to use low-refractive-index materials, such as silicone
rubber [77], Efiron halogenated polymers, [78,79] and Teflon [66,80], which

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have refractive indices n of ⬃1.4, ⬃1.373 and ⬃1.3 at ␭ = 1.55 µm, respectively.
Silicone rubber is a thermocurable polymer that has been used to embed
8.5 µm OFMs and OFM resonators [77]. The Efiron UV37x family consists of
UV-curable polymers manufactured by Luvantix (South Korea) [81] widely
used to coat fibers used in optical fiber lasers. Teflon is a fluoropolymer with
extremely low solubility in most chemicals. Still, a modified version exists
that can be dissolved in fluorinated solvents [82]. This represents the best option
to achieve high-confinement in embedded OFN or OFMs because of its low
refractive index: the mode confinement is significantly higher than that achieved
with other polymers because of the large refractive index difference between
the OFN or OFM and the Teflon coating. The temporal stability of OFNs
embedded in Teflon has also been studied over a period of time longer than
100 h, and no change in transmitted power was observed [80]; for comparison,
over the same time period a 20 mm long uncoated sample with the same ␸
experienced an induced loss in excess of 30 dB. Similar experiments carried out
on silicon rubber and Luvantix polymers showed that all the above-mentioned
materials successfully protect OFNs and OFMs from degradation. For this
reason, sensors and applications are based on embedded OFNs or OFMs.

4. Applications

Applications of OFMs and OFNs can be classified into three main groups
according to what property they exploit:
Evanescent field
Confinement
Transition regions
Evanescent field applications take advantage of the power propagating outside
the physical boundary of the wire and include high-Q knot, loop, and coil
resonators (Subsection 4.1), particle manipulation (Subsection 4.2), and sensors
(Subsection 4.3).
Applications exploiting the confinement properties of OFMs correspond
approximately to region I in Fig. 5 and include supercontinuum generation
(Subsection 4.4), particle trapping (Subsection 4.5), and nonlinear switching or
bistability [83,84].
Finally, transition regions have been exploited to convert and filter modes.
Applications will be presented in Subsection 4.6.

4.1. High-Q Resonators

High Q resonators have been widely studied because of their broad range of
applications [85] ranging from optical communications to nonlinear
optics, cavity QED, and sensing. If an OFN (or OFM) is coiled onto itself, the
modes in the two different sections can overlap and couple, creating a
resonator with an extremely compact geometry. A schematic of the transmission
spectrum of a high-Q resonator is shown in Fig. 7.
Several resonator parameters can be easily estimated from the transmission
spectra: quality factor (Q), free spectral range (FSR), and finesse (f) are the most
important. Q is proportional to the confinement time in units of the optical
period and can be expressed as [86]

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 Figure 7

Schematic of a spectrum with the related notation for FWHM, free spectral
range (FSR), and resonant wavelength 共␭res兲.

␭res
Q= , 共6兲
FWHM
where ␭res is the resonance wavelength and FWHM its full width at
half-maximum. The typical Q of OFN single-loop resonators is in the range
103 – 106 [60,66,78,79].
The FSR is the inverse of the round-trip time (round-trip group delay) of an
optical pulse. In the loop resonator spectrum, the FSR is the wavelength or
frequency period of the peaks as shown in Fig. 7. It can be expressed as
[86]

c
FSR共Hz兲 = 共7兲
2neffL
(where c is the light’s speed, neff the effective index of the mode propagating in
the OFM, and L the loop length). FSR can also be expressed as the difference
⌬␭ of two adjacent resonator wavelengths near ␭res:

␭2
FSR ⬇ ⌬␭ ⬇ . 共8兲
4␲neffL
Finally, f can be evaluated from the ratio between FSR and FWHM [86]:

FSR
f= . 共9兲
FWHM

4.1a. Single-Loop Resonators

Single-loop resonators are the simplest resonators manufactured from OFNs
and OFMs. Two different single-loop resonators have been demonstrated: the
loop resonator and the knot resonator. Figure 8 shows an example of a
single-loop knot resonator fabricated by knotting an OFM.
Loop resonators can be easily manufactured by coiling an OFN or OFM. The
use of XYZ stages to coil the OFM allows a great deal of control of the
resonator geometry. Still, the geometry stability is based on surface forces;

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 Figure 8

Knot resonator with radius R ⬃ 45 µm manufactured from an OFM with r

⬃ 1 µm.

thus loop resonators are compromised in terms of long-term reliability. In

contrast, knot resonators (like the one reported in Fig. 7) exhibit an enhanced
temporal stability because of the friction that different sections of the OFM
exert on one another. However, because the stiffness of the OFM is different than
that of its pigtails, the bending curvatures needed to manufacture knot
resonators induce an enormous stress in the OFM, which therefore breaks. The
knot resonator can be easily manufactured if the fiber taper presented in Fig.
1 is broken; knotting is performed in the region of uniform waist (OFM), and no
excess tension occurs. As a result, this type of resonator exhibits only one
input–output fiberized pigtail.
The optical properties of single-loop resonators can easily be recorded by
launching light from a broadband source into one of the OFM pigtails and
analyzing the transmitted light with an optical spectrum analyzer. A typical
transmission spectrum is shown in Fig. 9.
By using Eqs. (6)–(9), ␭res ⬃ 1.55 µm and FWHM⬃ 0.2 nm, the FSR, f, and Q
were estimated to be 4 nm, 20, and ⬃8 ⫻ 103, respectively.
The loop resonator’s temporal stability can be addressed by using aerogel as a
substrate. Aerogel is very light, extremely low-density material with
excellent thermal insulating properties and a refractive index close to 1. Also
known as “frozen smoke,” aerogel in its solid form has a texture similar to
that of foamed polystyrene and has a transparent optical spectral range similar
to that of silica. As aerogel is mostly air, it has a refractive index very close
to that of air and a very small loss. It has been previously used [67] to fabricate
linear waveguides, waveguide bends, and branch couplers.
Figure 10 shows the transmission spectra of a loop resonator sandwiched
between two pieces of aerogel after 1 h, 2 h, and 1 day. Even after 1 day,
there are no considerable changes in the spectral profile. This shows that aerogel
is a very good substrate material on which to assemble optical nanowire
loop resonators into functional microphotonics devices. However, aerogel is

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 Figure 9

Transmission spectrum of a loop resonator as recorded from an optical

spectrum analyzer (OSA).

brittle and ultimately does not protect OFMs and OFNs from degradation in
the same way as the polymers considered in Subsection 3.3b.
The loop resonator transmission coefficient can also be obtained analytically
[60] by considering the output to be the sum of two interfering contributions: the

Figure 10

after 1 hour
-54 after 2 hours
after 12 hours
-55

-56
Transmission (dBm)

-57

-58

-59

-60

-61

-62

1534.4 1534.6 1534.8 1535.0 1535.2 1535.4 1535.6

Wavelength (nm)

Transmission spectra of a loop resonator sandwiched between aerogels

recorded 1, 2, and 12 h after fabrication. The OFN radius is r = 400 nm.

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first is represented by a fraction of the beam a1, which is transmitted from
input to output without entering the resonator, while the second consists of the
remaining fraction of the beam a2, which propagates through the coil. This
leads to a simple relation for the transmitted power T as a function of the
wavelength [60]:

T共␭兲 = 兩a1 + a2 exp共ikL兲兩2 , 共10兲

where a1 and a2 represent the amplitudes of the two fractions of the beam, L
the coil length, and k the propagation constant.

4.1b. Coil Resonators

The flame-brushing or modified flame-brushing technique allows the fabrication
of OFNs and OFMs with extremely long lengths. As a consequence, they
can be coiled in more complicated resonant structures to form microcoil
resonators. This potentially provides Q factors much higher (in excess of 109
for losses approaching the material loss) and resonances much narrower
than those presented in Figs. 9 and 10. The OFN microcoil resonator (OMR) is
a 3D resonator consisting of many self-coupling turns (Fig. 11), and it can
be created by wrapping an optical fiber nanowire on a low-index dielectric rod.
Although there is no limit to the number of turns that the OMR can have,
practical technological issues (i.e., the OFN intrinsic propagation loss and the
loss induced by wrapping the OFN around a support rod) limit the useful
number of coils. In this subsection OMRs are studied with a particular focus
on the three- and four-loop resonators.
The OMR spectral response can be derived analytically by solving the coupled
wave equations for the amplitudes Am共␪兲 of the light propagating in the mth
turn of the OMR (Fig. 12).
If coupling between nonadjacent turns is ignored, the propagation of light
along the coil in an M-turn OMR is described [60,64,65] by the coupled wave
equations for slowly varying pitches:

Figure 11

Optical fiber nanowire microcoil resonator (OMR). Light can both propagate
along the OFN (red arrow) or be coupled into an adjacent coil (green arrow).

