Microstructured optical fiber devices

B. J. Eggleton*, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale

Optical Fiber Solutions, Lucent Technologies, Murray Hill, NJ 07974
*Also with Specialty Fiber Devices, Optical Fiber Solutions, Lucent Technologies, Somerset, NJ 08873
*Phone: 908 582 3087, Fax: 908 582 6055, Email: egg@lucent.com

Abstract: We present several applications of microstructured optical fibers

and study their modal characteristics by using Bragg gratings inscribed into
photosensitive core regions designed into the air-silica microstructure. The
unique characteristics revealed in these studies enable a number of
functionalities including tunability and enhanced nonlinearity that provide a
platform for fiber device applications. We discuss experimental and
numerical tools that allow characterization of the modes of the fibers.
2001 Optical Society of America
OCIS code: (060.0060) Fiber optics and optical communications; (060.2270) Fiber
characterization; (230.3990) Microstructure devices; (160.5470) Polymers.

References and Links

1. P.V. Kaiser and H.W. Astle, "Low-loss single-material fibers made from pure fused silica," The Bell
System Technical Journal, 53, 1021-1039 (1974),
2. J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, "Photonic crystal fibers: A new class of optical
waveguides," Optical Fiber Technology, 5, 305-330, (1999).
3. J.C. Knight, T.A. Birks, P.S.J. Russell, and D.M. Atkin, "All-silica single mode optical fiber with photonic
crystal cladding," Opt. Lett. 21, 1547-1549, (1996).
4. J.C. Knight, T.A. Birks, R.F. Cregan, P.S.J. Russell, and J.P. Sandro, "Photonic crystals as optical fibers-
physics and applications," Optical Materials, 11, 143-151, (1999).
5. R.S. Windeler, J.L. Wagener, and D.J. DiGiovanni, "Silica-air microstructured fibers: Properties and
applications," Optical Fiber Communications conference, San Diego (1999).
6. T.A. Birks, J.C. Knight, and P.S.J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22,
961-963, (1997).
7. R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P. S. J. Russell, P.J. Roberts, and D.C. Allan, "Single-
mode photonic bandgap guidance of light in air," Science, 285, 1537-1539, (1999).
8. T.M. Monro, W. Belardi, K. Furusawa, J.C. Baggett, N.G.R. Broderick, and D.J. Richardson, "Sensing
with microstructured optical fibres," Meas. Sci. and Tech. 12, 854-858, (2001).
9. R. Holzwarth, M. Zimmermann, Th. Udem, T.W. Hansch, P. Russbuldt, K. Gabel, R. Poprawe, J.C.
Knight, W.J. Wadsworth, and P.S.J. Russell, "White-light frequency comb generation with a diode-
pumped Cr:LiSAF laser," Opt. Lett. 17, 1376-1378, (2001).
10. T.A. Birks, D. Mogilevstev, J.C. Knight, and P.S.J. Russell, "Dispersion Compensation Using Single-
Material Fibers," IEEE Phot. Tech. Lett, 11, 674-676, (1999).
11. J.K. Ranka, R.S. Windeler, and A.J. Stentz, "Optical properties of high-delta air-silica microstructure
optical fibers," Opt. Lett. 25, 796-798, (2000).
12. T.M. Monro, D.J. Richardson, N.G.R. Broderick, and P.J. Bennet, "Holey optical fibers: An efficient
modal model," J. Lightwave Tech.. 17, 1093-1102, (1999).
13. J.C. Knight, T.A. Birks, R.F. Cregan, P.S.J. Russell, and J.P. Sandro, "Large mode area photonic crystals,"
Opt. Lett. 25, 25-27, (1998).
14. T. Erdogan, "Fiber Grating Spectra," J. Lightwave Tech. 155, 1277-1294, (1997).
15. R. Kashyap, Fiber Bragg gratings. 1st ed. ed. 1999: Academic Press.
16. B.J. Eggleton, P.S. Westbrook, C.A. White, C. Kerbage, R.S. Windeler, and G.L. Burdge, "Cladding
mode resonances in air-silica microstructure fiber," J. Lightwave Tech., 18, 1084-1100, (2000).
17. B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spalter, and T.A. Strasser, "Grating resonances in air-
silica microstructured optical fibers," Opt. Lett. 24, 1460-1462, (1999).
18. C. Kerbage, B.J. Eggleton, P.S. Westbrook, and R.S. Windeler, "Experimental and scalar beam
propagation analysis of an air-silica microstructure fiber," Opt. Express, 7, 113-123, (2000),
http://www.opticsexpress.org/oearchive/source/22997.htm
19. P.S. Westbrook, B.J. Eggleton, R.S. Windeler, A. Hale, T.A. Strasser, and G.L. Burdge, "Cladding-Mode
Resonances in Hybrid Polymer-Silica Microstrucutred Optical Fiber Gratings," IEEE Phot. Tech. Lett. 12,
495-497, (2000).

