Optical properties of a square-lattice photonic crystal within the partial bandgap

Optical properties of a two-dimensional square-lattice photonic crystal are systematically investigated within the partial bandgap through anisotropic characteristics analysis and numerical simulation of field pattern. Using the plane-wave expansion method and Hellmann-Feynman theorem, the relationships between the incident and refracted angles for both phase and group velocities are calculated to analyze light propagation from air to photonic crystals. Three kinds of flat slab focusing are summarized and demonstrated by numerical simulations using the multiple scattering method. (c) 2007 Optical Society of America

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions. (c) 2006 Elsevier Ltd. All rights reserved.

锥形光纤的功率分布特性

从波动理论出发,对锥形光纤的纵向传播常数进行泰勒(Taylor)级数展开,经近似得到了锥形光纤功率分布的解。基于此理论,对锥形光纤的功率分布特性进行了讨论,并分析了锥形光纤的长度、锥度和光纤折射率等参数对锥形光纤不同模式功率分布的影响。为了减小功率泄漏,当光从锥形光纤大端入射时,应当减小锥长,减小锥度,增大纤芯包层折射率差;当光从锥形光纤小端入射时,应当增加锥长,增加锥度,增大纤芯包层折射率差。在长锥长、大锥度情况下,光纤折射率分布的影响相对较小。

The impact of imperfect symmetry on band edge modes of a two-dimensional photonic crystal with square lattice

A theoretical analysis has been performed by means of the plane-wave expansion method to examine the dispersion properties of photons at high symmetry points of an InP based two-dimensional photonic crystal with square lattice. The Q factors are compared qualitatively. The mechanism of surface-emitting is due to the photon manipulation by periodic dielectric materials in terms of Bragg diffraction. A surface-emitting photonic crystal resonator is designed based on the phenomenon of slow light. Photonic crystal slabs with different unit cells are utilized in the simulation. The results indicate that the change of the air holes can affect the polarization property of the modes. So we can find a way to improve the polarization by reducing the symmetry of the structure.

Optical response of high-level bandgap in one-dimensional photonic crystal applying in-plane integration

A new broadband filter, based on the high level bandgap in 1-D photonic crystals (PCs) of the form Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si is designed by the plane wave expansion method (PWEM) and the transfer matrix method (TMM) and fabricated by lithography. The optical response of this filter to normal-incident and oblique-incident light proves that utilizing the high-level bandgaps of PCs is an efficient method to lower the difficulties of fabricating PCs, increase the etching depth of semiconductor materials, and reduce the coupling loss at the interface between optical fibers and the PC device. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Slow wave effect of 2-D photonic crystal coupled cavity array

We designed a two-dimensional coupled photonic crystal resonator array with hexagonal lattice. The calculation by plane-wave-expansion method shows that the dispersion curve of coupled cavity modes in the bandgap are much flattened in all directions in the reciprocal space. We simulated the transmission spectra of transverse electric (TE) wave along the Gamma K direction. Compared with the PC single cavity structure, the transmission ratio of the coupled cavity array increases more than three orders of magnitude, while the group velocity decreases to below 1/10, reaching 0.007c. The slow wave effect has potential application in the field of miniaturized tunable optical delay components and low-threshold photonic crystal lasers.

Optical response of high-order band gap photonic crystal applying in-plane in one-dimensional integration

A new broadband filter, based on the high-order band gap in one-dimensional photonic crystal (PCs) of the form Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si vertical bar air vertical bar Si, has been designed by the plane wave expansion method (PWEM) and transfer matrix method (TMM) and fabricated by lithography. The optical response of this filter to normal-incident and oblique-incident light proves that utilizing the high-order band gaps of PCs is an efficient method to lower the difficulties of fabricating PCs, increase the etching depth of semiconductor materials, and reduce the coupling loss at the interface between optical fibers and PC device. (c) 2007 Elsevier B.V. All rights reserved.

Photonic band structures of two-dimensional photonic crystals with deformed lattices

Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.

Quantum master-equation approach to quantum transport through mesoscopic systems

For quantum transport through mesoscopic systems, a quantum master-equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of Gurvitz's approach for quantum transport and quantum measurement, namely, to finite temperature and arbitrary bias voltage. Our derivation starts from a second-order cumulant expansion of the tunneling Hamiltonian; then follows the conditional average over the electrode reservoir states. As a consequence, in the usual weak-tunneling regime, the established formalism is applicable for a wide range of transport problems. The validity of the formalism and its convenience in application are well illustrated by a number of examples.