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 Figure 12

Cylindrical coordinates system used for the analytical description of the OMR.
The angle ␪ continuously increases along the coil.

冢冣
A1

A2

¯
d
Am
d␪
¯

AM−1

AM

冢 冣
0 R1共␪兲␹12共␪兲 0 ¯ 0 0 0

R2共␪兲␹21共␪兲 0 R2共␪兲␹23共␪兲 ¯ 0 0 0

0 R3共␪兲␹32共␪兲 0 ¯ 0 0 0

=i ¯ ¯ ¯ ¯ ¯ ¯ ¯

0 0 0 ¯ 0 RM−2共␪兲␹M−1M−2共␪兲 0

0 0 0 ¯ RM−1共␪兲␹M−2M−1共␪兲 0 RM−1共␪兲␹M−1M共␪兲

0 0 0 ¯ 0 RM共␪兲␹MM−1共␪兲 0

冢冣
A1

A2

⫻ Am , 共11兲
¯

AM−1

AM

where ␹pq is the coupling between turns p and q of the resonator, defined as

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 ␹pq共␪兲 = ␬pq共␪兲exp i 冉冕 2␲

0
␤p共␪兲Rp共␪兲d␪ − i 冕 0
2␲
冊
␤q共␪兲Rq共␪兲d␪ . 共12兲

␤p is the propagation constant in the pth turn, and ␬pq is the coupling coefficient
between the pth and qth turns that is due to the overlap of the field modes
between neighboring turns [59].
Defining the average coil radius R0 as

兺m−1
M
兰20␲Rm共␪兲d␪
R0 = , 共13兲
2␲M
the average coupling parameter Kpq can be written as

Kpq共␪兲 = 2␲R0␬pq共␪兲. 共14兲

K assumes values between 0 (when the coils are far apart and there is no
coupling) and KMAX (maximum coupling, which occurs when the OFN coils
touch) with intermediate values obtained by controlling the spacing of adjacent
coils.
The OMR transmissivity coefficient T is defined as

T=
Am共2␲兲
A1共0兲
再冕
exp i
2␲

0
␤M共␪兲Rm共␪兲d␪ , 冎 共15兲

and it is calculated from Eqs. (11)–(15), assuming field continuity between the
turns:

Am+1共0兲 = Am共2␲兲exp i 再冕 2␲

0
␤M共␪兲Rm共␪兲d␪ 冎 共16兲

for m = 1 , 2 . . . M − 1.
The OMR spectrum is strongly dependent on its geometry; in particular, the
resonance FWHM and FSR depend on the OMR geometry and the OFN size
through K.
OMR Geometry and Coupling. The Q of the uniform OMR presented in
Subsection 4.1b is extremely sensitive to the coupling strength. In theory, the
highest Q can be achieved by selecting a K for which the FWHM is
minimized, but in practice this is difficult to realize because the FWHM
fluctuates considerably for small changes in K, and K has an exponential relation
to the pitch [48–50,54–56]. It is therefore desirable to find a geometry for

A minute change in the coil distance implies an

enormous change in the FWHM, and thus in Q.

which the FWHM is at its minimum and changes slowly with K.

Several different profiles have been studied in the literature [64,65] to find the
optimum resonator shape that allows the easiest realization of OMRs with
high Q. Figure 13 presents some of the geometries considered.

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 Figure 13

R
H V X III T
III

Schematic of various OMR geometries. H represents the OMR with a constant

coil radius (along Z) and coil pitch (along R). V and X have a constant coil
pitch and a variable coil radius; I and T a constant coil radius and a changing coil
pitch.

The profiles have been described by the following mathematical formulas:

H 共uniform兲, R m共 ␪ 兲 = R 0, Kpp+1共␪兲 = Kc. 共17兲

V 共conical兲, R m共 ␪ 兲 = R 0 −
M
2
冉
dR + m − 1 +
␪
2␲
冊 dR, Kpp+1共␪兲 = Kc.

共18兲

X 共biconical兲, R m共 ␪ 兲 = R 0 + 冏 M+1
2
−m+
␪−␲
2␲
冏 dR −
M
4
dR,

Kpp+1共␪兲 = Kc. 共19兲

p − 1 + 共␪/2␲兲
I 共incrementing兲, R m共 ␪ 兲 = R 0, Kpp+1共␪兲 = Kc . 共20兲
M−1

T 共triangular兲, R m共 ␪ 兲 = R 0, Kpp+1共␪兲 = Kc 1 − 冉 冏 p − 1 + 共␪/2␲兲

共M − 1兲/2
−1 冏冊 ,

共21兲
where m = 1 , 2 , . . . , M; p = 1 , 2 . . . M − 1; dR / R0
1; dR = 兩Rm+1共␪兲 − Rm共␪兲兩 for
any two adjacent turns; Kmn is the coupling coefficient between turns n and m;
and Kc is the maximum coupling parameter.
These geometries can be realized by wrapping an OFN around a low-refractive
index rod, which is angled for the V and X geometries. Simulations showed
that the optimum fabrication tolerances are achieved with symmetric
geometries, where the coil diameter increases from the center toward the
extremities (X) or where the coupling is maximum at the center of the coil and
decreases toward the extremities (T). For best performance, OMRs with
larger numbers of turns are preferred, which imposes additional fabrication
difficulties. Still, simulations on the T geometry showed that high-Q resonators
can be obtained for nearly every value of the maximum coupling coefficient,
even for resonators with only three or four turns [65]. However, the fabrication of
OMRs with well-defined varying pitch is likely to be a very challenging
task.

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For this reason, a simpler way to tune the resonator properties has been
investigated. Since the slow change in coupling properties has been shown to
crucially affect Q, the possibility to easily achieve a high Q simply by
tuning the input–output pigtails has been investigated. To this end coupling has
been considered constant in the center [Kn共␪兲 = Kc for 2␲ ⬍ ␪ ⬍ ␪共M − 1兲2␲)]
and variable only at the ends, going to zero at the pigtail ends 共K0 = KM = 0兲.
Figure 14 shows five profiles of K for M = 4. It was found [65] that sharp K
profiles [such as Figs. 14(a) and 14(e)] have a FWHM strongly dependent on
Kc, while smoother profiles [Fig. 14(c)] can achieve flat FWHM profiles,
i.e., high Q at nearly any Kc. Although the realization of an OMR with the exact
profile of Fig. 14(c) is challenging, an OMR can be practically manufactured
by wrapping the coils on a support rod and then tuning the input and output
pigtails to achieve a slow decrease of coupling to zero.

Figure 14

Schematic of pigtail geometries in four-turn OMRs.

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These results can be explained by noting that a resonance in the transmission
spectrum of an OMR occurs when there is a mode with light circulating in
the inner rings of the coil while the intensities at the input and at the output end
vanish. This requires two conditions to be fulfilled:
1. The circumference of the coil must be a multiple of the wavelength.
2. In one round trip the light must be entirely coupled back to the previous
ring.
Moreover, the conditions must be fulfilled simultaneously at both sides of the
coil. It is believed that slowly varying profiles provide a range of different
coupling conditions for which condition 2 is more easily fulfilled. An increase
of the coupling in the input–output pigtails with a small gradient ensures
that the condition of perfect coupling of light from an outer ring of the coil to
an inner ring is met somewhere at the coil ends, thereby producing a low-loss
high-Q resonator mode inside the coil.

In summary, very high fabrication tolerances can be

achieved by microtuning the input and output pigtails,
provided that the change of the pitch in the input
and output ends of the OMR is sufficiently slow.

OMR Internal Field Distribution. The field distribution inside an OMR has
been found to depend strongly on the OMR geometry. Simulations were
performed assuming an OFM with r = 1 µm, n = 1.457, the effective index neff
= 1.182 at 1.55 µm, coil radius R0 = 62.5 µm, dR = 0.05 µm, and K in the
range 0–20. The field amplitudes A1共␪兲, A2共␪兲, and A3共␪兲 were calculated for
M for profiles H, V, and X in Fig. 13, choosing the wavelength and K that
maximize the field amplitude. Figure 15 shows the dependence of the internal
field distributions on the angle ␪ in three coils.
The internal field amplitude in the H and X profiles is much larger than that in
the V profile, meaning that more energy can be stored in OMRs with the H
and X geometries.
OMR Manufacture. OMRs have been demonstrated in a liquid [79], in air [87],
and in Teflon [66]. In all cases an OFM and a support rod were used. In fact,
because of the high value of the support rod refractive index or of the liquid or
Teflon refractive index, the V value experienced by the mode propagating in
the wire is low, and the fraction of power in the evanescent field is large even for
relatively large diameters.
To test the resonator properties in real time during fabrication, the OFM had
its pigtails connected to an erbium-doped fiber amplifier (EDFA) and an optical
spectrum analyzer (OSA). Although early experiments were carried out by
coiling the OFM on a low-refractive-index rod by hand with the aid of a
microscope [Fig. 16(a)], the demands of continuous uniform coupling over the
entire coil length necessitated the use of automated setups including a rotation
stage (which controls the actual coiling) and a translation stage (which
controls the coil pitch). It is clear from Fig. 16 that the coil uniformity is
considerably better in the latter case. In the last stage of fabrication, the OFM

