This study demonstrates the use of photonic crystal directional couplers to separate light of wavelengths 1.31 and 1.55µm. The photonic crystal structure consists of InAlGaAs nano-rods arranged in square lattice. The coupling length of the light in the directional coupler at a wavelength of 1.31µm was designed to be four times greater than that at 1.55µm. This behavior helps in designing devices to split the two wavelengths. The devices are fabricated by e-beam lithography and conventional photolithography. The measurement results confirm that 1.31µm/1.55µm directional couplers can be realized in PC structures formed by nano-rods.
©2005 Optical Society of America
Two-dimensional photonic crystal (PC) waveguides are investigated because of their potential use as polarization filters, power splitters, demultiplexers, lens and so on. [1–4] Slab waveguides are typical structures used to obtain the lateral and vertical light confinements by PC structures and by index guiding, respectively. The propagation characteristics of light vertically confined by different cladding layers have been studied. [5–6] Although air-bridge (air cladding) PC slab waveguides  provide very strong vertical mode confinement and can greatly reduce the losses associated with leaky waveguides and scattering from the bottom of the etched holes, the minimum propagation loss remains 1.7dB/mm . We recently demonstrated experimentally the semiconductor hollow optical waveguide with an omni-directional reflectors (SHOW-ODR).  The polarization-independent propagation loss has been reported to be 1.7dB/cm for both TE and TM modes. The guiding material was air minimizing the problems associated with absorption. The group velocity dispersion due to the materials dispersion and the waveguide dispersion can also be reduced.
PC directional couplers have been realized in semiconductor slab waveguides with periodically arranged air-holes. [10–13] Several theoretical studies have predicted that directional couplers formed by dielectric rods can act as all-optical switches  and electro-optical switches . The PC directional couplers formed by periodically arranged rods have been demonstrated only in the microwave region.  The advantages of the air-core PC waveguide mentioned above are such that this work demonstrates PC directional couplers with periodically arranged rods in InAlGaAs. The device is designed to separate wavelengths of 1.31 and 1.55µm. E-beam lithography is performed to define the nano-structures of the device. The results confirm that 1.31µm/1.55µm directional couplers can be realized in PC structures.
2. Simulation and results
III–V materials are chosen for the fabrication of the device to obtain high index contrast between the rods and air. The material of the rods should be transparent to the wavelengths 1.31µm and 1.55µm. Additionally, the refractive index of the guiding materials should be higher than that of the substrate to obtain the vertical confinement in the input/output slab waveguides. Therefore, InP and In0.53Al0.16Ga0.31As are chosen as the materials for the substrate and the guiding layer, respectively. The refractive index of In0.53Al0.16Ga0.31As, which is 3.24 and 3.13 for the wavelength 1.31µm and 1.55µm, respectively, is calculated using interpolation of that of InGaAs  and AlGaAs .
The band structures of the periodically arranged dielectric rods in square lattice are calculated by the two-dimensional plane wave expansion method for the polarization of the light parallel to the dielectric rods. The refractive index of the rods is 3.19. The band structures are calculated for different ratios of the radius of the rods (r) to the lattice constant (a) to obtain a large band gap. The maximum band gap is obtained as the r/a ratio is between 0.18 and 0.2. The r/a ratio is chosen to be 0.185. The photonic bandgap is illustrated in Fig. 1 (a). The normalized frequency of the photonic bandgap is between 0.32 and 0.45. The PC line defect waveguide is formed by removing a column of rods. The propagation mode is calculated by the two-dimensional plane wave expansion method to confirm the single-mode operation at wavelengths of 1.31µm and 1.55µm.
Two parallel PC waveguides are separated by a column of dielectric rods to form a PC directional coupler as shown in Fig. 1(b). The even and odd modes of the PC couplers are also shown in Fig. 1(a). For different normalized frequencies, the difference between the propagation constant of the even mode and that of the odd modes varies resulting in the different coupling lengths. Using the two-dimensional finite-difference time-domain method (2D-FDTD), the light of different normalized frequencies is launched in the PC directional coupler to calculate the relation between the coupling length and the normalized frequency. The refractive index of the rods is 3.24 and 3.13 at wavelengths of 1.31µm and 1.55µm, respectively. To separate the light at these two wavelengths into the different output ports, the coupling length for the wavelength of 1.31µm should be designed to be four times larger than that for the wavelength of 1.55µm. According to the relation between the coupling length and the normalized frequency, the requirement above can be achieved as the normalized frequency is chosen to be 0.417 and 0.352 where the coupling length is 27a and 6.8a, respectively. Fig. 1(a) shows that the light of these two normalized frequencies can propagate in the line defects of the PC couplers. The corresponding wavelengths are 1.31µm and 1.55µm, respectively. The lattice constant can be obtained to be 0.546µm and the corresponding radius of the rods is around 0.101µm. The refractive index of In0.53Al0.16Ga0.31As for the wavelength 1.31µm and 1.55µm is used to re-calculate the photonic bandgap with the refractive index of 3.24 and 3.13, respectively. The normalized frequency of the photonic bandgap is between 0.31 and 0.45 for the wavelength 1.31µm. The normalized frequency of the photonic bandgap is between 0.32 and 0.45 for the wavelength 1.55µm. The results confirm that both wavelengths are included in the photonic bandgap revealing the light of both wavelengths can be confined in the PC waveguides.
