760 Vol. 8, No.

5 / May 2021 / Optica Research Article

Giant terahertz polarization rotation in ultrathin

films of aligned carbon nanotubes
Andrey Baydin,1,4 Natsumi Komatsu,1 Fuyang Tay,1 Saunab Ghosh,1 Takuma Makihara,2
G. Timothy Noe II,1 AND Junichiro Kono1,2,3,5
1
Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA
2
Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
3
Department of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, USA
4
e-mail: baydin@rice.edu
5
e-mail: kono@rice.edu

Received 16 February 2021; revised 16 April 2021; accepted 16 April 2021 (Doc. ID 422826); published 20 May 2021

For easy manipulation of polarization states of light for applications in communications, imaging, and information
processing, an efficient mechanism is desired for rotating light polarization with a minimum interaction length. Here,
we report giant polarization rotations for terahertz (THz) electromagnetic waves in ultrathin (∼45 nm), high-density
films of aligned carbon nanotubes. We observed polarization rotations of up to ∼20◦ and ∼110◦ for transmitted and
reflected THz pulses, respectively. The amount of polarization rotation was a sensitive function of the angle between the
incident THz polarization and the nanotube alignment direction, exhibiting a “magic” angle at which the total rotation
through transmission and reflection becomes exactly 90◦ . Our model quantitatively explains these giant rotations as
a result of extremely anisotropic optical constants, demonstrating that aligned carbon nanotubes promise ultrathin,
broadband, and tunable THz polarization devices. © 2021 Optical Society of America under the terms of the OSA Open Access
Publishing Agreement

https://doi.org/10.1364/OPTICA.422826

1. INTRODUCTION carbon nanotubes (SWCNTs) [21] have enabled new fundamental

Terahertz (THz) technology has made impressive advances in the studies and applications [22–24]. For example, owing to their
last decade, finding a wide variety of applications in spectroscopy, strong anisotropic optical properties in a broad spectral range [23],
imaging, sensing, and communications [1]. However, basic com- such films have been shown to be excellent THz polarizers [21,25–
ponents such as polarizers, wave plates, and filters are still limited 27], which are comparable to commercial wire-grid polarizers in
for THz optics. For example, the widely used THz polarizers are terms of extinction ratio and natural hyperbolic materials in the
wire-grid polarizers [2], which are fragile, inflexible, and non- mid-infrared [28,29]. We observed record-high values of THz
adjustable; they also require precise fabrication procedures and polarization rotation in ultrathin (∼45 nm) films of aligned CNTs:
have low extinction ratios compared to polarizers available in the
up to ∼20◦ through single-pass transmission, and up to ∼110◦
infrared or visible spectral range [3]. Wave plates in the THz range
upon a single reflection. The amount of polarization rotation
are usually limited to bulk crystals [4]. Reports on giant Faraday
and Kerr rotations in thin films and crystals require stringent con- sensitively depended on the polarization angle, θ, of the incident
ditions, like applied magnetic fields and low temperatures [5–8]. THz wave with respect to the nanotube alignment direction. At
To further advance various THz applications, robust material a “magic” angle (θ ∼ 30◦ ), the total rotation due to transmis-
platforms as well as new easily implementable polarization con- sion plus reflection became exactly 90◦ . We developed a detailed
trol schemes are desired. Realizing accessible THz technologies theoretical model that quantitatively explains all experimental
requires developing robust and easily implementable polarization observations. We demonstrate that the observed giant polarization
control for this spectral region. Recent studies have focused on rotations are a result of the extremely anisotropic optical constants
exploiting metamaterials, which enable efficient polarization of the CNT films, and that the magic angle can be tuned by chang-
rotation and conversion of THz waves [9,10] with a large band-
ing the substrate refractive index and the film thickness. These
width [11,12], but their fabrication is typically realized based on
expensive methodologies. easy-to-fabricate, robust, high-temperature resistible, ultrathin,
Here, we utilize carbon nanotubes (CNTs) for THz polariza- broadband, flexible, and tunable THz polarization devices based
tion control. CNTs are one-dimensional materials with unique on macroscopically aligned and densely packed CNTs will address
photonic [13–17] and optoelectronic [18–20] properties. Recent a fundamental challenge in the development of THz optical
advances in fabricating macroscopic films of aligned single-wall devices.