Gain measurement and anomalous decrease of peak gain at long wavelength for InAs/GaAs quantum-dot lasers

Mode gain spectrum is measured by the Fourier series expansion method for InAs/GaAs quantum-dot (QD) lasers with seven stacks of QDs at different injection currents. Gain spectra with distinctive peaks are observed at the short and long wavelengths of about 1210 nm and 1300 nm. For a QD laser with the cavity length of 1060 mu m, the peak gain of the long wavelength first increases slowly or even decreases with the injection current as the peak gain of the short wavelength increases quickly, and finally increases quickly before approaching the saturated values as the injection current further increases.

Structure dependence of mode edges in photonic crystal waveguide with silicon on insulator

The mode edges of photonic crystal waveguide with triangular lattice based on a silicon-on-insulator slab are investigated by combination of the effective index method and two-dimensional plane wave expansion method. The variations of waveguide-mode edges with structure parameters of photonic crystal are deduced. When the ratio of the radius of air holes to the lattice constrant, r/Lambda, is fixed and the lattice constant of photonic crystal, Lambda, increases, the waveguide-mode edges shift to longer wavelengths. When Lambda is fixed and r/Lambda increases, the waveguide-mode edges shift to shorter wavelengths. Additionally, when r/Lambda and Lambda are both fixed, the radius of the two-row air holes adjacent to the waveguide increases, the waveguide-mode edges shift to shorter wavelengths.

A two-dimensional photonic crystal slab mirror with silicon on insulator for wavelength 1.3 mu m

A concrete two-dimensional photonic crystal slab with triangular lattice used as a mirror for the light at wavelength 1.3 mu m with a silicon-on-insulator (Sol) substrate is designed by the three-dimensional plane wave expansion method. For TE-like modes, the bandgap in the F-K direction is from 1087nm to 1559nm. The central wavelength in the bandgap is about 1.3 mu m, hence the incident light at wavelength 1.3 mu m will be strongly reflected. Experimentally, such a photonic crystal slab is fabricated on an SOI substrate by the combination of EBL and ICP etching. The measurement of its transmission characteristics shows the bandgap edge in a longer wavelength is about 1540mn. The little discrepancy between the experimental data and the theoretical values is mainly due to the size discrepancy of the fabricated air holes.

Light-propagation characteristics of photonic crystal waveguide based on SOI materials at different polarized states

Straight single-line defect optical waveguides in photonic crystal slabs are designed by the plane wave expansion method and fabricated into silicon-on-insulator (SOI) wafer by 248-nm deep UV lithography. We present an efficient way to measure the light transmission spectrum of the photonic crystal waveguide (PhC WG) at given polarization states. By employing the Mueller/Stokes method, we measure and analyse the light propagation properties of the PhC WG at different polarized states. It is shown that experimental results are in agreement with the simulation results of the three-dimensional finite-difference-time-domain method.

Electronic structures of GaAs/AlAs lateral superlattices

The electronic energy subbands and minigaps in lateral superlattices (LSLs) have been calculated by the plane-wave expansion method. The effect of the lateral modulation on the critical well width at which an indirect-direct (X-Gamma) optical transition occurs in the LSLs is investigated. Our theoretical results are in agreement with the available experimental data. Totally at variance with the previous variation calculational results, the minigaps between the first two subbands in LSLs, as functions of the modulation period, exhibit a maximum value at a specific length and disappear on decreasing the modulation period further. The modulations of several types of lateral potential are also evaluated; the indication is that the out-of-phase modulation on either side of the wells is the strongest while the in-phase modulation is the weakest. Our calculations also show that the effect of the difference between the effective masses of the electrons in the different materials on the subband structures is significant.

Two-dimensional photonic crystals with a large photonic band gap designed by a rapid genetic algorithm

We used Plane Wave Expansion Method and a Rapid Genetic Algorithm to design two-dimensional photonic crystals with a large absolute band gap. A filling fraction controlling operator and Fourier transform data storage mechanism had been integrated into the genetic operators to get desired photonic crystals effectively and efficiently. Starting from randomly generated photonic crystals, the proposed RGA evolved toward the best objectives and yielded a square lattice photonic crystal with the band gap (defined as the gap to mid-gap ratio) as large as 13.25%. Furthermore, the evolutionary objective was modified and resulted in a satisfactory PC for better application to slab system.