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A terahertz-scale two-dimensional photonic-crystal waveguide based on a silicon-on-insulator was fabricated, and the optical transmission spectrum was measured. Terahertz beam propagation characteristics were observed using a thermal imaging camera, with incident light in the 10.1–10.7 µm range. The measured transmission spectrum was in good agreement with a three-dimensional finite-difference time-domain calculation
©2004 Optical Society of America
1. Introduction
Terahertz radiation, which occupies a region of the spectrum between infrared and microwave, the so-called “terahertz gap”, represents one of the last unexplored frontiers of the spectrum. However, with the higher-power sources and more sensitive detectors emerging, terahertz (THz) technology now is an extremely attractive research field, with interest from semiconductors, medical images, space and defense industries to chemical and biological sensing [1–3]. Most current THz applications are based on free space devices systems. The problem is that the whole system is bulky and expensive. An integrated solid-state platform for THz signal generation, propagation, guidance, manipulation and readout would be preferable. As to integrate circuit, an important element is a linear waveguide to carry light to and from components. Recently, the hot pursuit of photonic crystal opens a new opportunity for integrated optical circuits [4, 5]. The existence of a photonic bandgap, a frequency range in which propagation of light is prevented in all directions, makes photonic crystals very useful in applications where special localization of light is required. That, together with its ultrasmall size, provides unique advantages for wavegudies. As a result, photonic crystal waveguides are formed by a line defects in PhCs that produces waveguide modes within the photonic bandgap. These modes, guided by the band gap of the bulk crystal, can exhibit near-zero reflection and loss through straight waveguides and sharp bends, which are expected to lead to ultrasmall lightwave integrated circuits. Although theoretical and experimental studies of photonic crystal waveguides within the optical wavelength region have been reported [6, 7], none of these present waveguides in the THz wave regime.
To this end, in this paper, we present a THz wave-propagation and transmittance study of Two-dimensional (2D) photonic crystal waveguides, which are formed by single channel defects in the photonic crystal (PhC) lattice which based on a silicon-on-isolator (SOI) wafer. Comparison between the experimentally measured transmittance spectrum and a three-dimensional (3D) FDTD calculation showed that the experimental and theoretical results agree with each other.
2. Experimental results
Fig. 1. (Left) SEM picture of PhC waveguide, the total length of it is 120µm, and the width of it is 100µm. (right) SEM pictures of side view and top view of the PhC Waveguide, the thickness of it is 9.49 µm, the lattice constant a=3.89 µm, and the hole diameter is 2.95 µm.
The fabrication of a THz PhC waveguide device on SOI are shown in Fig. 1. The thicknesses of the silicon and insulator layers are 9.49 µm and 1 µm, respectively. The input and output dielectric waveguides, which are used to couple the light into and out of the PhC waveguide, are 100 µm wide and approximately 2 mm long. Between them is a slab photonic crystal composed of a triangular lattice of air holes. It contains 35 rows along the optical beam propagation direction, which corresponds to a length of 120µm. The PhC lattice constant and the air-hole diameter are 3.89 µm and 2.95 µm, respectively. In this configuration, the ratios of the slab thickness and the radius of air hole to lattice constant are t/a=2.5 and r/a=0.38, respectively. In this case, we could roughly assume it as two-dimensional PhC [8], thus an effective index method can be used to reduce the full three-dimensional problem to a two-dimensional case. To this end, an effective refractive index of 2.96 is obtained to calculate the dispersion properties of PhC structure. Based on band diagram analysis of triangular unit cell by using the two-dimensional plane wave expansion method (PWEM) calculation, we found it opens a bandgap between normilized frequencies 0.3 (c/a) and 0.4 (c/a) for TE-like mode, which correspondes to wavelength from 9.72 µm to 13.2 µm. The PhC waveguide can then formed by removing a single row of air holes along Γ -K direction. The dispersion diagram of guided modes is obtained by using PWEM with supercell technique, as shown in Fig. 2. There are multimodes inside the bandgap due to the thickness of the slab. At normalized frequency of 0.37, or 28.5 THz there exists a ministop band that caused by the counter-crossing of the two modes in the bandgap [9].
Fig. 2. EPWM calculated dispersion diagram of the line-defect PhC waveguide, which was formed by deleting one row of air-holes along the ΓK direction. The yellow stripe was the bandgap of the PhC. The arrow in the right of the diagram indicated the position of ministop band, which was resulted from the two intercrossing modes.
Based on this dispersion diagram, we observed the tuning range of our CO2 laser, which is 10.1–10.7 µm, is in the wavelength of the guiding modes in the bandgap. To validate it, we simulated the 10.6µm wave propagation in the structure using a 2D-FDTD method. A perfect match layer is used as an absorbing boundary for the computation region [10]. To efficient couple the light into the PhC waveguide, a J-coupler was used to efficient couple light into the PhC waveguide [11], Fig. 3 shows the steady state results, we can observe a very good confinement within the waveguide.
Fig. 3. 2D- FDTD steady state results of 10.6 µm wave propagates in the THz PhC waveguide device, right picture is the zoom field of the wave propagates in the PhC waveguide.