2334-2536/21/050760-05 Journal © 2021 Optical Society of America

Corrected 3 August 2021
 Research Article Vol. 8, No. 5 / May 2021 / Optica 761

2. MATERIALS AND METHODS 1(c) shows a schematic diagram of polarization rotation of THz
We prepared aligned SWCNT films using the controlled pulses upon transmission (pulse 1) and reflection (pulse 2). The
vacuum filtration method [21–24]. Arc discharge CNTs detection polarizer was used to measure the E x and E y compo-
(P2-SWNT) were purchased from Carbon Solutions, Inc. The nents of the THz electric field. The experiments were performed
CNTs were a mixture of semiconducting and metallic species with for various incident polarization angles, θ , as defined in Fig. 1(d).
a ratio of 2:1. Then, a dilute aqueous suspension of SWCNTs
with sodium deoxycholate surfactant (0.01%) was filtered using a 3. RESULTS AND DISCUSSION
vacuum filtration system at a well-controlled speed, which resulted
in a wafer-scale (diameter ∼2 inches) crystalline SWCNT film in Figure 2(a) shows time-domain traces of measured THz electric
which nanotubes are nearly perfectly aligned (with nematic order fields for θ = 0◦ , 30◦ , and 90◦ when both the input and output
parameter S ∼ 1) and maximally packed (∼1 nanotube per cross- polarizers were oriented in the x direction [see E x in Fig. 1(c)].
sectional area of 1 nm2 ). After that, the film was transferred onto The traces are vertically offset for clarity. Both the first and second
a silicon substrate using a wet transfer method [21]. The average pulses are detected for any values of θ , except 30◦ . The second pulse
length and diameter values were 300 nm and 1.4 nm, respectively. is absent only for θ = 30◦ . We refer to this angle as the magic angle.
Polarization-dependent THz time-domain spectroscopy mea- Similar disappearance of the reflection pulse has been observed and
surements were carried out with the standard THz time-domain controlled by deposition of thin metal films [31]. Such a method is
spectroscopy technique in a transmission geometry. THz pulses based on impedance matching, i.e., matching of refractive indices
were generated via optical rectification in Mg-doped stoichiomet- between a sample and a metal film. In the present case, the second
ric LiNbO3 that was pumped by the output beam of an amplified pulse disappears only when the output polarizer is set to the E x
Ti:Sapphire laser system (Clark-MXR, Inc., CPA-2001), produc- orientation. When the output polarizer direction along the E y ori-
ing pulses centered at 775 nm with 1 kHz repetition rate and 150 entation, the second pulse is present except for θ = 0◦ and θ = 90◦ .
fs pulse duration. The THz beam spot diameter was estimated This can be clearly seen in Figs. 2(e) and 2(f ), which show the
to be ∼2 mm. The THz pulses were probed in the time domain E x and E y peak electric fields of the first and second THz pulses,
via electro-optic sampling using a ZnTe crystal. Measurements respectively. Additional time-dependent data are shown in Fig. S1
were performed inside a box purged with dry air to remove excess of Supplement 1.
water vapor. The sample, an aligned SWCNT film on a substrate, Clearly, the magic angle value depends on the anisotropic
was mounted on a rotation stage. When the THz pulse traverses refractive index of the CNT film, which can be further tuned by
the CNT-film/silicon-substrate system, it undergoes multiple doping/gating, and CNT chirality. However, these additional
reflections—first by the back side of the substrate and then by the experiments are beyond the scope of the present paper. Instead, Fig.
substrate–CNT film interface; see Fig. 1(a). This results in a second S2a of Supplement 1 shows the dependence of the magic angle on
pulse in the time domain, which is the focus of this paper; see Fig. the underlying substrate refractive index for a fixed film thickness.
1(b). Only the first pulse is considered for determining the opti- The magic angle decreases as the refractive index of the substrate
cal constants of the sample using traditional THz-time-domain increases. Such dependence can be understood by the fact that by
spectroscopy [30]. changing the refractive index of the substrate, the Fresnel trans-
Moreover, the first pulse has been demonstrated to effectively mission and reflection coefficients at the interface are modified.
determine the degree of alignment of aligned CNT films [21]. Furthermore, the magic angle also changes with the thickness of
Here, we focus on the second pulse because it can be used to deduce the CNT film, although the variation was small for the thickness
information on the reflection properties of the CNT film. Figure range utilized (25–100 nm); see Fig. S2b of Supplement 1.
To understand these experimental data, let us consider the fol-
lowing model: a THz pulse propagates in free space (or a vacuum,
“v”), enters a system consisting of a film (“f”) of thickness df on
a substrate (“s”) of thickness ds , experiences multiple reflections
inside the system (thus producing multiple trailing pulses), and
exits into free space. The complex electric field amplitude of the
first (E 1 ) and second (E 2 ) THz pulses can be written as

