Guided-wave propagation of sub-ps terahertz (THz) pulses in a highly birefringent plastic photonic crystal fiber was studied by using a THz time domain spectroscopy technique. The plastic photonic crystal fiber was fabricated by using high density polyethylene tubes and solid filaments. The fabricated THz plastic photonic crystal fibers exhibit an extremely large birefringence of ~2.1×10-2, which is almost one order of magnitude larger than that of previously reported photonic crystal fibers.
©2008 Optical Society of America
Photonic crystal fibers (PCFs) have engendered growing interest over the past few years since they offer the opportunity to fabricate optical waveguides with enhanced linear and nonlinear optical properties . Compared with the conventional optical fibers, the PCF exhibits broadband single-mode operation [2, 3], anomalous dispersion , and large mode area . A typical PCF consists of a guiding core and a periodic cladding region [6–9]. The fiber core is formed by introducing a defect into the photonic crystal structure to create a localized region with optical properties that are different from the surrounding cladding region. PCFs with the high index cores guide the light by the total internal reflection while those with the low refractive index defects guide the light by the photonic bandgap effect. In standard optical fibers, imperfections in the core-cladding interface introduce random birefringence that leads to the randomly polarized light. The conventional polarization-maintaining (PM) fibers such as PANDA or Bow-tie fibers [10, 11] have a modal birefringence up to ~5×10-4 by applying mechanical stress to the core region, and they have been used to overcome this random polarization problem. It has been reported that due to the intrinsically large index contrast, the PCFs can have much higher birefringence than the conventional PM fibers [12–14]. Recently, PM PCFs have been fabricated and have yielded a birefringence as high as ~3.9×10-3 at ~1.55 µm .
The recent progress in terahertz (THz) technology has attracted much attention in THz waveguides such as metallic waveguides , plastic ribbons , dielectric fibers , photonic crystal fibers [18, 19], and metallic wires [20, 21]. Among these waveguides, we are interested especially in THz photonic crystal fibers since they have mode properties useful for short pulse, broadband THz systems, such as broadband single-mode operation, anomalous dispersion, and large mode area, as already demonstrated for PCFs at optical frequencies. In this paper, we demonstrate the fabrication of the highly birefringent plastic photonic crytal fiber (PPCF) and characterize the sub-ps THz pulse propagation by using the THz time-domain spectroscopy technique. Furthermore, we show that the fabricated THz PPCFs have extremely strong birefringence, almost one order of magnitude larger than that of the previously reported PCFs.
2. Design and Fabrication
In general the guided modes of a fiber with rotational symmetry of order higher than 2 are either nondegenerate or two-fold degenerate pairs of lower symmetry . Corresponding to the latter case, the fundamental modes of PCFs with symmetric cores are not birefringent. Only intentional symmetry breaking in PCFs with asymmetric cores can lead to birefringence. The PPCFs with a single solid filament have the six-fold symmetry and are not birefringent . However, when this six-fold symmetry is destroyed with the asymmetric core consisting of two solid filaments, the degeneracy of two orthogonal polarization modes is removed.
The PPCF was fabricated by using high density polyethylene (HDPE) tubes [18, 23]. The HDPE tubes were stacked to form a two-dimensional triangular photonic crystal, and then fused at ~135 °C in a conventional furnace. The lattice constant of the PPCF was 500 µm, and the tube thickness was 50 µm, which corresponds to an air filling factor of 0.673. The total length of the fiber was approximately 2 cm-long. At the center of the triangular lattice structure, two solid HDPE filaments were inserted to create a highly asymmetric refractive index defect. The optical micrograph of a fabricated PPCF is shown in Fig. 1.
Since the PPCF has the large air hole with high index contrast, it is crucial to use a rigorous model for the field calculation. We used a full-vectorial method based on plane wave expansion [24, 25]. The calculated field distributions of two lowest order guided modes are shown in Fig. 2 where the first and second modes predominantly have x-polarization (Ex) and y-polarization (Ey), respectively. Since the input THz pulse in the experiment is a fundamental Gaussian beam and the two lowest order guided modes in the PPCF are symmetrical along the x or y axes, the input THz pulse is coupled predominantly to the first or second guided modes, depending on the polarization of the input THz pulse. Therefore the fabricated PM PPCF exhibits broadband single mode propagation. At high frequencies, the THz field is highly confined in the defects, and the field distributions for the two polarizations become almost identical.
3. Experiment and Results
The experimental setup for the measurements of THz pulse transmission through the PPCF is similar to that of other THz waveguides measurements [14–18]. It consists of a THz transmitter/receiver and a lens-fiber-lens beam steering/coupling system. The THz pulse is generated via the standard optical rectification method using a (111) semi-insulating GaAs substrate. The generated THz pulse was collimated and focused by off-axis parabolic mirrors. The PPCF was placed at the THz beam waist between two off-axis parabolic mirrors for efficient coupling in and out of the fiber core. By using a hyperhemispherical silicon lens, the THz beam was focused to a nearly frequency-independent beam waist of ~500 µm at the entrance face of the PPCF. An identical arrangement was used at the exit face of the PPCF. The transmitted THz signal was then detected by a photoconductive antenna fabricated on a low-temperature grown GaAs, applying the standard optical gating and phase-sensitive detection techniques. The photoconductive antenna in the THz detector measures the photocurrent induced by the electric field of the incident THz pulse. Since the THz pulse generated by optical rectification is highly polarized, after measuring the x-polarized THz pulse, the PPCF was rotated by 90°, then the y-polarized THz pulse was measured.