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 Figure 15
15
5
a A1
4.5
b VII A2
A1 A3
A2 4
A3
10 3.5

Amplitude

Amplitude
3

Amplitude
2.5

2
5
1.5

HI 1

0.5
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
θ/(2π)-(M-1) θ/(2π)-(M-1)
16
c
14
A1
12 A2
A3

10
Amplitude
Amplitude

4
XIII
2

0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Angle(x2Pi)
θ/(2π)-(M-1)

Internal field amplitude in three-turn OMRs for profiles H, V, and X (Fig. 13).

pigtails were fixed to 3D stages and were tuned to find the optimum resonator
spectrum.
If the coil was to be embedded, the fine tuning of the OFM pigtails was
performed on uncured polymer, and the curing was carried out by checking the
resonator properties in real time as the pigtails were adjusted. The polymer
was then cured when the suitable adjustment had been completed. OMRs were
wrapped on a low-refractive-index support rod to maximize the OMR
temporal stability and robustness. Losses can be significant because of
microbends and confinement losses. However, the loss can be minimized by
increasing the microfiber thickness and the rod diameter, by using a
low-refractive-index material for the rod, and by improving the smoothness of
the rod surface. It was found [87] that using a rod coated with Teflon AF
(DuPont, United States) or UV373 (Luvantix, Korea) provided good
confinement because of the polymer’s low refractive index at the interface with
the microfiber (n ⬃ 1.3 and n ⬃ 1.37 at ⬃1.55 µm, respectively). Support
rods as small as 250 µm have been used without any significant observed loss.
Most recent results seem to show that the particulate nature of the Teflon
used in these experiments might induce higher losses than those observed for
UV-curable fluoropolymers. Micrometer-size Teflon particles can in fact
increase the Mie scattering and the overall OFM transmission loss [80].

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 Figure 16

OMRs manufactured (a) by hand and (b) by an automated stage. The number
of turns is three in (a) and two in (b).

4.2. Particle Manipulation

The radiation pressure exerted by light on matter was demonstrated by
Lebedev more than a century ago [88]. However, until the laser was invented,
light sources with high intensity were not readily available, and the radiation
pressure was minute. Kawata and co-workers initially demonstrated the
movement of dielectric microspheres initially by exploiting the evanescent
field produced on the surface of a high-refractive-index prism [89] and
subsequently by using the evanescent field of a single-mode channel waveguide
[90]. Two effects take place: (1) the gradient force attracts and traps the
particles laterally with an action similar to optical tweezers [91] while (2) the
axial force due to absorption and scattering propels the microspheres along
the direction of propagation of light in a waveguide [92]. The drag force opposes
the propelling forces and acts to limit continuous acceleration, so that the
particles ultimately reach a terminal velocity. This method may simultaneously
manipulate several particles and provides a way to sort micrometer-size
particles and biological cells. Driving microparticles by using the evanescent
field produced by various types of planar waveguides has been investigated
in more detail in the past two decades [93–96]. Recently, the evanescent field
of an OFN has also been exploited to propel 3 µm [51] and 10 µm [52]
diameter polystyrene microspheres and microsphere clusters with diameters
larger than 20 µm. In Subsection 3.2 the beam size ␻ was shown to decrease for
decreasing OFM–OFN diameters ␸ until a minimum for V ⬃ 2, after which

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it sharply increases. For small sizes, a considerable fraction of the power
propagates outside the physical dimension of the OFN; the evanescent field
can extend for several micrometers into the surrounding medium, and it can be
exploited to propel particles.
The propulsion experiments were carried out by positioning OFNs on MgF2
substrates with their extremities fixed with adhesive tape. One of the pigtails was
connected to a CW diode-pumped fiberized Nd:YLF laser. The power
propagating in the fiber before the OFN was estimated to be ⬃400 mW at
1047 nm. While the power was completely confined within the fiber boundary
in the fiber pigtails 共Vcl  2兲, in the liquid the OFN had ␸ ⬍ 1 µm 共Vcl ⬍ 2兲;
thus a considerable fraction of the power was propagating in the surrounding
water. The water-based suspension containing polystyrene microspheres
(refractive index nPS = 1.59 and specific gravity ␳PS ⬃ 1.05 g / cm3) was used to
surround the OFN. Real-time monitoring was performed with a CCD camera
mounted on top of the microscope with a 10⫻ objective and connected to a
computer. A diagram of the experimental apparatus is given in Fig. 17.
Figures 18 (media 1) and 19 (media 2) show two movies taken by the CCD
camera for suspensions of 3 and 10 µm spheres, respectively. Bright spots
appear in Figs. 18 and 19 because no filter was inserted into the microscope to
reduce the collection of scattered laser light. The bright spots are explained
as the excitation of whispering gallery modes in microspheres whose size is in
resonance with the laser beam launched in the OFN. When the laser is
switched on, the microspheres around the OFN were first attracted laterally to
the OFN and then driven along it in the direction of light propagation. The
particle velocities were evaluated from a measurement of the average
displacement over a few seconds and were estimated to be of the order of
⬃10 µm / s. It is notable that even clusters of 6–7 particles with overall diameters
larger than 20 µm can be propelled along the OFN (media 2).
The optical force experienced by particles is proportional to the optical
intensity at their surface; in Subsection 3.2 the electric field (E field) at the

Figure 17

CCD

Microscope
PC

10x
Water
Polystyrene spheres

Laser

MgF2 Substrate

Schematic of the experimental apparatus used to demonstrate optical propulsion

of polystyrene microparticles.

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 Figure 18

Single-frame excerpt from the video recording (Media 1) of 3 µm polystyrene

particles propelled along an OFN with ␸ = 0.95 µm.

surface of the OFN has been evaluated, and Fig. 4 shows how there is a
maximum at ␸ = 0.7 mm. For a laser output of 500 mW, the average velocity of
3 µm particles was ⬃9 µm / s along the OFN, compared with the ⬃2.6 µm / s
observed along glass waveguides [95]. The larger velocity observed in Fig. 18
with respect to the glass planar waveguide can be explained in terms of a
better source or waveguide coupling and/or a larger evanescent field and higher
field intensity at the interface between the optical guide and the water–
particle suspension.
Figure 20 presents a comparison of the evanescent fields near the surface for
three waveguides used in propulsion experiments: an OFN, a Si3N4 ridge
waveguide [96], and a glass waveguide [95]. Simulations were carried out by
using the beam propagation method as before. The waveguide width and
depth were taken to be 3 and 1 µm for the glass waveguide [95] and 1 and 0.2 µm
for the Si3N4 waveguide [96]. The refractive indices of the glass substrate,
glass waveguide, Si3N4 waveguide, and its substrate were taken to be 1.55, 1.58,
1.97, and 1.45 respectively. From Fig. 20 it is clear that the E field at the
interface of the OFN is several times larger than that experienced in the glass
planar waveguide, but about half of that calculated for the Si3N4 ridge
waveguide. This can be easily explained by the mode confinement geometry:
while in planar waveguides the mode can leak into the substrate (which

Figure 19

Single-frame excerpt from video (Media 2) of 10 µm polystyrene particles

propelled along an OFN with ␸ = 0.95 µm.

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 Figure 20

(b) Si3NSi
1 4 waveguide
N Waveguide
3 4
OFNSMOW
Ion-exchanged glass
Ion-exchanged waveguide
Glass Waveguide

E-field
Normalised E-field
0.1

Normalised
0.01

0.0 0.5 1.0 1.5 2.0

Distance from surface (µm)
Distance from surface (µm)

E field distribution in an OFN and planar waveguides in the space adjacent the
surface. The E field was normalized per unit power traveling in the
waveguide.

can host a large fraction of the power), in the OFN the mode can only extend
into the solution because of its cylindrical symmetry. Moreover, mode
confinement is related to the numerical aperture of the optical waveguide:
since the Si3N4 waveguide has an extremely high refractive index 共nSi3N4
⬃ 1.97兲, the numerical aperture that the waveguide has with respect to water
共nH2O ⬃ 1.33兲 and to the substrate 共nSub ⬃ 1.45兲 is considerably larger than that
experienced by the modes propagating in the glass waveguide and OFN.
However, the evanescent field in the planar waveguides decreases more sharply
than in the OFN; in fact, although the Si3N4 waveguide has a stronger field
up to 250 nm from the interface, at distances longer than 250 nm the OFN E field
is consistently larger and even extends beyond 2 µm above the surface. In
addition, the OFN exhibits the great advantage of manipulating particles in 3D.