Figure 1(b) presents the structure of the PC directional coupler, of which the performance is calculated. The two output ports of the devices are separated from each other using bent waveguides. The length of the coupling region is varied to maximize the extinction ratio which is the ratio of intensities between 1.31 and 1.55 µm received at the output ports. When the length of the coupling region is 26a, the extinction ratio, is around 3.9 and 6.2 at the 1.31µm and 1.55µm output ports, respectively. The influence of the refractive index variation of the nano-rods to the coupling length is also estimated. As the refractive index of the materials is changed with an index difference of +0.1 and -0.1, the ratio of the coupling length between the two wavelengths which is four in the design above varies to 4.1 and 3.8, respectively. This behavior reveals that the tolerance of refractive index error within 0.1 does not significantly change the coupling effect of the device.
3. Sample preparation and characterization results
The sample was grown by molecular beam epitaxy. The guiding layer of the samples was 400nm-thick layer of In0.53Al0.16Ga0.31As sandwiched between an InP substrate and a 500nm-thick InP cladding layer. The fabrication process consists of e-beam lithography to define the PC waveguide patterns and conventional photolithography to define the input and output slab waveguides. The thickness of the guiding layer was designed to support only the fundamental mode for the TM polarization in the slab waveguides. The effective index of the waveguides can be calculated to be 3.204 and 3.122 for the wavelengths 1.31 and 1.55µm, respectively. The corresponding difference between the effective index and the guiding material index is 3.6×10-2 and 8×10-2. This difference is within the tolerance of the refractive index and is omitted in the design to simplify the calculation. A 150nm-thick Si3N4 film was deposited by plasma-enhanced chemical vapor deposition on the InP cladding layer which was used as a hard mask for dry etching. After the sample has been coated by the positive photoresist, PMMA A4 950K, and baked at 180°C for 60 min, the pattern of the rod array was defined by an e-beam writer. Dry etching was performed using a high density plasma etcher with O2/SF6 mixture plasma to etch the Si3N4 film followed by CH4/H2 gas mixture plasma to etch away the semiconductor materials. After e-beam lithography has been performed, the slab waveguides of the input and output ports were patterned by conventional photolithography and dry etching. The width of the slab waveguides was 5µm. The coupling efficiency between the conventional slab waveguides and the PC waveguides is estimated by 2-D FDTD to be 26% and 27% for the wavelengths of 1.31 and 1.55µm, respectively. The Si3N4 film was removed by dry etching. The InP substrate was thinned by polishing and cleaved to yield a mirror-like facet at the end of the input and output slab waveguides. Figure 2 shows the scanning electron microscopic image of the PC directional coupler. The insets in Fig. 2 show the schematic cross-section structure of the samples and the image of the nano-rods. The diameter of the nano-rods is not uniform for the top and the bottom of the nano-rods. The diameter of the nano-rod bottom is around 200nm which corresponds to the design diameter. The non-uniformity of the nano-rod diameter may affect the extinction ratio of the devices.
Laser diodes emitting at wavelengths 1.31µm and 1.55µm with the identical power were coupled into a fiber with an optical fiber directional coupler. The polarization of the light was controlled using a polarizer. The input waveguide was excited by TM-polarized light using an objective lens. The output spectra were analyzed using an optical spectrum analyzer. Figure 3 show the optical spectra of the 1.31µm and 1.55µm output ports, respectively, The extinction ratio at the 1.31µm port was three, and that at the 1.55 µm port was 4.1. The results show that the PC directional coupler can indeed separate the light at wavelengths 1.31 µm and 1.55 µm.
The extinction ratio of the device seems to be too low for practical application in fiber-optic communication. The extinction ratio can be improved by tuning the refractive index of the materials or the geometry of the PC directional couplers. The former method requires stable material growth to obtain the material with exactly the desired composition. The latter method depends on e-beam lithography with high resolution. The diameter of the rods between the PC waveguides or the diameter of the rods throughout the whole device may be parameters to be tuned. Such tuning may vary the coupling lengths of both wavelengths. A detail analysis is under way to improve the extinction ratio.
A GaAs/AlAs-oxide multilayer system has been demonstrated to form an omnidirectional reflector.  The vertical confinement can be obtained if the omni-directional reflectors cover on and below the two-dimensional PC directional couplers. Figure 4 shows the schematic structure. The device can be realized by growing the GaAs/AlAs multilayer and In0.53Al0.16Ga0.31As guiding layer on InP substrate. The AlAs can be selectively converted to an oxide by wet thermal oxidation technique. E-beam lithography and dry etching can be used to obtain the PC patterns on the In0.53Al0.16Ga0.31As guiding layer. One another omni-directional reflector covers on the top of the device by wafer bonding. The input light can be confined horizontally and vertically by the PC structure and omni-directional reflectors, respectively. This structure can reduce the propagation loss due to the lack of the vertical confinement in our present devices.
This study demonstrated PC directional couplers formed by InAlGaAs rods. The large band gap of the designed PC structure enables PC waveguides to support light of wavelengths 1.31 and 1.55µm: the device can separate these two wavelengths. The extinction ratio may be modified by varying the diameter of the rods between the PC waveguides. Light can be vertical confined in the devices by combining omni-directional reflectors on and below the two-dimensional PC structures as outlined in Ref. 9 to reduce the propagation loss.
The authors are grateful for the financial support of the MOE Program for Promoting Academic Excellence of Universities. (Grant number 91-E-FA06-1-4), and that of the Ministry of Economic Affairs of Republic of China under the Program for Industrial Technology Development (91-EC-2-A-17-0285-029).
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