#37441 - $15.00 US Received October 31, 2001; Revised December 05, 2001
(C) 2001 OSA 17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 698
 20. J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosin ski, X. Liu, and C. Xu, "Adiabatic Coupling in
Tapered Air-Silica Microstructured Optical Fiber," IEEE Phot. Tech. Lett. 13, 52-54, (2001).
21. X. Liu, C. Xu, W.H. Knox, J.K. Chandalia, B.J. Eggleton, S.G. Kosinski, and R.S. Windeler, "Soliton
self-frequency shift in a tapered air-silica microstructured fiber," Opt. Lett. 26, 358-360, (2000).
22. C. Kerbage, A. Hale, A. Yablon, R.S. Windeler, and B.J. Eggleton, "Integrated all-fiber variable
attenuator based on hybrid microstructure fiber," App. Phys. Lett. 79, 3191-3193, (2001).
23. M.J. Steel, T.P. White, C. Martijn de Sterke, R.C. McPhedran, L.C. Botten, “Symmetry an degeneracy in
microstructured optical fibers,” Opt. Lett. 26, 488-490, (2001).

1. Introduction

Microstructured optical fibers (MOFs) [1] are typically all silica optical fibers in which air-
holes are introduced in the cladding region and extend in the axial direction of the fiber [1-6].
These fibers, which have been known since the earliest days of silica light guide research [1],
come in a variety of different shapes, sizes, and distributions of air-holes. Recent interest in
such fibers has been generated through potential applications in optical communications [1-8],
optical fiber based sensing [8], frequency metrology and optical coherence tomography [9].
The earliest work reported by Kaiser et al, and shown in Figure 1(a), demonstrated low loss
single material fibers made entirely from silica. A number of years later Russell and
coworkers demonstrated the so-called photonic crystal MOF, shown in Fig. 1(b) [6]. These
fibers incorporate a periodic array of air-holes in the cladding region and guide light through
modified total internal reflection [4,8]. This advance generated enormous interest in this new
class of MOFs leading to the first demonstration of a true photonic bandgap MOF by Cregan
et al. in 1999 [7]. These fibers, shown in Fig. 1 (c), can guide light in a central air-core region
through coherent Bragg scattering off the periodic array of air-holes [2]. MOFs that
incorporate an array of air-holes surrounding a very small silica core, as shown in Fig. 1 (d),
can provide unique dispersion [10] and nonlinear characteristics that have been used to
demonstrate a number of novel effects, including the generation of a broadband
supercontinuum and a zero GVD as low as 765 nm [11].

(a) (b) (c) (d)

(e)
Devices

βcore
polymer

Hybrid MOF Grating Based Tapered MOF

Tunable Filter Device
Fig. 1. Historical outline of different MOFs (a) Air-silica MOF, Kaiser et al. (1974) (b)
Photonic crystal MOF, Russell et al. (1996), (c) Photonic bandgap MOF, Cregan et al. (1999),

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 and (d) Dispersion control MOF, Ranka et al. (1999). (e) Possible device applications based on
MOFs.

Most research activities in this field have been concerned with the guidance properties of
the fundamental mode localized in the core region of these fibers, for example, bend loss,
cutoff wavelength [6], mode field diameter [12], and dispersion [10,12] and have focused on
potential applications requiring long lengths of fiber where, for example, the fiber provides
unique dispersion characteristics [11], reduced nonlinearity [13], or broad single-mode
spectral ranges [6].
Another important application that we explore in this paper is the use of MOFs for
optical fiber devices. In these applications the microstructured cladding region is designed to
manipulate the propagation of core and leaky cladding modes. The core region can
incorporate a doped region allowing for the inscription of grating structures and the air-holes
can allow for the infusion of active materials yielding novel tunable hybrid waveguide
devices. The resulting hybrid waveguide can be exploited in the design of optical devices,
such as grating-based filters, tunable optical filters, tapered fiber devices and variable optical
attenuators. We present a detailed modal characterization of different MOFs with limiting
characteristics (e.g., air-fill fraction, ratio of propagation wavelength to air-hole diameter and
air-hole distribution). By inspection of the transmission spectrum of the fiber Bragg grating
written into the core of these fibers, we obtain a “mapping” of the different modes of the fiber.
The spectra of these gratings are analyzed and explained qualitatively and compared to
simulations using beam-propagation method (BPM). We discuss the implications of these
results in more detail for the design of grating based devices and describe a range of
applications of MOFs.
The paper is structured as follows: In Section 2, we present a brief background on the
propagation of core and cladding modes in optical fibers and how they manifest in optical
fiber grating devices. We then briefly describe the BPM for computation of waveguide
properties. In section 3, we present characterization of grating spectra and near-field mode
distributions for different MOFs. The transmission spectra are analyzed and compared to
numerical simulations using BPM. In section 4, we demonstrate a number of device
applications of MOFs including applications to fiber Bragg gratings with reduced cladding
mode loss, tunable resonant filters, variable optical attenuators and nonlinear devices.