Shown in Fig. 3 are the temporal shapes of the THz pulses for two different polarizations after transmitting through a 2 cm-long PPCF. The inset in Fig. 3(a) shows the input THz pulse which was measured by removing the PPCF and by moving two silicon lenses to back-to-back position. The dot and solid lines indicate the measured and calculated results, respectively. The temporal width of the input pulse was measured to be ~0.8 ps (FWHM). As can be seen in the figure, the incident THz pulses are chirped to ~6 ps (FWHM) after transmitting through the PPCF for both polarizations. However, the two polarization modes have different propagation constants, showing a relative time delay of ~460 fs in the peak position. The material dispersion of the HDPE contributed very little to the total dispersion of the PPCF. The theoretical curve was obtained assuming the single fundamental guided mode per polarization where a frequency-independent refractive index is 1.5. The theoretical results are in good agreement with the experiments.
The output THz signal can be calculated by a quasi-optical method  in the frequency domain, and it can be expressed as
where Ein is the normalized input Gaussian beam, T is the total transmittance including the Fresnel reflection losses at the entrance and exit planes of the PPCF, C is the coupling coefficient calculated from the overlap integral of measured input signal and calculated guided mode, α is the power attenuation constant, β is the propagation constant of the guided mode in PPCF, and β 0 is the propagation constant of the input Gaussian beam in air. C is calculated from the following equation,
where Em is the normalized guided mode of the PM PPCF for a given polarization.
Shown in Fig. 4 are the amplitude spectra of the THz pulses for two different polarizations after propagating through the 2 cm-long PPCF, where the dotted line represents the input wave spectrum, and the solid line and dots represent the measured and calculated transmission spectra, respectively. The small ripples in the transmission spectra are probably due to the Fabry-Perot effect from the air gap between the PPCF and the silicon lenses, and due also to the residual water absorption. The measured spectra below 0.2 THz and above 0.6 THz were significantly reduced for both x- and y-polarizations. This is due to the large mode mismatch (|C|2) between the focused Gaussian beam and the PPCF guided modes. The dashed lines show the calculated results for the mode mismatch in Fig. 4. From the measured and the calculated spectra, the power attenuation constant was estimated to be ~0.5 and 4 dB/cm at 0.3 and 1 THz, respectively. In general the low attenuation in the PPCF is limited by the material absorption of HDPE. Depending on the amount of impurities incorporated during the manufacturing process, the HDPE has been shown to have an absorption coefficient as small as ~1.5 dB/cm at 1 THz . This suggests that the absorption-limited attenuation in the PPCF can be further reduced by using better HDPE and improved fabrication technique.
The effective index of the PPCF was obtained from the amplitude and phase spectra of the measured THz pulses as shown in Fig. 5. Dot and triangles represent the measured effective indices of x-polarization and y-polarization modes, respectively. The solid lines are the theoretical results. At the high frequency limit, the effective indices approach the refractive index of the HDPE core (n=1.5) while at the low frequency limit they approach that of the cladding (nc=1.163) as expected. This is simply because the field confinement in the high index core gets tighter as the frequency increases.
The frequency dependence of the modal birefringence is shown in Fig. 6. The calculated birefringence is in reasonably good agreement with the experments below ~0.7 THz. However, above 0.7 THz, the difference beween the calculation and the measuremet becomes large due to the limitation of the signal-to-noise ratio. The measured effective indices of the two polarization modes are 1.296 and 1.275 at 0.3 THz, corresponding to a peak birefringence of 0.021, which is almost one order of magnitude larger than that of the previously reported PCFs at optical frequencies. The polarization mode dipersion has a maximum of ~70 ps/m at 0.3 THz, and it vanishes in both high and low frequency limits. The zero group velocity dispersion occurs at ~0.5 THz for both polarizations.
We have experimentally demonstrated highly birefringent PPCFs at THz frequencies. The PPCFs were fabricated by using HDPE tubes and two solid filaments, and they were characterized by a THz time-domain spectroscopic technique that simultaneously provides both amplitude and phase spectra. The peak birefringence measured was 0.021 at 0.3 THz, which is much larger than that of the optical PPCFs. It is expected that these highly birefringent THz PPCFs may find their applications in polarization-sensitive devices such as polarization controllers, filters, and isolators at THz frequencies.
This work was supported by the Korea Science and Engineering Foundation through the National Research Laboratory Program (R0A-2005-001-10152-0) funded by the Ministry of Science and Technology, and by the Korean Research Foundation through the Priority Research Centers Program (KRF-2005-005-J13103) and Brain Korea 21 Project funded by the Ministry of Education and Human Resources Development.
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