4.3. Sensors
The great majority of optical biochemical sensors can be classified according
to two sensing approaches: homogeneous sensing and surface sensing
[97]. In homogeneous sensing, the device is typically surrounded by an analyte
solution, and the homogeneously distributed analyte in the solution modifies
the bulk refractive index of the solution. In surface sensing, the optical device is
pretreated to have receptors or binding sites on the sensor surfaces, which
can selectively bind the specific analyte [97].
Surface sensors based on OFNs have been predicted [67] and experimentally
realized for the detection of hydrogen [53] by coating an OFM with
palladium. Because of the reduced sensor dimensions, the ultrathin palladium
film allowed sensor response times of approximately 10 s, up to 15 times
faster than that of most optical and electrical hydrogen sensors reported so far.
The detection range was 0.05%–5%, enough to detect hydrogen at the
lower explosion limit for gas mixtures. The sensor worked by checking the
absorption changes with a simple transmission measurement setup that

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consisted of a 1550 nm laser diode and a photodetector. OFNs can also be
coated with bioreceptors or gelatin to detect biological components [67] and
humidity [98], respectively. Polymers nanowires have also been bonded to silica
OFNs and used as sensors for humidity, NO2, and NH3 [99]. In this case, the
use of a polymeric material allows the gas to diffuse in it and modify its optical
absorption properties. By measuring the absorption changes it is possible to
measure changes in gas composition down to a sub-part-per-million level (to less
than 1 part in 106). Because of its large evanescent field, OFN sensors have
also found applications in the measurement of refractive index in microfluidic
channels [100] and even as a tool for probing atomic fluorescence [101].
However, in all of these configurations the interaction length is limited by the
OFN’s physical length.
In contrast, resonant sensors allow an effective multiplication of the interaction
length and thus allow incredibly compact devices to be manufactured. Small
size, high sensitivity, high selectivity, and low detection limits are the dominant
requirements for evanescent field optical resonating sensors. To date, the
resonators investigated include microspheres, photonic crystals, gratings, and
microrings [102–106]. Optical microresonators can provide large evanescent
fields for high sensitivity, high Q factors for low detection limits, and
corresponding small resonant bandwidths for good wavelength selectivity. The
drawback of the vast majority of high-Q resonators relates to the difficulty
of coupling light into and out of the resonator. Microcoil resonating sensors have

Because of their fiberized pigtails, OFN resonators

such as the ones presented in Subsection 4.1 do not
exhibit the input–output coupling problems
experienced in other high-Q resonators.

been manufactured by wrapping OFMs around copper wires [107]; although

they exhibit good sensitivities, they are prone to degradation. In Subsection 3.3b
embedding was examined and shown to preserve OFN from degradation;
yet the choice of the coating thickness is a challenge, because a thick coating
layer will limit the sensitive evanescent field, while a thin layer does not
provide appropriate protection to the device. In this Subsection, the possibility
of exploiting coated nanowire resonators for homogeneous [97] sensing
applications is investigated.

4.3a. Resonating Sensors: Schematic and Manufacture

To date, three resonating sensors based on OFNs–OFMs have been proposed
or demonstrated: the coated microfiber coil resonator sensor (CMCRS)
[55,57], the embedded optical nanowire loop resonator refractometric sensor
(ENLRS) [58], and the liquid ring resonator optical sensor (LRROS) [108].
While the first two exploit the resonances created in an OFM resonator, an
LRROS effectively uses an OFM to excite a whispering gallery mode in a
capillary, which acts as the real sensing device. In this subsection only the first
two sensors will be discussed.
Figure 21 shows a schematic of the CMCRS and the ENLRS. In Fig. 21(a) the
OFM is shown in violet and blue, the analyte channel in brown, and Teflon in

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 Figure 21

Schematics of (a) a coated microfiber coil resonator sensor (CMCRS) and (b)
an embedded optical nanowire loop resonator refractometric sensor
(ENLRS). Figures are not to scale.

green. The CMCRS is a compact and robust device with an intrinsic fluidic
channel to deliver samples to the sensor. In Fig. 21(b) a very thin polymer layer
covers the OFM loop of the ENLRS, while a thick coating deposit is used to
fix the two fiber pigtails. In the ENLRS two sides are exposed to the liquid to be
sensed. In both cases the embedded OFM has a considerable fraction of its
mode propagating in the fluidic channel; thus any change in the analyte
properties is reflected in a change of the mode properties at the sensor output.
When OFNs are used instead of OFMs, an even greater fraction of the
mode propagates in the evanescent field, thus increasing the overall sensitivity.
Since OFMs–OFNs are fabricated from a single tapered optical fiber, light
can be coupled into the sensor with essentially no insertion loss, which is a huge
advantage over other types of resonator sensors.
The CMCRS can be fabricated from a microcoil resonator (Subsection 4.1b)
by using an expendable rod, which is then removed. A candidate for the rod
material is PMMA (polymethyl methacrylate), which is a polymer with an
amorphous structure and which is soluble in acetone. In a similar way the
ENLRS can be made by using two substrates fabricated with disposable
materials such as PMMA coated with a thin layer of a low-loss,
low-refractive-index polymer such as Teflon. Once the OFM loop resonator
(Subsection 4.1b) is manufactured on one of the substrates, the other substrate
is placed on top of the nanowire resonator and glued with the same low
refractive-index polymer, and the expendable materials are removed, leaving a
thin layer of low-refractive-index material on the nanowire. The use of a

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thick substrate allows easy handling of thin coating layers. A schematic cross
section of the sensors as manufactured is presented in Fig. 22.

4.3b. Resonating Sensors: Theory

Any change of the analyte refractive index na leads to a change in the effective
index neff of the propagating mode; thus it shifts the mode relative to the
resonance, which in turn modifies the transmissivity T, and it shifts the mode
relative to the resonance. A two-turn CMCRS can be easily evaluated by
using the coupled mode equations presented in Subsection 4.1b; Eqs. (11)–(16)
give

exp共i␤L − ␣L兲 − i sin K

T= , 共22兲
exp共− i␤L + ␣L兲 + i sin K

where ␤ is the real part of the propagation constant, ␣ the loss coefficient, and
K = ␬L the coupling parameter for coupling coefficient ␬ and coil length L.
Resonances occur if K and ␤ satisfy

Km = arcsin关exp共− ␣L兲兴 + 2m␲ , 共23兲

2␲neff 共2p + 1兲␲

␤n = = 共24兲
␭res 2L
for integer m and p. For resonant coupling 共K = Km兲 Eqs. (11)–(16) yield

Figure 22

Schematic cross sections of (a) a coated microfiber coil resonator sensor

(CMCRS) and two embedded optical nanowire loop resonator refractometric
sensors (ENLRS) with (b) one and (c) two surfaces exposed to the analyte.

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 FWHM =
␭res
2

␲neffL 2
冏 ␲
− arcsin 冋 e2aL + e−2aL
2共e2aL + e−2aL兲 − 2
册冏
⬇
␭res
2

␲neffL
冑 共e2aL + e−2aL兲 − 2
共e2aL + e−2aL兲 − 1
⬇
␭res
2

␲neff
␣
, 共25兲

while for nonresonant coupling

FWHM ⬀ ␣ + 共K − Km兲2 . 共26兲

The mode properties are particularly affected by the OFN radius r = ␸ / 2 and
the distance d between the OFN and the analyte (coating thickness). The sensor
response has been determined by calculating neff (using the
finite-element-method software COMSOL3.3 with perfectly matched layers)
and the related shift of ␭res as a function of the analyte concentration. neff has
been evaluated for a nanowire embedded in Teflon and coiled around a
microfluidic channel. The fundamental mode, which has the largest propagation
constant, is the only mode that is well bounded in the vicinity of the fiber
core [109,110]; thus it is the only mode considered here. Since neff is a function
of r and d, ␭res also varies with r and d through Eq. (24). Figure 23 shows
the intensity distribution of the fundamental mode for two different analyte
refractive indices [Fig. 23(a)] na = 1 and [Fig. 23(b)] na = 1.37 when nOFN
= 1.451, nTeflon = 1.311, d = 100 nm, r = 500 nm, ␭ = 1550 nm. When na is small
[Fig. 23(a)] the field is still bound within the OFN physical boundary,
while it shifts into the coating and leaks into the analyte when na is large [Fig.
23(b)].
Figure 24 shows the dependence of neff on the analyte refractive index na. The
OFN radius has been assumed constant at r = 500 nm, while three values 10,
100, and 500 nm have been considered for d. Generally, neff increases with na and
increases more quickly with smaller d, since in this case a larger fraction of
the mode is propagating in the analyte, as shown in Fig. 23. If na = nTeflon, light
cannot see the boundary between Teflon and the analyte solution; thus neff
is the same at any d, and in Figs. 24(a)–24(d) there is a crossing point for
different diameters. It is interesting that this behavior is independent of

Figure 23

Intensity distribution of the fundamental mode at the sensor–analyte interface

for nOFN = 1.451, nTeflon = 1.311, d = 100 nm, r = 500 nm. The analyte
refractive index is (a) na = 1 and (b) na = 1.37, respectively. The OFN section is
represented by the white circle.