2. Background

Fig. 2 shows several MOFs with different geometries of the air-holes. Each fiber incorporates
a germanium-doped core to allow for the inscription of periodic waveguide gratings. In order
to fully characterize both core and higher order modes, we can examine the transmission
spectra of gratings written in the core of the MOFs. Fiber Bragg gratings (FBG) and long
period gratings (LPG) written into the core of such fibers facilitate phase matching to counter
and co-propagating modes, respectively [14]. When excited, these modes manifest themselves
as resonant loss in the corresponding transmission spectrum thus providing a modal spectrum
of the waveguide, revealing effective indices (propagation constants) and mode profiles. As
we show below these characteristics can be compared to simulations using BPM.

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 (a) (b) (c) (d)

Fig. 2. SEMS and photographs of respective MOF (a) high delta MOF (b) photonic crystal
MOF; (c) grapefruit MOF; (d) air-clad MOF.

2.1 Fiber gratings and cladding mode resonances

The transmission spectra of a FBG and LPG written in the core of a conventional fiber are
shown in Fig. 3(a)-(b). Also shown in Fig. 3, is a schematic illustrating grating induced
coupling from a guided core mode to higher order modes, which are confined by the glass air
interface; these are referred to as cladding modes. The sharp resonant loss on the short
wavelength side of the Bragg resonance in Fig. 3(a) is due to coupling to the counter-
propagating cladding modes. Similarly, the coupling to the co-propagating cladding modes by
the LPG manifests as peak loss at a certain wavelength in the transmission of the fiber.

Cladding mode Cladding mode

core
FBG LPG
Core mode Core mode

0.0 0
-0.5 -4
Transmission (dB)

Transmission (dB)

-1.0
-8
-1.5
-12
-2.0 ∆λi
-2.5 -16
-3.0 λi -20 (b)
(a)
-3.5
-24
-4.0
1525 1530 1535 1540 1545 1550 1555 1500 1520 1540 1560 1580 1600
Wavelength (nm) Wavelength (nm)

Fig.3. (a) Typical transmission spectrum of FBG in standard fibers exhibiting short wavelength
loss. Each dip in the transmission spectrum is associated with grating facilitated phase
matching to a counter-propagating cladding mode. The inset shows a schematic of Bragg
grating in the core of a conventional optical fiber. Fig. 3. (b) The corresponding transmission
spectrum of LPG.

A simple description of the core and cladding modes can be obtained through
inspection of the transmission spectrum of a FBG written into a photosensitive core of a
MOF. The effective index of the fundamental mode localized in the core region (n co) can be
determined using the Bragg condition λB=2n coΛFBG [15], where ΛFBG is the period of the FBG.
The effective indices of the cladding modes (n clad,i ) can then be determined using the phase
matching condition for a cladding resonance: βclad,i +β01 =2π/ΛFBG , where βclad,i is the
propagation constant of the ith cladding mode propagating in the opposite direction to the

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fundamental LP01 with propagation constant β01 . The phase matching condition is then given
by:

λ FBG, i = ( nco + nclad ,i ) Λ FBG (1)

The effective indices obtained from inspection of the FBG spectrum can be used in the design
of LPGs, which couple the fundamental core mode to co-propagating cladding modes. For the
co-propagating grating couplers the phase matching condition can be written as,
λ LPG,i =( nco −nclad ,i ) Λ LPG (2)

where λLPG,i is the resonant coupling wavelength and ΛLPG is the period of the LPG.
Neglecting chromatic dispersion of the core and cladding modes, the LPG resonance
wavelength is then proportional to the wavelength interval between the Bragg resonance and
the ith cladding resonance in the FBG [16]:

λ LPG, i ∆λ i
= (3)
Λ LPG Λ FBG

where ∆λi =λB-λclad,i is the difference between the fundamental Bragg resonance (given by the
Bragg condition) and the wavelength of the ith cladding mode resonance. Predicting the peak
intensities of the experimental grating spectra, however requires detailed knowledge of the
modal distributions and use of coupled mode theory.
For uniform gratings (constant index modulation and grating period), which we consider
in this paper, the transmission coefficient at the peak of the nth resonance is given by:

Ti = 1 − tanh
2
(κ i L) (4)

where L is the length of the grating [15] and κi is the coupling coefficient between the core
and cladding mode i [15]. The spectra consist of the contribution of each mode at wavelengths
determined by the modal composition, multiplied by a grating dependent shape factor.
2.2 Beam propagation method applied to MOF
The BPM provides a simple intuitive method of determining the modal spectrum and modal
profiles for complex waveguides. The beam-propagation correlation method has been used
extensively in the study of complex waveguides and is particularly well suited to computing
mode evolution in waveguides that vary in the longitudinal direction and in geometries where
leaky modes are important [16]. This latter point is of particular interest in this work where
we consider the propagation of leaky modes in the claddings of different MOFs. Briefly, the
BPM correlation method, summarized schematically in Fig. 4, propagates a launched field
profile within a waveguide. The propagation of the field along the z direction through a
transverse guide can be written as:
− iβ i z
E ( x, y, z ) = ∑ α i Ei (x , y )e (5)
i
where for each mode i, Ei (x,y) is the transverse modal profile, αi is the amplitude strength of
each mode, and βi =2kni is the wave vector in the propagation direction z.
The correlation function computes the initial launched profile and the profile at each
z value given by:

P( z ) = ∫ E (x, y ,0)E ( x, y, z ) dx dy
*
(6)

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 (a) (b)

Launch
Y

E(x,y,0) E(x,y,z)
Z

X
FFT
⇒
P(z) |α|

Position Effective index

Fig. 4. Launch mode field along MOF structure (a) the correlation function and (b) its Fourier
transform revealing the effective indices of the modes.

The BPM computes this function, E(x,y,z), for all z given only the initial starting field
E(x,y,0) and the refractive index profile of the waveguide

E ( x, y, 0) = ∆n( x, y )Ecore ( x, y ) (7)

( )
where ∆n x , y is the grating index profile [16].
This propagation is accomplished without a priori knowledge of the modal
decomposition, however; the propagation contains all the information about the modes. Here
the strengths αi within the launched profile are identical to the coupling constants (κi )
necessary for a coupled mode analysis.

λ
α i = ∫ Ei (x , y )∆n( x , y )E core ( x, y )dxdy ≡  κ i (8)
π 
where the relative intensities of the Fourier transformed peaks determine the squares of the
coupling coefficients.

3. Modal characterization

By examining the transmission spectrum of a FBG written into an MOF, we expect to

gain insight into the guidance properties of the core and cladding modes and to correlate these
properties with calculations of the cladding mode fields using BPM. The experimental setup
is shown in Fig. 5. A 1550 nm tunable source is launched into the fiber with a FBG written in
the core, using a 10× microscope objective and a beam-splitter. When the wavelength of the
incident light satisfies the Bragg conditions, different counter-propagating cladding modes,
are excited; facilitated by phase matching provided by the FBGs. Light reflected off the FBG
is imaged in the near field on an IR camera using a 40× microscope objective. When
capturing images of the reflected mode-field the far end of the fiber is placed in index-
matching gel so as to minimize back reflections.

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 0

Tunable laser 1.4 -1.6µm -5

Loss (dB)
Screen -10

-15

Screen:Near -20

field image of -25

1549 1550 1551 1552 1553 1554

mode Wavelength(nm)
×10
Bragg
×40 grating

IRCamera Beam Phase matching condition

splitter
βcore + βclad,i =2π/Λ

Fig. 5. Experimental setup used to characterize near field images for respective air-silica
MOFs. Bragg grating selectively excited counter-propagating “cladding modes” which are
imaged in the near field on the VIDECON camera.

3.1 Photonic crystal fiber

Fig. 6 shows a cross section of the “photonic crystal MOF” and the transmission
spectrum of a FBG written in its core. The fiber was designed with a sufficiently small
photosensitive germanium-doped core such that it would appear as a small perturbation on the
guided modes of the fiber but contain sufficient germanium to write a grating. The core radius
is ~1µm and ∆=(n core-n clad )/ncore~0.5%, where ncore and nclad are the refractive indices of the
germanium-doped core and silica cladding, respectively. The core is surrounded by a
hexagonal array of holes in a silica matrix with an air-hole diameter d~2µm and spacing
Λ~10µm extending to a radius ~60µm, corresponding to 7 layers. This MOF guides by total
internal reflection and satisfies the criterion provide in Ref. [6] for being endlessly single
mode. In particular the fiber should support only one single bound mode in the 1.5µm
wavelength regime.
Effective index
1.42 1.43 1.44 1.45
1.0 0.20

0.8
03 0.15 Exp.
Transmission

0.6 04 02 01
0.10
|α|
Relative Power

1.0
0.4 0.8 LP03
0.6 LP04
0.4
0.2 0.05
0.2 0.0
0.0 0.4 0.8
z (cm) Sim..
0.0 0.00
1540 1545 1550 1555 LP03 LP04
Wavelength (nm)
(a) (b) (c)

Fig. 6. (a) Measured transmission spectrum of FBG written in photonic crystal MOF (solid
line), calculated modal spectrum (dashed line). Light form the near field images reflected off
FBG when the tunable laser wavelength is tuned to: (ab 1549.196nm, corresponding to the
resonance labeled “LP 03”; and (c) 1546.990nm corresponding to the resonance labeled “LP 04 ”.

