Guimin Lin

Polarization-independent Fabry–Perot interferometer in a hole-type silicon photonic crystal

We propose and numerically demonstrate a polarization-independent Fabry-Perot interferometer (PI-FPI) based on the self-collimation effect in a hole-type silicon photonic crystal (PhC). By use of the polarization peak matching method, a resonance frequency of the transverse-electric modes can equal that of the transverse-magnetic modes in the PI-FPI, although the transmission spectra are quite polarization dependent due to birefringence of the PhC. For the operating wavelength of 1550 nm, the PI free spectral range of the PI-FPI is up to 32.3 nm, which nearly covers the whole optical communication C-band window. With its small dimensions, simple structure, and silicon-based material, this PI-FPI may play an important role in photonic integrated circuits.

Transmission spectrum of Fabry-Perot interferometer based on photonic crystal

A Fabry-Perot interferometer (FPI) constructed in a two-dimensional photonic crystal (2D PhC) has been proposed and demonstrated theoretically. The perfect 2D PhC consists of square-lattice cylindric air holes in silicon. Two same line defects with spacing of d = 16a, which is the physical length of the FP resonant cavity, are introduced in the PhC to form the FPI. The two line defects have high reflectivity and low transmission. Their transmission is between 4.81% and 11.1% for the self-collimated lights with frequencies from 0.275c/ato 0.295c/a and thus they form the two partial reflectors. Lights propagate in the FPI employing self-collimation effect. The transmission spectrum of the FPI has been investigated with the finite-difference time-domain method. The calculation results show that peaks have nearly equal frequency spacing 0.0078c/a. Even slight increases of d can cause peaks shift left to lower frequencies. As a result, the peak spacing decreases nonlinearly from 0.0142c/a to 0.0041c/a when dis increased from 9a to 30a. Through changing the configuration of the reflectors which results in transmission between 4.18% and 7.73%, the varieties of the sharpness of peaks and the degree of extinction of the frequencies between the peaks are obviously observed.

1x4 optical splitters based on self-collimation ring resonators in an air-hole silicon photonic crystal

We report the 1x4 optical splitters (OSs) for TE modes based on an air-hole type silicon photonic crystal selfcollimation (SC) effect ring resonator (SCRR). The OS has four beam splitters which are formed by changing the radii of the air holes. With the self-collimation effect and the radii we set for beam splitters, the light beams propagation will be well controlled. Using the multiple-beam interference theory, we analyse the theoretical transmission spectra and make the simulation, which is realized by two-dimensional finite-difference time-domain (FDTD) simulation technique. As we expected, the results have a good agreement with the theoretical calculation Small-dimensions, low-loss of the OSs will have an important role in photonic integrated circuits in the future.

Drop filters in a rod-type photonic crystal based on self-collimation ring resonators

We design a rod-type drop filter (RTDF) in a two-dimensional photonic crystal (2D PhC) employing self-collimation (SC) effect. The perfect 2D PhC consists of a square-lattice of cylindrical silicon rods in air. The dielectric constant and the radius of host rods are ε=12.25 (correspondingly the refractive index n = 3.5) and r=0.40a respectively, where a is the lattice constant. In such a PhC, self-collimation phenomenon occurs for transverse-magnetic (TM) light beams with frequencies between 0.176c/a and 0.192c/a. The proposed RTDF based on a self-collimation ring resonator (SCRR) consists of two beam splitters and two mirrors. The performances of the SCRR are investigated with the finite-difference time-domain (FDTD) simulation technique. The calculation results show that the transmissivity spectrum at the drop port has nearly equal peak spacing which will decreases when the geometrical length of the SCRR is increased. Moreover, the full width at half maximum (FWHM) and thus quality (Q) factor of peaks can be easily tuned by changing the reflectivity of two beam splitters.

Tunable drop filters based on photonic crystal self-collimation ring resonators

A tunable drop filter (TDF) based on two-dimensional photonic crystal (PC) self-collimation ring resonator (SCRR) is proposed. The PC consisting of square-lattice air cylinders in silicon has square-shaped equal frequency contours (EFCs) in the wavevector space at the frequencies between 0.172-0.188c/a for TE modes. The SCRR includes two mirrors and two splitters. The air holes inside the SCRR are infiltrated with a kind of liquid crystal whose ordinary and extraordinary refractive indices are 1.522 and 1.706, respectively. The effective refractive index neff of liquid crystal depends on the applied electric field. Simulated with the FDTD method, the transmission spectra at the drop port of SCRR are in the shape of sinusoidal curves with uniform peak spacing between 0.172-0.188c/a. Transmission peaks will shift to the lower frequencies when neff is increased. When neff changes from 1.522 to 1.706, the peaks will experience red-shift over 0.003c/a. So this SCRR can work as a tunable drop filter. For the operating wavelength around 1550nm, its dimensions are only tens of microns.