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 Figure 24
1.415
(c)
(a) d=10nm
d=100nm
d=500nm

1.415
1.4145

neff
eff
1.41

n
1.414
1.405 bare OFN
d=10nm, 2 surfaces
d=100nm 2 surfaces
d=10nm, 1 surface
d=100nm, 1 surface
1.4135 1.4
1 1.1 1.2 1.3 1.4 1 1.1 1.2 1.3
na
na

1.375
(b) d=10nm
d=100nm
(d)
d=500nm

1.36
1.37

n eff
eff
n

1.34
1.365
Bare OFN
d=10nm, 2 surfaces
1.32 d=100nm, 2 surfaces
d=10nm, 1 surface
d=100nm, 1 surface
1.36
1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1 1.1 1.2 1.3
n
a
na

Dependence of the effective index of a coated OFN neff on the index of the
analyte na for nTeflon = 1.311, nOFN = 1.451, r = 500 nm, for several distances
between OFN and analyte in a (a), (b) CMCRS and (c), (d) an ENLRS. The
wavelength of the propagating mode is ␭ = 600 nm in (a) and (c) and ␭
= 970 nm in (b) and (d). A bare OFN is reported in (c) and (d) for reference.

the sensor geometry, to the degree that the overlap between analyte and mode
propagating in the OFN is the same: the CMCRS has the same overlap
with the analyte as the ENLRS with one surface interface [Fig. 22(b)]; thus
they have the same dependence of neff on na. The ENLRS with two interface
surfaces [Fig. 22(c)] has an overlap that is twice as large, and thus the
dependence of neff on na is twice as strong.

4.3c. Resonating Sensors: Sensitivity

The most important attribute of refractometric sensors is the homogeneous
sensitivity S, defined as the shift of the resonant wavelength ␭res [corresponding
to the solutions of Eq. (23)] with respect to the change in the analyte refractive
index na [97,111]:

⳵␭res ⳵␭res ⳵neff 2␲ ⳵neff ␭res ⳵neff

S= = = = . 共27兲
⳵na ⳵neff ⳵na ␤n ⳵na neff ⳵na
Since most analytes are predominantly water and device performances are
affected by high losses [Eqs. (21)–(25)], it is convenient to work in a wavelength
region of low water absorption. Water absorption has a minimum at ␭
= 500 nm, and it generally increases with wavelength up to 3000 nm [112–115];

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© 2009 Optical Society of America
 therefore, to limit its effect on device performance, it is beneficial to work at
wavelengths shorter than 1000 nm.
S was calculated by using Eq. (27) near na = 1.332 at operational wavelengths
of ␭ = 600 nm and ␭ = 970 nm. Figure 25 shows the dependence of S on r
for different values of d. S increases when d decreases or ␭ increases because
of the increasing fraction of power in the evanescent field. Decreasing r
also increases S because this increases the fraction of the mode field inside the
fluidic channel. S reaches 500 nm/ RIU (where RIU is refractive index unit)
at r ⬇ 200 nm for ␭ = 600 nm and 700 nm/ RIU at r ⬇ 300 nm for ␭ = 970 nm.
This is higher than in most microresonator sensors [102,104,106,124,122,123].
For the same ␭ and OFN radius r, the sensitivity for the ENLRS with two
sensing surfaces is larger than that with only one because of the larger overlap
between the evanescent field and the analyte (Subsection 4.3b). For very
small values of r the sensitivity reaches a plateau because the fundamental mode
is no longer well confined and most of the evanescent field is in the analyte.

Figure 25
4
4
10 10
d=10nm (c)
(a) d=100nm
2 d=500nm d=10nm , 2 surfaces
10 2 d=100nm, 2 surfaces
10
d=500nm , 2 surfaces
d=10nm, 1 surface
0
S (nm/RIU)

10 d=100nm, 1 surface
S (nm/RIU)

0 d=500nm, 1 surface
10
-2
10

-2
-4 10
10

-6
10 -4
200 600 1000 1400 1800 10
200 400 600 800 1000 1200 1400 1600 1800 2000
r (nm) r (nm)

3 4
10 10
(b) d=10nm (d)
d=100nm
3
2 d=500nm 10 d=10nm, 2 surfaces
10 d=100nm, 2 surfaces
d=500nm, 2 surfaces
2
S (nm/RIU)

10 d=10nm, 1 surface
1 d=100nm, 1 surface
10
S (nm/RIU)

d=500nm, 1 surface
1
10
0
10
0
10

-1
10 -1
10

-2
10
400 800 1200 1600 2000 200 400 600 800 1000 1200 1400 1600 1800 2000
r (nm) r (nm)

Dependence of the sensitivity S on the OFN radius r for nTeflon = 1.311, nOFN
= 1.451, and several coating thicknesses d in (a), (b) a CMCRS and (c), (d) an
ENLRS. The wavelength of the propagating mode is ␭ = 600 nm in (a) and
(c) and ␭ = 970 nm in (b) and (d). Schematics of the ENLRS with one or two
surfaces are shown in Figs. 22(b) and 22(c).

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In this case neff becomes linearly dependent on na, and the derivative in the last
term of Eq. (27) reaches a uniform value, and so the sensitivity reaches a
plateau.
It is interesting to note that the sensor sensitivity is strongly dependent on the
embedding material. Figure 26 shows S for a CMCRS embedded in UV375
共nUV375 ⬃ 1.375兲 versus r at ␭ = 600 nm [Fig. 26(a)] and ␭ = 970 nm [Fig. 26(b)]
for different values of d. As before, na = 1.332 and nOFN = 1.451.
S in UV375 is smaller than that obtained in Teflon: S ⬃ 50 nm/ RIU for r
= 400 nm, d = 10 nm and ␭ = 970 nm, compared with S ⬃ 130 nm/ RIU in Teflon

Figure 26
2
10
(a) d=10 nm
d=100 nm
1
10 d=500 nm

0
10
S (nm/RIU)

-1
10

-2
10

-3
10

-4
10
400 800 1200 1600 2000
r (nm)
2
10
(b)
d=10nm
d=100nm
1 d=500nm
10
S (nm/RIU)

0
10

-1
10

-2
10
400 800 1200 1600 2000
r (nm)

Dependence of the sensitivity S on the OFN radius r for nUV375 = 1.375, nOFN
= 1.451, and several coating thicknesses d in a CMCRS for (a) ␭ = 600 nm and
(b) ␭ = 970 nm.

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[Fig. 25(b)]. Since the refractive index of UV375 is higher than that of Teflon,
the overlap between the evanescent field and the analyte is smaller; thus the
last expression of Eq. (27) for UV375-coated CMCRSs is smaller than that for
Teflon-coated CMCRSs.

4.3d. Resonating Sensors: Detection Limit

Another important figure of merit of refractometric sensors is the detection
limit, defined as the smallest refractive index change that can be measured. If ␦␭0
is the smallest measurable wavelength shift, then the detection limit DL can
be defined as [55,97,111]:

␦␭0
DL = . 共28兲
S
␦␭0 is generally limited by the instrument resolution and is empirically
assumed to be 1 / 20 of the resonance FWHM [104]. The FWHM depends on
the resonator coupling and loss. Losses in the CMCRS and the ENLRS arise
from surface scattering, material (analyte, coating, and fiber) absorption,
and bending. The smallest reported OFN loss is about ␣ = 0.001 dB/ mm with
radii in the range of hundreds of nanometers (Subsection 3.1). Water
absorption can be reduced to levels well below 0.0001 dB/ mm by operating at
short wavelengths (Subsection 4.3c). Low-loss embedding materials (such
as Teflon or UV375) can be used: losses of 1 dB/ m have been reported [116,117]
for water-core Teflon waveguides. Bend losses can be estimated from [70]

␣bend =
U2
2VclWK1共W兲 r␳
冉冊 冋 冉
␲
exp −
4W
3Vcl
1−
2
nOFN
n2Teflon
冊册
␳
r
, 共29兲

where ␳ is the bend curvature radius, r the OFN radius, and U, Vcl, and Wthe
normalized modal parameters defined by Eqs. (2), (29), and (30):

2␲r
U= 共nOFN
2
− n2eff兲1/2 , 共30兲
␭

2␲r
W= 共n2eff − n2Teflon兲1/2 . 共31兲
␭
For r = 200 nm and R = 250 µm, ␣bend ⬃ 0.0001 dB/ mm at ␭ = 600 nm, which
quickly decreases further with increasing coil size. Assuming ␣ = 0.01 dB/ mm,
the other losses can be neglected, and for a CMCRS or an ENLRS with r
= 200 nm at ␭ = 600 nm, Eq. (22) gives FWHM⬃ 410−4 nm and DL⬃ 10−6
− 10−7 RIU, which is comparable with the best reported experimental results
[55,118–121]. Although these values of FWHM can be easily measured
with a high-resolution OSA, cost and practical considerations limit the
resolution to few picometers, leading to a practical detection limit of the order
of several 10−6 RIU (see Table 1).
In traditional microresonators input–output coupling occurs via a prism,
antiresonant reflecting waveguides, or a fiber taper [102–106]. With probably
only the exception of fiber taper coupling, which has been proved to be
reasonably efficient [124], coupling to a microresonator has considerably
complicated device design and/or has resulted in a significant increase in the

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 Table 1. Sensitivity S, FWHM, and Detection Limit DL for Evanescent Field
Resonating Refractometric Sensorsa

S ␭res FWHM DL
Type of Sensor (nm/RIU) (nm) (nm) (RIU) Ref.