The PhC waveguides are defined using standard electron-beam lithography (EBL). One of the advantages of using EBL (or e-beam) to directly write the structure on the sample is that it can produce high-resolution patterns. However, when using an e-beam to write large fields, such as those required here (3 mm×3 mm), achieving high pattern fidelity can be very time consuming. So, instead of directly writing the structure on the SOI, we first used e-beam lithography to fabricate a mask, and then used this mask for UV lithography as well as image reversal process to define the structure on the SOI [12]. By using this procedure, the patterning efficiency was greatly improved and good quality devices were obtained after etching. A custom passivation and etch process employing SF6, CF4, H2 and He was utilized in the reactive-ion etching process to produce the sharp, vertical etch profile [13].
The optical characteristics were measured by end-fire coupling a tunable CO2 laser (10.1–10.7 µm) into the input dielectric waveguide. By tuning the CO2 laser from 10.1 to 10.7 µm, the transmittance spectrum of the PhC waveguide was measured. The light was focused into the PhC waveguide by the J-coupler, which is an offset parabolic mirror that focuses the light from a dielectric waveguide into the PhC waveguide to achieve high coupling efficiency. Another dielectric waveguide was used to couple the light out of the PhC waveguide.
The setup for optical characterization is shown in Fig. 4. The laser light was tightly focused into the dielectric waveguide by a 0.5”-focal length focusing lens. The light was then focused by the J-coupler into the PhC waveguide, and the output light was collected and imaged by a reflecting microscope objective onto a pyroelectric thermal detector array (Electrophysics PV-320). The thermal imager was also employed to obtain optimal optical alignment, to monitor the scattering of the light from the top, as well as to view the output light from the outputwaveguide. This was accomplished in situ by the use of a gold-coated mirror mounted above the sample at a 45-degree angle mirror which provided a top-down view for the camera. A broadband-emitting silicon carbide filament was used to illuminate the sample through a beamsplitter to image the sample and to facilitate the alignment of the end-fire coupled input. Figure 4 shows the image obtained by the thermal camera with CO2 laser light incident on the waveguide.
Fig. 4. Schematic layout of the optical setup for measuring transmittance spectra and optical propagation.
The input and output facets were polished to get a better coupling result. The left and right upper images are the top view of the input facet, the J-coupler, and PhC waveguides, respectively. The lower photo is the image of the output light.
From the top view of the sample, we observe that vertical out-of-plane losses from the PhC waveguide were not detectable; this indicates good vertical confinement within the PhC waveguide. The output picture, which is in the lower right of Fig. 5, was obtained by positioning the IR camera directly facing the output faucet. The output light can be clearly seen from the picture.
Fig 5. Image acquired by thermal imager, (left upper) upper view of the output facet, (right upper) topview of the output facet, (lower left) top view of the input facet, (lower right) top view of the 2D-PhC waveguide.
The transmittance spectrum was obtained by processing the data collected by the thermal image using IRAF image reduction software. Fig. 6 shows both the measured and 3D-FDTD calculated transmittance spectra. For the 3D FDTD calculation, a pulse source, which is a product of a Gaussian temporal function (timewise) and the exact solution (at the center frequency) of the guided mode in the waveguide, was located at the entrance The use of a wide-bandwidth pulse allows a scan of the whole frequency range corresponding to the PBG at one time by taking the Fourier transform of the time-dependent output field. The output spectrum was normalized to the spectrum of the input pulse. For the measured transmission, the output coupled light is normalized to the laser power. This normalized result is exclusive of the coupling loss that results from the spatial mismatch of the free space CO2 laser beam, which is about 100µm in diameter, and the cross section of the input waveguide, about 100µm×10µm. From the measured transmission spectrum, we observed a maximum transmission about 38% at 28.6 THz. Furthermore, from the figure we can see a very good agreement from theoretical calculation and experimental result. We note that the calculated and measured spectra are all show dips, these represent a ministopband that caused by the counter-crossing of the two modes that we pointed out in the dispersion diagram, as shown in Fig. 2. The gap between 28.7 to 29 Thz of the transmission in the experimental result is because of the unavailable tuning frequency of CO2 laser in this region. The remaining discrepancies may be attributed to unavoidable fabrication-induced defects, such as size and pitch fluctuations, which result in the coupling of light into the leaky modes that are above the light cone. Another possibility is that the tuning of the CO2 laser changes the efficiency of the end-fire coupling into the input waveguide; we observed that the transverse mode profile of the CO2 laser beam in free space changed when the laser was tuned via an intra-cavity grating. This effect can be eliminated by fabricating a reference waveguide which lacks the PhC section but has the same structure as the input/output waveguides on the same sample in close proximity to the PhC structure, and normalizing the data by the transmission through the reference guide. Such experiments are in progress but are not yet complete.
We have reported on the fabrication and optical characterization of a THz PhC waveguide on a SOI. The plane-wave method was used to obtain the band gap of the designed device and the transmittance spectrum was measured in the wavelength range 10.1–10.7 µm. Optical beam propagation through the waveguide was successfully observed using a thermal imaging camera. The FDTD calculation results and experimental transmittance spectra are shown to be in good agreement. These results show that 2D photonic-crystal waveguides offer the potential to be used in THz integrated circuit applications.
Acknowledgments
This work was supported by the Air Force Office of Scientific Research.
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