Wavelength division demultiplexing with photonic crystal self- collimation interference

A theoretical model of wavelength division demultiplexer (WDD), which is based on an asymmetric Mach-Zehnder interferometer (AMZI) constructed in a two-dimensional photonic crystal (2D PhC), is proposed and numerically demonstrated. The 2D PhC consists of a square lattice of cylindric air holes in silicon. The AMZI includes two mirrors and two splitters. Lights propagate between them employing self-collimation effect. The two interferometer branches have different path lengths. By using the finite-difference time-domain method, the calculation results show that the transmission spectras at two AMZI output ports are in the shape of sinusoidal curves and have a uniform peak spacing in the frequency range from 0.26c/a to 0.27c/a. When the path length of the longer branch is increased and the shorter one is fixed, the peaks shift to the lower frequencies and the peak spacing decreases nonlinearly. Consequently, the transmission can be designed to meet various application demands by changing the length difference between the two branches. For the dimensions of the WDD are about tens of operating wavelengths, this PhC WDD may be applied in future photonic integrated circuits.

Tunable Mach-Zehnder interferometer in a two-dimensional photonic crystal with liquid crystal infiltration

A theoretical model of a tunable Mach-Zehnder interferometer (TMZI) constructed in a 2D photonic crystal is proposed. The 2D PhC consists of a square lattice of cylindric air holes in silicon. The TMZI includes two mirrors and two splitters. Lights propagate between them employing self-collimation effect. The two interferometer branches have different path lengths. Parts of the longer branch are infiltrated with a kind of liquid crystal (LC) whose ordinary and extraordinary refractive indices are 1.522 and 1.706, respectively. The transmission spectra at two MZI output ports are in the shape of sinusoidal curves and have a uniform peak spacing 0.0017c/a in the frequency range from 0.26c/a to 0.27c/a. When the effective refractive index neff of the liquid crystal is increased from 1.522 to 1.706, the peaks shift to the lower frequencies over 0.0017c/a while the peak spacing is almost kept unchanged. So this TMZI can work as a tunble power splitter or an optical switch. For the central operating wavelength around 1550nm, its dimensions are only about tens of microns. So this device may be applied to photonic integrated circuits.

1×5 optical splitter for TE modes in air-hole photonic crystal based on self-collimation effect

We propose a novel 1×5 optical splitter (OS) for TE modes based on self-collimation effect in an air-hole silicon photonic crystal. The OS consists of two cascaded resonators which is formed with eight beam splitters. The theoretical transmission spectra of the OS is derived with multiple-beam interference theory. From our analysis of transmission spectra, it is found that the transmission spectra at five drop ports will reach the maximum values while the transmission spectra at two through ports reach zero for resonant frequencies. By scanning the radius of a beam splitter, the relationship between the radius and the reflectivity is obtained. Therefore, by changing the radii of the air-hole in eight beam splitters, we can manipulate the output light-intensity ratio at five drop ports to meet requirement. Theoretically, when reflectivity of beam splitters R1=2/11, R2=8/11, R3=5/8, R4=2/5, R5=7/12, R6 =6/7, R7=1/2, R8 =2/3, the light intensity ratio at five drop ports is 1:1:1:1:1. When R1=2/7, R2=6/7, R3=1/2, R4=2/3, R5=1/7, R6=6/7, R7=2/3, R8 =1/4, the light intensity ratio at five drop ports is 2:2:1:2:3. By means of finite-difference time-domain (FDTD) simulations, the numerical transmission spectra of OS can be figured out. The simulation results are consistent with the theoretical results. Considering micro processing technology of silicon materials is already available, this OS can be used in the photonic integrated circuits because of its small size, whole-silicon material and low insertion loss.

A 1 × 4 optical splitter for TE modes based on a silicon photonic crystal self-collimation ring resonator

A 1 × 4 optical splitter (OS) is proposed for TE modes based on a self-collimation (SC) effect ring resonator (SCRR) in an air-hole type silicon photonic crystal. A 1 × 4 OS consists of four beam splitters formed by varying the radii of the air holes. Utilizing multiple-beam interference theory, the theoretical transmission spectra at each port in the OS were analyzed. By forming four splitters in a SCRR properly, self-collimation light can come out from four ports with the light-intensity ratio we set. OSs were investigated using the two-dimensional finite-difference time-domain (FDTD) simulation technique. The simulation results have good agreement with the theoretical prediction. Because of its small dimensions, whole silicon material, and air-hole type, this structure may have an important role in photonic integrated circuits.

1×3 optical drop splitter in a rod-type silicon photonic crystal

We report an 1×3 optical drop splitter (ODS) based on a self-collimation ring resonator (SCRR) in a rod-type silicon photonic crystal. The proposed 1×3 ODS consists of four beam splitters which are formed by changing the radius of one row of silicon rods. When the self-collimated light with resonance frequency is launched into the ODS, the light beam can be split into three parts come out from three drop ports while no light coming out from the through port. The splitting ratio of the three drop beams can be controlled by tuning the radii of the beam splitters. The FDTD method is employed to calculate the transmission of the 1×3 ODS. For the drop wavelength of 1550 nm, the free spectral range is 28.7 nm, which almost covers the whole optical communication C-band window. This 1×3 ODS may have applications in photonic integrated circuits.