Microsphere 30 980 2 ⫻ 10−4 6 ⫻ 10−6 [104]

Photonic crystal microresonator 228 1500 ⬃1 3 ⫻ 10−3 [102]
Microcapillary 45 980 1.55⫻ 10−4 3⫻10−6 [106]
Grating 1000 1550 ⬎0.1 10−5 [122]
Hollow-core ARROWbb 555 700 ⬎1 2 ⫻ 10−3 [123]
LRROS 800 1550 10−6 [108]
CMCRS or ENLRS 700 970 4 ⫻ 10−4 10−7 [55,58]

a
␭res represents the resonating working wavelength.
b
ARROW, antiresonant reflective optical waveguide.

overall loss. In contrast, CMCRSs and ENLRSs have an extremely low

insertion loss: the ease of mode size control and the lossless input–output
coupling via the fiber pigtails are unique features of devices based on OFNs.

4.3e. Resonating Sensors: Experimental Demonstration

A CMCRS was fabricated from an OFM with a length and diameter of the
uniform waist region of 50 mm and ⬃2.5 µm. The OFM was then wrapped on
a 1 mm diameter PMMA rod. The whole structure was repeatedly coated
with the Teflon solution 601S1-100-6. The dried embedded OMR was then left
in acetone to remove the support rod, which was completely dissolved in
1 – 2 days at room temperature. Thereby, a CMCRS with a ⬃1 mm diameter
microchannel and two input–output pigtails was obtained. A picture of the sensor
is shown in Fig. 27. The sensor consists of an OFM resonator with five turns
and a microfluidic channel inside. The adjacent coils are very close, and the
major coupling area is on the left side of the picture. Although some bubbles are
left inside the CMCRS during the drying process, these seem to be far from
the OFM and did not affect overall sensor operation.
To simulate the sensor behavior in aqueous solutions, the sensor was connected
to an erbium-doped fiber amplifier and to an optical spectrum analyzer and

Figure 27

Microscope picture of a CMCRS. The yellow dashed lines and red arrows
show the fluidic channel and input–output pigtails, respectively.

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then inserted into a beaker containing mixtures of isopropanol and methanol.
The isopropanol ratios were (1) 60%, (2) 61.5%, (3) 63%, (4) 64.3%, (5)
65.5%, (6) 66.7%, and (7) 67.7%. The refractive indices of isopropanol and
methanol at 1.5 µm are reported to be 1.364 and 1.317, respectively [125]. The
sensor was then immersed into the mixtures, and spectra were recorded at
1530 nm. Figure 28 shows that for increasing isopropyl concentrations the
resonator peak shifts to longer wavelengths. The extinction ratio increases,
achieves a maximum, and then decreases: this can be explained by a change in
the coupling coefficient due to the change in the mixture’s refractive index.
The transmission properties of a multiturn microfiber coil resonator depend on
the resonator coupling and loss and can be simulated by solving Eqs.
(11)–(16). The FWHM (and therefore the Q factor) in the traditional
microsphere and microring resonators is controlled primarily by modifying the
input–output coupling by means of prism coupling, antiresonant reflecting
waveguide coupling, and fiber taper coupling [102–106].
There is only one primary resonance, which can be easily evaluated in a way
analogous to that for a single-loop resonator. neff of the fundamental mode was
calculated for several values of d by using Eqs. (22)–(26). Figure 29 shows
the measured wavelength shift (dashed curve) and calculated (solid lines)
wavelength shift as a function of the analyte refractive index na and polymer
thicknesses d for r = 1250 nm.
The best fit occurs for d ⬃ 0, showing that the average coating thickness is
small, possibly because the tight wrapping of the OFM on the support rod left

Figure 28

Dependence of the OMCRS spectrum on the analyte refractive index for

different mixtures of isopropanol and methanol. The isopropyl fractions in (1),
(2), (3), (4), (5), (6), and (7) are 60%, 61.5%, 63%, 64.3%, 65.5%, 66.7%,
and 67.7%, respectively.

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 Figure 29
0.50
Measurement
d=100 nm

Wavelength Shift(nm)
Simulations
d=500nm
0.45

0.40 d=0 nm

0.35

0.30
1.345 1.346 1.347 1.348 1.349
Analyte refractive index na

Dependence of the measured (dashed) and calculated (solid) wavelength shifts

on the analyte refractive index na for r = 1250 nm and different polymer
thicknesses d.

little space for the coating to fill. The small difference observed in Fig. 29 has
been attributed to the unevenness in the OFM diameter profile, to the
imprecision in the coil winding, to the channel roughness, and to the uneven
coating thickness (OFM distance from the microfluidic channel). S was obtained
from the line slope as ⬃40 nm/ RIU. This value is comparable with those
reported previously for microsphere, microring, and liquid-core resonators
[103,104,108], but smaller than recently reported values for a slot waveguide
(212.13 nm/ RIU) [126]. The relatively low value of S can be attributed to
the small overlap between the mode propagating in the OFM and the analyte.
In fact, S has been shown to increase by orders of magnitude for increasing
na [108]. Another factor that has probably contributed to the degraded S is the
surface roughness of the device in contact with the analyte, possibly caused
by the PMMA support rod. This roughness might also be responsible for the
moderately low Q factor 共Q ⬃ 104兲 observed.

4.4. Supercontinuum Generation

Since its first observation in 1970 [127], supercontinuum generation has
attracted much attention owing to the large range of applications associated
with ultrabroadband light sources. As a physical phenomenon, supercontinuum
generation involves a number of nonlinear optical effects, including self-
and cross-phase modulation, four-wave mixing, soliton effects, and stimulated
Raman scattering, combined with appropriate dispersion properties. High
intensity is a fundamental requirement for the observation of the phenomenon.
This can be achieved either by using high-energy ultrashort pulses or, more
practically, by using tight spatial confinement within a suitably nonlinear
waveguide. The higher the nonlinearity of the material, the lower the required
power levels. Silica holey fiber and tapers have previously been used
extensively [128–131]; however the intrinsic nonlinearity of silica is relatively
low (Subsection 3.2), and there has therefore been growing interest in
using optical fibers and microstructured optical fibers fabricated from highly
nonlinear glasses [132–135]. Most recently, OFMs have attracted an increasing
interest for continuum generation because of the high nonlinearity associated

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© 2009 Optical Society of America
with their tight confinement (Subsection 3.2), easy connectivity to fiberized
components, and extreme flexibility in tailoring the zero dispersion wavelength.
In particular, OFMs provide higher confinement than untapered fibers and
lower input–output coupling losses than small-core microstructured fibers of
similar minimum core dimensions. If the bandwidth is measured at −20 dB from
the peak, supercontinuum generation over a width of 1000 nm has been
observed [45–47]. The use of highly nonlinear materials for OFMs has been
studied to increase the optical nonlinearity even further (Subsection 3.2):
bismuth silicate [136] and chalcogenide [48] OFMs have been successfully used
to generate supercontinua over a broad range of wavelengths. In particular,
bismuth silicate can be considered a promising material because of a much wider
transmission window in the IR than silica, the lack of Raman peaks, and the
extremely smooth spectral profiles of the generated supercontinua. In fact, while
spectra generated in silica OFMs have spectral oscillations in excess of
10 dB, an extremely smooth spectrum has been obtained for a bismuth silicate
OFM over 1000 nm.
The OFM used for supercontinuum generation was manufactured by using the
modified flame-brushing technique (Section 2) on a highly nonlinear fiber
(n2 ⬃ 3.2⫻ 10−19 m2 / W [137]) fabricated by Asahi Glass Ltd. (Japan). The
optical fiber had core and cladding diameters and refractive indices at 1.55 µm of
␸core ⬃ 6.9 mm and ␸cladding ⬃ 125.6 mm, ncore ⬃ 2.02 and ncladding ⬃ 2.01,
respectively. The total loss of the taper (fiber input facet to fiber output facet)
was monitored continuously during the fabrication process by injecting
light at 1.55 µm from a fiberized laser source and measuring the total throughput
power with a powermeter. The total loss of the taper at the end of the
fabrication process was approximately 13 dB. The material group-velocity
dispersion of the OFM is given by the dispersion of the cladding material of the
original untapered fiber, as shown in Fig. 30(a), with a zero-dispersion
wavelength at ⬃2.6 µm. The total group-velocity dispersion D of the guided
mode has a strong contribution from the waveguide design [138]:

D=
1 dng
c d␭
−
␭2
冋
2␲⌬ n2gVcl ⳵2共Vclb兲
n␻ dV2cl
+
dng ⳵共Vclb兲
d␻ dVcl
册 , 共32兲

where Vcl is defined by Eq. (2) and is dependent on the OFM radius r. Figure
30(b) shows the dependence of the (first) zero-dispersion wavelength on r.
To generate a supercontinuum, the OFM radius was chosen as r ⬃ 1.6 µm so that
its zero-dispersion wavelength coincided with the pump central wavelength
at 1.63 µm [Fig. 30(b)]. Femtosecond laser pulses at this wavelength from an
optical parametric amplifier (Coherent Opera pumped by Coherent Legend)
were injected into the OFM by using a 10⫻ microscope objective 共NA⬃ 0.2兲.
The pulse duration and repetition rate were ⬃120 fs and 1 kHz, respectively.
The output spectra were measured by using an OSA for the wavelength range
0.85– 1.75 µm and an extended InGaAs detector with a monochromator for
the range 1.55– 2.4 µm.
Figure 31 compares the spectra of laser pulses at the laser output and at the
OFM output for pumping at ⬃1.63 µm. With a laser output pulse energy of Ep
⬃ 5 nJ, a supercontinuum spectrum has been generated extending from 1 to
⬎2.3 µm, with a 3 dB spectral width of 700 nm. It is interesting to note that the
supercontinuum profile is remarkably flat with ⬍5 dB variation over the
spectral range 1.2– 2 µm. Moreover, the spectrum is more than 1000 nm broad

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© 2009 Optical Society of America
 Figure 30

(a) Dependence of the dispersion of the cladding material on the wavelength.

(b) Correlation between diameter and zero-dispersion wavelength in OFMs
manufactured from the Asahi bismuth silicate fiber: simulations were performed
using the exact solution of Maxwell’s equations for an air-suspended rod
having the dispersion characteristics of the fiber cladding glass [128].

at the 10 dB level. The observed decrease in the output power at long

wavelengths is probably, at least in part, due to the roll-off in our detection
system’s sensitivity.

4.5. Particle Trapping

While tight confinement in an OFM is associated with large nonlinearity, at a
cleaved fiber end tight mode confinement results in high beam divergence.
Because of the large numerical aperture of the OFM, the intensity profile at the
fiber output experiences large gradients within very short distances
(Fig. 32).
This characteristic can be exploited to trap particles with the so-called optical
tweezers [139,140], which use forces exerted by a strongly focused beam
of light to trap small objects. Small particles develop electric dipole moments

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© 2009 Optical Society of America
 Figure 31

Comparison of output spectra from the laser source and the OFN for pulse
energies of 5 and 3 nJ. The spectra have been shifted vertically for clarity.

as a consequence of the optical field; thus they are shifted toward the focus by
intensity gradients in the electric field [140]. In contrast, large objects are
depicted as acting as lenses, refracting the rays of light and redirecting the
momentum of their photons; this reaction moves them toward a focus, where the
intensity peaks [139]. In free space, beam focusing is limited by diffraction:
the minimum focal spot size is typically half of the wavelength (of the order of
a fraction of a micrometer, typically). Metallic probes have also been
proposed to trap small particles [141,142], where strong field enhancement
from light scattering at a metallic tip could generate a trapping potential deep
enough to overcome Brownian motion and to capture a nanometric particle
[141]. Alternatively, a combination of evanescent illumination from a substrate
and light scattering at a tungsten probe apex is used to shape the optical
field into a localized, 3D optical trap [142]. All these approaches require high
powers for the illumination (well above 1 W) and are difficult to integrate
in conventional microscopy instruments. Lensed optical fibers have
been demonstrated to be highly efficient optical traps [143–145] and can easily
be integrated with microscope technology but have the drawback of a large
size, difficult end face processing, and large mode field diameter (typically of the
order of 10 µm).
Short adiabatic tips can be manufactured by breaking an OFN at its minimum
waist region. These tips can be used to trap 1 µm polystyrene particles in
water with low powers 共⬃10 mW兲. The use of an OFN allows for small probe
size and optimal confinement (submicrometer spots) and potentially reduces
the trapping power by orders of magnitude. Trapping experiments were carried
out at ⬃1.5 µm by connecting an OFN to an EDFA capable of delivering
0.2 W of maximum power. The OFN tip was immersed in a solution containing
silica microspheres with 1 µm diameter and was analyzed by using an
optical microscope. The EDFA power was increased in steps of 0.1 mW, and
pictures were taken every ⬃1 s. At low powers, because of Brownian motion and
other environmental factors, the microparticles move quickly, and no trapping
was observed. With powers of ⬃10 mW, single particles were trapped at

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© 2009 Optical Society of America
 Figure 32

Electric field profile at an OFM cleaved end (a). Cross sections at different
distances along the z direction. (b) The OFN cleaved end is positioned
at ⬃3.2 µm. Simulations were carried out using a beam propagation method.

the OFN tip. Figures 33(a) and 33(b) present photos taken at an ⬃1 s interval
where one particle is clearly trapped at the fiber tip while the others move
within the liquid. When the power was reduced [Fig. 33(c)], the particle was
released from the optical trap at the OFN tip. When the power was increased
again, other particles were trapped at the fiber tip when the EDFA power
was of the order of 10 mW.
This experiment demonstrated that optical trapping with OFN and adiabatic
tapers uses lower intensities 共⬃10 mW兲 than that used in free space 共⬃1 W兲
[146] or with lensed fibers 共22 mW兲 [145]).

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© 2009 Optical Society of America
 Figure 33

Microscope pictures of an OFM tip in a solution of 1 µm silica spheres. (a),

(b) At laser outputs of ⬃10 mW a particle (indicated by an arrow) is trapped at
the OFN tip. (c) The particle is released when the laser is switched off.

4.6. Mode Filtering

In addition to allowing efficient focusing of light (Subsection 4.5), OFN
transition regions can act as an efficient tool for higher-order mode filtering in
multimode waveguides [147]. A conventional telecom fiber with a 1 µm
OFM shows broadband single-mode operation with minimal optical loss
共⬍0.1 dB兲 for the fundamental mode. Figures 34 and 35 represent a schematic
of the device: if the conical transition regions are adiabatic (Fig. 34), guided
modes in the core of the multimode fiber are continuously mode converted to
guided cladding modes in the OFN on a one-to-one basis by the downtaper
and are then coupled back into guided modes in the multimode fiber by the
uptaper; however, when the transition regions are not adiabatic (Fig. 35),
high-order modes are converted in even higher-order modes, which can be
effectively suppressed by controlling the OFN diameter [148].
The single-mode operation range is determined by the mode cutoff conditions
[148] and the OFN small cladding V number Vcl [Eq. (2)] limits the number
of propagating modes without the use of additional index matching oil to strip
away the high-order modes [149,150]. The different mode evolution
(adiabatic for fundamental mode and nonadiabatic for higher-order modes)
allows only the transverse single mode to propagate along the waveguide, which

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© 2009 Optical Society of America
 Figure 34
LP01+LP11 LP01+LP11

+
Adiabatic Uniform Adiabatic
Transition Waist Transition
(LP01, LP11)

LP01 LP01
in core in clad

LP11 LP11
in core In clad

Schematic of an OFN with adiabatic transition regions: all modes continuously

evolve from core modes to cladding modes and are collected at the fiber
output. The evolution of the spatial profile of the first two guided modes along
the transition tapers is also shown.

permits single-mode operation for a conventional fiber over an extremely wide

range of wavelengths.
The experimental demonstration was carried out by manufacturing low-loss
OFMs by the modified flame-brushing technique (Section 2). A telecom optical
fiber (Corning SMF-28) was selected as a simple example of a fiber providing
multimode operation at short wavelengths; in fact, while above 1250 nm
only the LP01 mode propagates, at shorter wavelengths the SMF-28 supports
an increasing number of modes: this is clearly seen by the increased fiber output
in the wavelength range 850– 1250 (where two modes are supported) with
respect to the single-mode operation range above 1250 nm (Fig. 36).
The profile of the transition regions was approximated by a decreasing
exponential function, achieved by an appropriate control of the translation
stage movement during fabrication [151]. Transmission spectra were recorded

Figure 35

Schematic of an OFN with nonadiabatic transition regions: higher-order core

modes are converted to even higher-order cladding modes or radiation
modes that are not guided by the OFN because of its low cladding V number
Vcl.