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 The solid line in Fig. 6 (a) is the measured transmission spectrum of the FBG. The
dashed line is the computed modal spectrum. The right vertical axis is the mode overlap,
defined in Eq.8, and calculated using BPM assuming symmteric launch conditions. Note that
a number of discrete resonances appear in the transmission spectrum of the FBG indicating
excitation of higher order modes propagating in the PCF, apparently contradicting the single-
modedness of the PCF. In fact, these higher order modes correspond to leaky cladding modes
that are quickly dissipated upon propagation. The cladding modes of this PCF, have effective
indices below that of silica, and are stripped off by the high index outer silica region and that
there is negligible coherent feedback from the outer silica air interface [16,17]. The measured
and calculated mode profiles for the lower order cladding modes LP03 and LP 04 are shown in
Fig. 6(b) and (c) respectively. The shape of these modes reveals the hexagonal symmetry of
the lattice and that most of the energy is confined in the inner few rings or holes. Simulations
confirm that these modes have a relatively high propagation loss and complex propagation
constants [17]. The energy of the modes tunnels between the air-holes into the cladding and is
revealed as loss (~2 dB/cm) as depicted in the simulations (see inset in Fig. 6), these are thus
leaky modes.
3.2 “Grapefruit” MOF
Fig. 7(a) shows the experimental transmission spectrum and the corresponding mode images
(bottom) of a MOF (“grapefruit” MOF) with six large air-holes surrounding an inner cladding
region of ~30 µm in diameter. A Bragg grating with a period of 0.5 µm was written in the
germanium core of diameter 8 µm and ∆=((n 1 -n 2 )/n1 ) ~ 0.35%, where n1 and n2 are the
refractive indices of the germanium core and silica cladding, respectively. The first peak on
the right side of the transmission spectrum, labeled A in Fig. 7, corresponds to excitation of
the backward propagating core mode. The other resonances on the shorter wavelength side of
the main peak correspond to coupling to higher order cladding modes. Only the four lowest
order-cladding modes (labeled B, C, D and E) in the transmission spectrum of the MOF are
surrounded by the holes and their propagation is governed by the total internal reflection at
the interface of the cladding-holes. Higher order mode (F) spreads throughout the fiber
through the interstitial region in the cladding between the holes [18]. Also note that the
cladding mode resonances are spaced farther apart in wavelength due to the reduced inner
effective cladding of the MOF. As the inner cladding diameter decreases the cladding mode
spacing increases. We return to this point further below.

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 F E D C B A

60mm

Effective index
1.421 1.428 1.435 1.442

Transmission (a.u.) Relative Power (a.u.)

(a) D
C B A
E
F 125mm

F
Simulated structure
E

(b)
D
A 125mm
C B

1536 1540 1544 1548 1552 1556

Wavelength (nm) Experimental structure
F E D C B A
F
60µm

Fig. 7. (a) Part of transmission spectrum of FBG written into the core of the grapefruit MOF
(solid line) with the corresponding observed near field images of light reflected off FBG when
the laser was tuned to (A) 1553.96nm (the LP 01 mode); (B) 1552.39nm (LP 02 ); (C) 1550.84nm
(LP 03) mode; (D) 1547.82nm (LP 04 mode); (E) 1547.36nm (LP 05 mode); (F) 1535.82nm, and
(b) calculated modal spectrum of the grapefruit MOF (dashed line) and its corresponding
simulated modes.

Fig. 7 (b) shows the simulated mode spectrum and the simulated mode profiles using
BPM (top). The simulated plot reveals the values of the relative power, which is related to the
overlap ratio between the core and each of the excited modes, versus wavelength. The profile
and the distribution of the energy of the modes are in good agreement with experiments and
are clearly affected by the presence of the holes. The circular shapes of the modes of a
conventional fiber are lost in this MOF. Instead the images exhibit symmetry of the air-hole
geometry. The optical devices described further in this paper exploit lower order cladding
modes that are predominantly confined to the inner cladding region.

4. Applications
The unique characteristics revealed in the above mentioned studies enable a number of
functionalities including tunability and enhanced nonlinearity that provide a platform for fiber
device applications.
4.1 Reduction of cladding mode loss in optical fiber Bragg gratings.
Cladding mode resonances are exploited in the design of FBG [16] and LPG [17] devices. In
the case of LPGs these cladding modes are exploited in the design of band-rejection filters for
flattening of optical amplifiers. In the case of a FBG the cladding mode loss is often regarded
as a nuisance where the short wavelength loss reduces the usable bandwidth. As described
above the microstructured cladding region manipulates cladding mode propagation. This

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manifests in the spectral characteristics of optical fiber gratings, as is evident in Fig. 7. When
the microstructured cladding region creates an inner effective cladding the fiber resembles a
fiber with a reduced cladding diameter. We show that in such fiber the cladding mode loss can
be reduced significantly.