E 1 = tf Ps tsv E in , (1)

E 2 = tfr f Ps3 tsv E in , (2)

where E in is the input electric field, tjk = 2n j /(n j + n k ) and

r jk = (n j − n k )/(n j + n k ) are Fresnel transmission and reflection
coefficients, respectively, and P j = exp(ik0 d j n j ) is the propa-
Fig. 1. Experimental setup for showing giant THz polarization rota- gation factor for the j th layer. tf and r f are the transmission and
tion in an aligned CNT film. (a) Schematic of THz transmission and reflection coefficients, respectively, for the CNT film in a thin-film
reflection through the CNT film and substrate; (b) THz waveform in the approximation [30,31],
time domain indicating the existence of a second pulse due to reflections
in the substrate as shown in (a); (c) experimental configuration showing 2n s
wire-grid polarizer, the sample, and the schematic of the polarization tf =
rotation of the propagating THz pulse; (d) polarization angle θ defined as
n s + 1 + Z0 d σ
the angle between the CNT alignment direction and the polarization of n s − 1 − Z0 d σ
the incident THz electric field. rf = , (3)
n s + 1 + Z0 d σ
 Research Article Vol. 8, No. 5 / May 2021 / Optica 762

Fig. 2. Polarization angle dependence of THz signal and optical anisotropy. (a) Waveforms of THz pulses transmitted through the aligned SWCNT film
on a silicon substrate at different angles, θ , between the CNT alignment direction and the incident THz field polarization direction; (b) time-domain wave-
form of the first pulse for a reference (a silicon substrate), and for the CNT film for two polarization orientations with respect to the CNT alignment direc-
tion; (c) real (solid) and imaginary (dashed) parts of the complex refractive index; and (d) real part of optical conductivity obtained for the CNT film. The
peak amplitude of the THz electric field of the (e) first and (f ) second pulses as a function of θ; (g) phase of the THz electric field as a function of θ . Open
circles represent experimental data, and solid lines are theoretical curves. Superscript (i = 1, 2) indicates the pulse number.

where Z0 ≈ 377 is the impedance of free space, d is the film There have been many theoretical [32–36] and experimental
thickness, and σ is the complex conductivity of the film. Using the [16,37–44] studies on the optical conductivity of CNTs. However,
Jones matrix formalism, the projection of the THz electric field different types of CNTs (HiPco, CoMoCAT, CVD, arc discharge,
onto the output polarizer direction as a function of θ is obtained as and laser ablation) were used, and the degree of alignment signifi-
cantly varied from study to study, and thus, universal behaviors
E x(i) = E k(i) cos2 θ + E ⊥(i) sin2 θ, have not been achieved as to the frequency dependence, anisotropy,
and magnitude of the optical conductivity. Additionally, most of
E y(i) = (E k(i) − E ⊥(i) ) sin θ cos θ, (4) the samples experimentally studied were a mixture of semiconduct-
ing and metallic nanotubes with a wide distribution of diameters
where E k and E ⊥ indicate the electric field components that are and lengths, which prevented workers from achieving universal
parallel (θ = 0◦ ) and perpendicular (θ = 90◦ ) to the CNT align- conclusions. The main difference between our films and the films
ment direction, respectively, and the superscript (i) stands for the reported elsewhere is the degree of alignment and high packing
first (i = 1) and second (i = 2) pulses. density, which we achieved using the controlled vacuum filtration
The complex permittivity tensor and the complex refractive method [21].
index can be obtained from the first THz pulse alone, using the By plugging the obtained conductivity into Eqs. (1)–(4), we
thin-film approximation; see Eq. (3). Figure 2(b) shows THz wave- can calculate the magnitude and phase of the electric field for
forms of the first pulse for the sample and a reference. The THz both pulses, which are shown by solid lines in Figs. 2(e) and 2(f ),
pulse is significantly attenuated for parallel polarization, whereas respectively, together with experimental data (open circles). The
no attenuation is seen for the perpendicular case. This is a result of calculated results for a center frequency of 0.76 THz are in good
a highly anisotropic complex refractive index, as shown in Fig. 2(c). agreement with the data. In contrast to the first pulse, whose
The corresponding real part of the extracted conductivity is shown amplitude monotonically varies with θ , the peak amplitude of
in Fig. 2(d). the second pulse as a function of θ has a minimum at the magic
 Research Article Vol. 8, No. 5 / May 2021 / Optica 763