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 Figure 36

Comparison between the transmission spectra of a standard telecom optical

fiber (SMF-28) without (black) and with (red) a 1 µm OFN. ␭c_LP11, ␭c_LP21,
and ␭c_LP02 represent the cutoff wavelengths for the LP11, LP21 and LP02
modes.

for various outer diameters during fabrication. Figure 37 shows the spectral
output of an SMF28 for different radii r in the uniform waist region.
As r decreases from 62.5 to 35 µm, intermodal interference appears in the
multimode spectral region, while no change is observed above 1250 nm
(single-mode operation region). This can be explained by the interference and

Figure 37

Transmission spectra of a SMF-28 telecom fiber with an OFM for different

minimum waist radii r. When r = 500 nm, single-mode operation is observed for
the whole range of wavelengths.

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© 2009 Optical Society of America
beat of high-order modes that have been excited by a nonadiabatic transition
region. When r ⬃ 2 µm, the higher-order mode cutoff shifts to shorter
wavelengths, enlarging the single-mode operation region. For r = 500 nm there
is no higher-order mode cutoff, and the optical loss is negligible (⬍0.1 dB
at ␭ = 1.55 µm). For even smaller r, propagation [Eq. (1)] and bending [Eq. (28)]
losses pose limitations at long wavelengths. Therefore, r ⬃ 500 nm appears
to be the optimal size for efficient single-mode operation. Usually, the
single-mode operation bandwidth is limited at short wavelengths by a
higher-order mode cutoff. However, Fig. 37 shows that a very broad range
共400– 1700 nm兲 of single-mode operation was successfully realized by applying
the efficient mode filtering scheme based on an OFM and a nonadiabatic
transition region.
Figure 38 shows far-field images taken with a 50⫻ lens and a CCD camera
when laser light at ␭ = 633 nm was launched into one of the fiber pigtails. In
the multimode fiber, interference between guided modes produces degradation
of the laser beam quality at the fiber output [Fig. 38(a)]. Moreover, the
output pattern is extremely sensitive to external perturbations such as bending:
severe modal interference occurs when bending is applied [Fig. 38(b)].
However, when a mode filter is inserted, the fiber output shows a single-mode
beam [Fig. 38(c)] that is unperturbed by external bends [Figs. 38(d)]. No
optical degradation was detected in the mode profile or in the transmission
spectrum even after several bends and multipoint splices were applied to the
SMF with the mode filter.

4.6a. Mode Filtering: Theory

An explanation of the mode filtering effect has been provided by the study of
the mode propagation in the transition regions: the adiabaticity criterion

Figure 38

(a) straight (b) bending1

(c) straight (d) bending1

Far-field image of a beam propagating at ␭ = 633 nm in a SMF (a), (b) without

and (c), (d) with ) the mode filter based on OFM and nonadiabatic tapers.
In (a) and (c) the fiber was kept straight; in (b) and (d) it was bent.

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© 2009 Optical Society of America
[152,153] has been examined by calculating the beat length and taper angle
necessary to ensure adiabatic behavior between points B and C of Fig. 3. A
profile is called adiabatic for a mode when there is no power transfer between
modes. In an ideal adiabatic transition taper, the taper angle is small enough that
the core modes can be considered unperturbed on transition from being core
guided to being cladding guided. In particular, the beat length zb between two
modes having propagation constants ␤1 and ␤2 in a fiber with radius r has
been assumed to be the defining factor for the manufacture of lossless tapers
[152]. For distances larger than zb the two modes do not exchange power and the
taper is adiabatic: this yields the critical angle ⍀ to be defined as

r r共␤1 − ␤2兲
⍀= = . 共33兲
zb 2␲

For nonadiabatic tapers, core modes couple to higher-order cladding modes of

the same symmetry [152]. Coupling to the next high-order mode (LP01
→ LP02, LP11 → LP12, LP21 → LP22) is dominant with respect to the coupling to
other higher-order modes (LP01 → LP03, LP11 → LP13, LP21 → LP23); thus it
represents the limiting factor for an adiabatic transition. Figure 39 shows the
calculated effective indices of the first three LP0m modes as a function of the
core V number [Eq. (2)] at the wavelength ␭ = 1 µm.
Similarly, Fig. 40 shows the calculated effective indices of the first three LP1m
modes as a function of the core V number at the wavelength ␭ = 1 µm.
Figure 41 shows ⍀ for LP01 and LP11 modes evaluated by applying Eq. (33) to
the curves in Figs. 39 and 40. It is notable that the LP11 adiabatic curve is
located at smaller tapering angles than the LP01 one; this implies that for a wide
range of tapering angles the LP01 mode converts adiabatically into a LP01
mode guided by the cladding–air interface, while the LP11 mode experiences

Figure 39
1.454

LP01
1.452
Effective index, neff

LP02
LP03
nclad
1.450

1.448
0.83

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Core guidance parameter, V(z)

Mode effective index versus core V number [Vco, Eq. (2)] for the first three
LP0m modes. nclad and neff represent the cladding and the mode effective indices,
respectively. V = 0.83 corresponds to point C in Fig. 3.

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 Figure 40
1.454

LP11
1.452
LP12

Effective index, neff

LP13
nclad
1.450

1.448
2.405

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Core guidance parameter, V(z)

Mode effective index versus core V number [Vco, Eq. (2)] for the first three
LP1m modes. nclad and neff represent the cladding and the mode effective indices,
respectively. V = 2.405 corresponds to the LP11 cutoff.

nonadiabatic conversion into higher-order modes. Smaller taper angles and

relatively longer taper transition lengths are needed for the adiabatic conversion
of LP11.
The dashed blue curve in Fig. 41 also represents the exponential taper profile
used in this set of experiments. The taper lies in the lossy region of the

Figure 41

10
-2 Lossy
Lossless
LPLP
01 01
Lossy
Lossless
Core taper angle, Ω

LPLP
11 11
-3
10

Taper profile
-4
10
0.0 0.2 0.4 0.6 0.8 1.0
Inverse taper ratio, ρ (z)/ρ0

Adiabatic profiles for LP01 and LP11 modes obtained from Eq. (33) and Figs.
39 and 40. The dashed blue curve represents the profile of the transition region.
Since between inverse taper ratios r共z兲 / r0 = 0.65 and r共z兲 / r0 = 0.8 it is above
the LP11 adiabatic curve, the LP11 mode will not experience adiabatic conversion
for r共z兲 / r0 ⬍ 0.8 and will be converted in LP1m 共m ⬎ 1兲 modes.

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adiabatic curve for the LP11 mode for inverse tapering ratios between 0.65 and
0.8, meaning that the LP11 mode is coupled into LP1m modes m ⬎ 1兲. This
seems in good agreement with the results of Fig. 37: at r ⬍ 50 µm Fig. 41 predicts
conversion of the LP11 mode into higher-order cladding modes that interfere
and produce oscillations at ␭ ⬍ 1250 nm. Figure 41 can also be used to design an
optimal adiabatic taper profile: the LP01 curve provides a solution for optimal
adiabatic tapers (less than a few millimeters) that convert all modes apart
from the LP01 into unguided higher-order modes.
Finally, as was shown in Subsections 3.3a and 3.3b, embedding is necessary
for long-term device reliability. In addition to protection, embedding provides
mode filters with a high-refractive-index surrounding medium; because of
this, the diameter of the uniform waist region necessary to strip the higher modes
off is larger than that used in the experiments in air, allowing for increased
device robustness.

5. Conclusions

In summary, nanowires manufactured from optical fibers have been shown to

provide outstanding optical and mechanical properties. Among the
manufacturing methods, the flame-brushing and modified flame-brushing
techniques provide optical fiber microwires and nanowires with minimum
optical losses and maximal robustness. Ultimate strength similar to that achieved
in carbon nanotubes has been shown. The issue of device degradation over
time and its solution by embedding has been proposed and demonstrated. Three
groups of optical applications have been explained: (1) applications based
on evanescent fields, which take advantage of the power propagating outside the
physical boundary of the wire and include high-Q knot, loop, and coil
resonators, particle manipulation, and sensors; (2) applications exploiting the
confinement properties, which include supercontinuum generators and
particle trapping (Subsection 4.5); and (3) applications exploiting transition
regions to convert and filter modes.
Although still in its early development, the use of nanowires for optical
devices opens the way to a host of new optical applications for communications,
sensing, lasers, biology, and chemistry.

Acknowledgments

The authors acknowledge financial support from the Engineering and Physical
Sciences Research Council (UK, EPSRC). G. Brambilla gratefully
acknowledges the Royal Society (London, UK) for his research fellowship.

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