(a) (b) 1.0

0.8

Transmission
0.6

0.4
20µm
0.2
(c)
0.0
1490 1495 1500 1505
Wavelength (nm)
Ge

Fig. 8. (a) Transmission spectrum of FBG written into the core of the MOF (b) photo of the
inner region and (c) schematic diagram

Fig. 8(a) shows a photo and schematic of a high-delta microstructured optical fiber
that was designed to suppress cladding mode loss in a FBG MOF. This fiber incorporates five
air-holes that are placed very close to a Germanium doped core. A length of the fiber was first
loaded with deuterium to enhance the photosensitivity of the germanium region that and then
was exposed using 242nm through a conventional phase mask with a period of
Λmask=1.075µm where ΛFBG =Λmask/2. This produced a peak index modulation of ∆n~10-5 . The
transmission spectrum of the FBG is shown in Fig. 8(b) where the Bragg resonance is at λB=
1504 nm. The effective index of the core mode is then determined to be n eff ~1.405. Note the
absence of any significant cladding mode loss for wavelengths shorter than the Bragg
resonance. Because of the small effective inner cladding diameter of this fiber, the cladding
modes are offset significantly from the Bragg resonance.
The computed modal spectrum using BPM, shows a core mode with an effective
index of n eff~1.405, in good agreement with the experimental measurements described above,
and indicates a second mode of the inner cladding region with an effective index of n eff~1.25.
Indeed the difference between the lowest modes of the inner cladding region is ∆~10%, and is
much larger than the core-cladding index step in standard fiber; it exhibits similar modal
properties to a step-index fiber with ∆~30%. The corresponding cladding mode spectrum in
this fiber is thus offset from the Bragg resonance by as much as 80nm, consistent with the
measured grating spectra shown above. These cladding modes (with n eff>n core) have negligible
spatial overlap with the grating in the central core region and thus are not excited by
interaction of core guided light with the grating.
4.2 Hybrid tunable optical fiber waveguides
Active materials, such as polymers, can be infused into the relatively large air-holes of the
grapefruit MOF. Fig. 9(a) shows one end of the fiber immersed in a reservoir of material and
sealed on the other end where vacuum is applied. The material then can be introduced into
the air-holes of the fiber as shown in Fig. 9(b). In our case, the material is an acrylate
monomer mixture (viscosity ~30 centipoise), which was infused into the air-holes at a rate of
0.03 cm/sec and was UV-cured for about 15 minutes to form a polymer with a desired

#37441 - $15.00 US Received October 31, 2001; Revised December 05, 2001
(C) 2001 OSA 17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 707
refractive index. The refractive index of the polymer (n p ) has higher temperature dependence
than that of glass (n silica) sketched in Fig. 9(c). Since the fundamental mode is not affected by
the presence of the air-holes, mode guidance in the cladding can be strongly affected simply
by changing the hybrid waveguide temperature by 10-50°C [19].

(a) to (b) Air- (c) n pol

filling vacuum holes
reservoir line n
n silica

Material T

Fig. 9. (a) Schemaitc drawing of material (polymer) infused in the air-holes of the MOF. (b)
Picture showing material in the air-holes of the fiber. (c) Refractive indices of the polymer and
silica dependence on temperature.

4.3 Tunable grating filters

When polymer is infused into an MOF with a LPG written in the core the cladding resonances
may be wavelength shifted and also suppressed entirely through temperature tuning. Fig. 9(a)
shows a cross section of such a fiber with the infused polymer and silica regions as well as a
conventional Ge -doped core.

0
Transmission (dB)

o
25 C o
35 C
o
40 C
-3
o
(a) (b) 60 C
-6 o
80 C
o
100 C
o
120 C
polymer

polymer
silica

silica
silica

1400 1450 1500 1550 1600

Wavelength (nm)

Fig. 10. (a) Photo of hybrid polymer air-silica microstructured optical fiber and a schematic
diagram (b) Spectrum of LPG in hybrid polymer-silica fiber at different temperatures

Fig. 10(b) shows the transmission spectrum of an LPG written into the hybrid MOF.
The LPG is first UV written in the waveguide, then the polymer is infused into the air regions
and UV cured to form the hybrid waveguide at the grating. The LPG resonance shows over
100nm of tunability, 10 times more than in a standard LPG. The tunability results from both
the high temperature dependence of the polymer refractive index and the geometry of the
microstructure.
After polymer infusion into a LP G at room temperature, the cladding resonances have
been completely suppressed, indicating that the waveguide defined by the polymer cladding
interface has become very lossy. The polymer refractive index decreases with increased
temperature, while that of silica increases. Moreover, the polymer refractive index varies
about 10 times as fast as that of silica. Therefore, as the temperature increases, and the

#37441 - $15.00 US Received October 31, 2001; Revised December 05, 2001
(C) 2001 OSA 17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 708
polymer index drops below that of silica, the waveguide defined by the inner polymer-silica
interface becomes guiding. The large tuning range is due to the geometry of the
microstructure because it creates a small inner cladding whose cladding modes have relatively
large wavelength spacing. Because the phase shift upon total internal reflection is
proportional to the spacing, the tuning range is enhanced.
4.4 Tapered MOF
Another interesting characteristic of MOFs is that they allow for both the group velocity
dispersion and the mode field diameter to be controlled. This can be exploited in a range of
different applications, including compensating chromatic dispersion [11] and allows for fiber
designs with very small effective area for enhanced nonlinear interactions [12]. Although
these fibers exhibit interesting and attractive properties, they have several practical
difficulties, such as coupling light into the small core. Here, we demonstrate efficient
coupling into an MOF, which has been tapered to very small diameter sizes and exhibits
similar dispersion characteristics to previous work [20]. Furthermore, because of the
supporting cladding region, the tapered MOF is mechanically stronger, and more robust than
tapered conventional fibers that have demonstrated similar nonlinear effects [11], and also
exhibit negligible sensitivity to external index, potentially allowing for packaging.
Fig. 11 shows a schematic of the tapered MOF device and the evolution of the
computed and observed fundamental intensity mode profile of the MOF. The un-tapered
grapefruit fiber is well matched to standard single-mode fiber, ensuring low loss due to
splicing (< 0.1 dB) [20,21].

