2D Square-lattice Photonic Crystal Research Articles

Design of All-Optical Logic Half-Adder Based on Photonic Crystal Multi-Ring Resonator

In this paper, a novel design of an all-optical half-adder (HA) based on two two-ring resonators in a two-dimensional square-lattice photonic crystal (PC) structure without nonlinear materials is proposed. The all-optical HA comprises AND and XOR gates where each gate is composed of cross-shaped waveguides and two-ring resonators in a 2D square-lattice PC that are filled with silicon (Si) rods in silica (SiO2). The AND and XOR gates are analyzed and simulated using plane-wave expansion (PWE) and finite-difference time-domain (FDTD) methods. Simulation results show that light guiding inside the device functions as AND and XOR gates. Thus, the proposed device has the potential for use in optical arithmetic logic units for digital computing circuits. The structure comprises an optical AND gate and an optical XOR gate that were designed to work at the C-band spectrum. Results show that there is a clear distinction between logic states 1 and 0 with a narrow power range that leads to a better robust decision on the receiver side for minimized logic errors in the photonic decision circuit. Thus, the proposed HA can be a key component for designing a photonic arithmetic logic unit.

Band gap of silicon photonic crystal with square-lattice and windmill-shaped defects

A new type of 2D square-lattice photonic crystal with different windmill-shaped defects is proposed. Based on the plane wave expansion method and super cell theory, the band gaps of defect models are numerically analyzed according to the symmetry. We aim at further reducing the defect symmetry of photonic crystals compared to previous studies and researching the effect of translation and rotation of different windmill-shaped defect structures on the transverse magnetic (TM) band gap. The results reveal that the translation distance of defects brings great impacts on the band gap of 2D square-lattice photonic crystals and the width of the TM band gap can be further expanded after rotating on the basis of translation. In addition, we discovery that the band gap of the model with even-numbered fan-shaped defects is wider than that of the model with odd-numbered fan-shaped defects. Among the five different defect models (three-wings, four-wings, five-wings, six-wings, rotating-cross), the four-wing windmill defect model produces the largest band gap, which reaches 5.307 × 10−2 (ɷa/2πc). This research is helpful to understand the band gap characteristics of photonic crystals, which will contribute to the design of photonic crystal devices.

Tuning beam power-splitting characteristics through modulating a photonic crystal slab’s output surface

Light-beam-splitting characteristics are theoretically and experimentally studied in 2D square-lattice photonic crystals (PhCs) with delicately designed and modulated output surfaces. Compared with the traditional branch-waveguide and self-collimation-type PhC splitters, our proposed structure can not only split the input light beam into different numbers of branches but also realize the adjustment of their relative light intensities in each branch. Moreover, the influence of a light beam’s incident angle on both the output branch beams’ relative intensity and propagation direction is investigated. This proposed light beam splitter is able to work within a broad frequency range, and the propagation directions of the output split beams can be modified with the incident beam’s frequency. In addition, when the PhC device becomes thicker, a kind of light-beam-focusing phenomenon is observed. Advantageously, our light-beam-splitting device has no restriction as to the incident light beam’s location and width, so it is much more convenient and practical for achieving optical connection with other functional devices in complicated, large-scale, all-optical integrated circuits.

An approach to achieve all-angle, polarization-insensitive and broad-band self-collimation in 2D square-lattice photonic crystals

We have investigated the possibility for achieving (in the same structure), an all-angle, polarization-insensitive and broad-band self-collimation (SC), one of...

圆环杆与平板连杆的适合光路集成的二维正方晶格光子晶体

圆环杆与平板连杆的适合光路集成的二维正方晶格光子晶体

Comparative study of photonic band gaps of germanium-based two-dimensional triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals

Photonic band gaps (PBGs) of germanium-based two-dimensional (2D) triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals (PCs) with the scatterer radius in the range of [0,0.3a] and within two cases of the construction (germanium cylinders being placed in air, air cylinders being placed in germanium) have been calculated by using the plane wave expansion (PWE) method. Germanium-based 2D triangular-lattice PC and 2D decagonal quasi-periodic PC are more easily to generate PBG than 2D square-lattice PC. 2D decagonal quasi-periodic PC is more easily to generate complete band gap than the other two kinds of PCs. The PBG properties of the three PCs are similar to the properties of silicon-based system as the radius of the scatterer cylinder increases. Nevertheless, the germanium-based system is more likely to generate PBG than silicon-based system. These findings will guide the design of PBG-type microstructure devices.

A 2D rods-in-air square-lattice photonic crystal optical switch

A 2D photonic crystal optical switch is proposed based on a rods-in-air square-lattice photonic crystal by removing two cross-lines of rods from a 2D square-lattice photonic crystal to form four optical channels. The simulation results show that, when inserting a single rod along the diagonal line of the intersection area of two removed cross-lines of rods, the position of the single inserted rod determines how much incident energy goes into different channels. In the case of transverse magnetic (TM) Gaussian point source, time domain simulation shows that up to 87.3% of the incident energy can be switched into a channel, which is vertical to the source channel. Because there are two diagonal lines in the intersection area of two removed cross-lines of rods, the optical switch feature is achieved by shifting the inserted rod between two diagonal lines. It is also found that the magnitude of the reflected wave in the source channel varies greatly with spatial position of the single inserted rod. The larger the magnitude of the reflected wave in the source channel, the less the energy that goes into the switched channel. The time delay between the incident wave and the reflected wave in the source channel is also related to the position of the single inserted rod. In addition, the large time delay between the incident wave and the reflected wave in the source channel shows that the reflected wave encounters many reflections with the walls of the source channel, instead of waves reflected back from the single inserted rod.

Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum

The Cherenkov radiation is substantially modified in the presence of a medium with a nontrivial dispersion relation. We consider Cherenkov emission spectra of a point or line charge, respectively, moving in general, three- (3D) and two-dimensional (2D) photonic crystals. Exact analytical expressions for the spectral distribution of the radiated power are obtained in terms of the Bloch mode expansion. The resulting expression reduces to a simple contour integral (3D case) or a one-dimensional sum (2D case) over a small fraction of the reciprocal space, which is defined by the generalized Cherenkov condition. We apply our method to a specific case of a line source moving with different velocities in a 2D square-lattice photonic crystal. Our method demonstrates a reasonable agreement with numerically rigorous finite-difference time-domain calculations while being less demanding on computational resources.

Negative refraction and flat-lens focusing in a 2D square-lattice photonic crystal at microwave and millimeter wave frequencies

We report on a study of the wave propagation and refraction in a 2D square-lattice photonic crystal for the first two photonic bands as well as the coupling of the external waves and criteria for flat-lens focusing. Microwave experiments and numerical simulations are performed. Main results concern the transition from positive to negative refraction below the first band gap, the flat-lens focusing using a novel criterion, viz. the constancy of the ratio of the tangents of the incident and refracted angle. Focusing results for medium ( approximately 10) and ultra-large dielectric contrast ( approximately 100) are presented. In the latter case focusing with a spot size below one wavelength at distances several wavelengths behind the photonic crystal is achieved.

Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Padé approximation. The decaying constant β of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity vg as β=ω/(2Qvg). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 103 to 10−4cm−1 can be reliably obtained from 8×103-item FDTD output with the FDTD computing time of 0.386ps. And at most 1ps is required for the mode with the Q-factor of 4×1011 and the decaying rate of 10−7cm−1. In the triangular-lattice photonic crystal slab, a 104-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5×108 and the decaying rate of 0.05cm−1.