Fig. 3. Giant polarization rotations by an aligned CNT film through transmission and reflection. (a) Angle of polarization rotation upon transmission
through the CNT film. (b) Angle of polarization rotation upon reflection from the CNT film. Arrows in (b) indicate polarization rotation direction as the
angle, θ , between CNT alignment direction and input THz polarization changes. Schematics on top show definition of the polarization rotation angles.

angle (θ = 30◦ ) and a maximum at θ = 45◦ , as shown in Fig. 2(f ). of the second pulse [Fig. 2(g)], the polarization rotates counter-
Another interesting observation is a 180◦ or π phase flip of the clockwise (clockwise) when θ is below (above) the magic angle,
second pulse as θ is swept through the magic angle, as can be seen in which is depicted schematically by arrows in Fig. 3(b). The phase
Fig. 2(g). flip occurs due to the anisotropic conductivity of the film [Fig.
The observed effects can be understood as a result of giant 2(d)]. The huge conductivity for the parallel direction leads to a
polarization rotation induced by transmission through and reflec- negative real part of the reflection coefficient [Eq. (3)], while it is
tion from the aligned CNT film. As an incoming THz pulse of positive in the perpendicular case.
particular polarization propagates through the CNT film, its While the magic angle depends on the refractive index of the
polarization plane rotates because the electric field components underlying substrate, its effect on the angle of rotation is small, as
that are parallel, E k , and perpendicular, E ⊥ , to the CNT align- can be seen in Fig. S3 and Fig. S4 of Supplement 1. It is important
to note that the polarization rotation reported here arises from
ment direction get attenuated and retarded differently. The parallel
retardation as well as attenuation of the electromagnetic field due
component, E k , is attenuated more than the perpendicular one,
to the large anisotropy of both the real and imaginary parts of the
E ⊥ , as shown in Fig. 2(a). A further polarization rotation occurs
refractive index with respect to the nanotube alignment direction.
when the second THz pulse (produced by the reflection at the However, if the attenuation along one direction (i.e., for light
bottom surface of the substrate) gets reflected by the film-substrate parallel to nanotubes) is too strong, as is the case with thicker CNT
interface; i.e., E k is reflected more than E ⊥ [see the refractive index films (>250 nm) or wire grid polarizers, the effect discussed in this
in Fig. 2(c)]. Therefore, the polarization direction of the second paper will not be observed.
THz pulse can become orthogonal to the output polarizer, which
results in reflection disappearance at the magic angle [see Fig. 2(f )].
Thus, upon transmission through and reflection from the ultrathin 4. CONCLUSION
CNT film, the THz pulse polarization direction rotates by 90◦ Our experiments and theoretical explanations demonstrate that,
when θ is at the magic angle. upon a single reflection by the aligned CNT film, the THz polari-
To assess how much the plane of polarization rotates for the first zation plane rotated by up to ∼110◦ . To our knowledge, this is
and second pulses, we calculated the angle of polarization rotation the largest Kerr angle ever reported for a single reflection event
as 2 = arctan(Txy /Txx ). The real part of 2 represents the rotation by any material. In contrast to other reports on giant polariza-
of the polarization plane, while the imaginary part represents the tion rotations based on Faraday rotation [5,6], metamaterials
ellipticity. We refer to the angle of polarization rotation due to [9,11,12], and CNT functionalized gratings [45], the macroscop-
transmission through the CNT film as the “Faraday” angle, 2F , ically aligned CNT films are broadband and ultrathin and can
and that due to reflection from the CNT film as the “Kerr” angle, be put on a flexible substrate. The observed effects are explained
2K . Note, however, that no magnetic field is applied. When cal- by the extreme birefringence of the films arising from the nearly
culating the angle of polarization rotation for the second pulse, perfect alignment of CNTs. The results of this work can thus lead
2F+K , we must subtract the contribution from the first pulse, 2F , to CNT-based robust and flexible THz devices for manipulating
in order to obtain 2K . Both 2F and 2K are shown in Fig. 3 as a THz waves.
function of θ . After THz pulse transmission, we can see that the Funding. Japan Science and Technology Agency (CREST JPMJCR17I5);
THz pulse polarization has a rotation just over 20◦ [Fig. 3(a)], U.S. Department of Energy (DE-FG02-06ER46308); National Science
Foundation (ECCS-1708315); Welch Foundation (C-1509).
while the second THz pulse that is reflected from the CNT film
rotates by ∼110◦ when θ = 30◦ . Interestingly, due to the phase flip Disclosures. The authors declare no conflicts of interest.
 Research Article Vol. 8, No. 5 / May 2021 / Optica 764

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