(a)
Mode profile observed 16mm
16mm

12mm
125mm

SMF
SMF
Mode profile
profile calculated
calculated using
10 µm Mode
using Beam
Beam Prop simulations
Prop simulations

(b)

22cm
Fig. 11. (a) Schematic of the tapered MOF to 10µm with calculated and observed cross-
sectional intensity plots of the mode field at different points along the taper. (b) Packaged
tapered MOF device.

The fiber is tapered by heating and stretching in a flame to reduce the outer diameter while
maintaining the same cross-sectional profile. The flame temperature is chosen such that the
air holes do not collapse, ensuring that the fiber cross section does not change throughout the
taper. The MOF can be tapered down to less than 10 µm in outer-diameter with a waist
length of 20 cm. Tapering of the MOF is adiabatic so that the fundamental mode evolves into
the fundamental mode of the central silica region with low loss (<0.1dB), where it is confined
by the ring of air-holes. Because the mode is confined within the air-ring, the total fiber
diameter can be maintained at an acceptable level, which increases robustness and allows for

#37441 - $15.00 US Received October 31, 2001; Revised December 05, 2001
(C) 2001 OSA 17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 709
packaging as shown in Fig. 11(b). In addition, the fundamental mode is guided in the
germanium-doped core after adiabatic expansion, allowing for splicing to standard fibers.
4.5 Enhanced nonlinear interactions
Tapered MOF provide an ideal structure for demonstrations of dramatic nonlinear effects.
Laser pulses at 1.3 µm generated by a femtosecond Ti-sapphire pumped optical parametric
oscillator were free-space coupled into the un-tapered portion of the MOF and then
propagated through the taper. Tunable self-frequency shifting solitons were generated over
the important communications windows from 1.3µm to 1.65 µm with input pulse at 1.3µm
[21]. As the light propagates through the MOF the light is continually shifted towards the red
due to intrapulse Raman scattering, which transfers the energy of the high frequency part of
the pulse spectrum to the low frequency part, we observe 60% of the input photons being self-
frequency shifted. The soliton wavelength can be tuned from 1.2 to 1.8 µm by adjusting the
input power. These dramatic results are possible because the fiber exhibits a large anomalous
dispersion over a wide wavelength range as shown in Fig. 12, which ensure that the pulse is
stable against modulational instability at high peak intensities. These dramatic nonlinear
effects confirm the adiabaticity and low loss of the taper.

(a) 100
75
50 Dispersion
25 (ps/ nm- Km)
0
130 110 90 70 50 30 10

16
12
8 Enhanced
4 Intensity
0
130 110 90 70 50 30 10

Diameter of Taper (mm)

(b)

Diameter=2mm

Diameter=3mm

Fig. 12 (a) Dispersion and intensity plots along the taper calculated at wavelength 1.5 µm.
(b) Group velocity dispersion as a function of wavelength for different diameters in the waist.

4.6 Variable optical attenuator microstructure fiber device

In this section we present a tunable all-fiber optical device based on an MOF that exploits the
temperature dependence of the refractive index of a polymer incorporated into the air-holes of
the MOF, which has been tapered. The fiber design enables efficient interaction between

#37441 - $15.00 US Received October 31, 2001; Revised December 05, 2001
(C) 2001 OSA 17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 710
tunable materials with the propagating mode field thus permitting a range of different
functionalities [22]. Here we demonstrate an electrically tunable attenuator device (loss-
filter), which is fully integrated, packaged and spliced with about 30 dB dynamic range,
insertion loss of less than 0.8 dB, and minimal polarization dependence.
Fig. 13 shows the schematic of the MOF fiber used in the modulation device. As
mentioned before, the lowest order mode of the fiber is guided in the germanium doped core
of the fiber by total internal reflection at the core-cladding interface and is unaffected by the
presence of the air voids in the cladding.

polymer Air-holes Mode field polymer

(a) (b)

125 µm core taper 30µm

waist

Fig. 13 (a) Schematic diagram of the all-fiber variable attenuator device based on tapered MOF
and (b) mode profile evolution along the fiber.

In order to achieve an efficient field interaction between the core mode and the air
voids, the fiber needs to be adiabatically tapered. Again, the fiber is heated and stretched such
that the fiber diameter is decreased while the cross-sectional profile remains approximately
the same. As shown in Fig. 13, by tapering the fiber down to small diameter sizes, the core
diameter decreases and becomes extremely small. The core mode spreads into the cladding
region where it is confined by the air-hole interface. In the waist of the tapered fiber, the
waveguide resembles a very high-delta fiber (∆~35%) similar to a glass rod surrounded by air.
The large modal field interaction with the surrounding air voids in the waist of the fiber
makes the core mode very sensitive to any index change at the air-holes-cladding interface.
Tunable refractive index materials , such as polymers, with a thermal coefficient that is an
order of magnitude larger than that of silica may be introduced into the holes and will affect
the guiding mechanisms of light in the optical fiber.

air 30 30

(a) (c)
15 15

0 0
30 30

(b) (d)
15 15

0 0
0 15 30 0 15 30 0 15 30 0 15 30 0 15 30 0 15 30
polymer Radius ( µm) Radius ( µm) Radius ( µm) Radius ( µm) Radius (µm) Radius ( µm)
polymer
silica silica
Fig. 14 Index cross-sectional profile in the waist of the fiber (a) with no polymer and with
polymer of index (b) lower (n p =1.42), (c) same as (np =1.44) and (d) higher (np =1.5) than that of
silica. The corresponding calculated intensity cross sectional mode profile are shown at (1) z=0
cm, (2) z=1cm and (3) z=2 cm along the length of the waist.

Fig. 14 shows the cross sectional index profile for different values of polymer
refractive index, and the corresponding calculated mode field cross-sectional intensities,

#37441 - $15.00 US Received October 31, 2001; Revised December 05, 2001
(C) 2001 OSA 17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 711
calculated using BPM. The outer diameter of the waist of the taper is 30 µm with
corresponding inner diameter of ~8 µm. The simulation includes absorption losses in the
polymer of 0.2 dB/mm [19]. Fig. 14(a) shows the device when no polymer infused in the air-
holes and the mode field propagates in the fiber without any change. Fig. 14(b)-(d) show the
corresponding waveguide index profiles and the associated intensity mode profiles for the
case when the air-holes are infused with polymer of varying refractive index. If the index of
the infused polymer is lower than that of silica (n p =1.42) as shown in Fig. 14(b), the mode is
confined in the cladding by total internal reflection, and only a small percentage of the optical
field will be in the material. In this case the mode propagates through the taper with minimal
loss. On the other hand, if the index of the material is close to that of silica, as shown in Fig.
14(c) (n p =1.44) or higher than that of silica (n p =1.5), as in Fig. 14(d), the mode field will
refract into the high index medium, resulting in dramatic loss and attenuation for the
propagating mode, exacerbated by material losses of the polymer and interstitial region
between air-holes, which results in leakage of modes.
refractive index
1.42 1.41 1.40 1.39
0
experiment
simulation
-5
Transmission (dB)

-10

-15

-20

-25

-30
40 60 80 100 120
Temperature (C)

Fig. 15 Transmission (output) of the tapered microstructure fiber plotted in dB scale as a

function of temperature and refractive index at 1550 nm.

Fig. 15 shows both the experimental (dots) and simulated (circular) plot of the
transmission through the fiber as a function of temperature (bottom axis) and corresponding
polymer refractive index (top axis) at 1550 nm. The attenuation of the device varies from –
30dB to –0.8dB with the highest insertion loss occurring at the lowest temperature. The
circular dots in Fig. 14 represent the results of numerical simulations using BPM. The
simulated waveguide, defined by the geometry and the index profile, closely matches the real
cross section and dimensions of the tapered fiber. A Gaussian beam profile centered on the
core axis was launched into the structure. The simulated results are in very good agreement
with the experimental measurements. The measured PDL was less than 0.5 dB, which may be
attributed to the material absorption and irregular boundaries that vary along the tapered fiber,
between the cladding and air-holes. We note that microstructured fiber exhibits 6-fold
rotational symmetry and is expected to exhibit very low birefringence and thus minimal PDL
[23]. The wavelength dependence of the device is about 0.3 dB over a range of 30 nm (1530-
1560 nm). The maximum power consumption is 375mW, corresponding to about 2V of
applied voltage. Even though the fiber is tapered to a small diameter size, the device is robust
and easily packaged with very low loss.

#37441 - $15.00 US Received October 31, 2001; Revised December 05, 2001
(C) 2001 OSA 17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 712
5. Conclusion

In summary, we have presented different device applications of MOFs and we have reviewed
mode propagation in these MOFs . By inspection of the transmission spectra of FBG and LPG
written in the core of the MOFs, we obtain knowledge of the optical properties of higher order
modes that are unique to the geometry of the microstructure fiber. The mode profiles and
guidance properties of these modes are measured experimentally and calculated using BPM.
By gaining insight into the properties of these modes, we demonstrate fiber designs whose
characteristics are unique providing a platform for future photonic devices.

#37441 - $15.00 US Received October 31, 2001; Revised December 05, 2001
(C) 2001 OSA 17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 713