Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.

CCD扫描检测光束准直度

提出一种检测光束准直度的新方法。在对波面矢高进行定义的基础上，提出CCD轴向扫描检测激光束准直度的方法。利用采样光波在会聚透镜后形成的衍射图样，测量两个相同基准衍射图样之间的距离，即可确定入射光波的波面矢高，进而确定入射光波的准直度。在给出测量原理及模拟基准衍射图样的基础上．进行了实验验证。CCD轴向扫描方法具有结构简单、加工便利、操作方便的特点，是检测光束准直度的有效方法。

Electromagnetic wave propagation and scattering in a randomly-inhomogeneous dielectric sphere

Electromagnetic wave propagation and scattering in a sphere composed of an inhomogeneous medium having random variations in its permittivity are studied by utilizing the Born approximation in solving the vector wave equation. The variations in the permittivity are taken to be isotropic and homogeneous, and are spatially characterized by a Gaussian correlation function. Temporal variations in the medium are not considered.

Two particular problems are considered: i) finding the far-zone electric field when an electric or magnetic dipole is situated at the center of the sphere, and ii) finding the electric field at the sphere's center when a linearly polarized plane wave is incident upon it. Expressions are obtained for the mean-square magnitudes of the scattered field components; it is found that the mean of the product of any two transverse components vanishes. The cases where the wavelength is much shorter than correlation distance of the medium and where it is much longer than it are both considered.

Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal

In this paper we theoretically study the left-handed behaviors in a two-dimensional triangular photonic crystal made of elliptical rods in air. An absolute left-handed region is found in the second photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Typical left-handed behaviors such as negative refraction, flat superlensing and plano-concave lensing are demonstrated by the finite-difference time-domain simulations. These behaviors are also compared with the quasi-negative refraction and the resulted focusing effects in a square-lattice two-dimensional photonic crystal. (c) 2005 Optical Society of America

Scattering by two degenerate anisotropic modes in square-lattice dielectric photonic crystals

We systematically investigate the square-lattice dielectric photonic crystals that have been used to demonstrate flat slab imaging experimentally. A right-handed Bloch mode is found in the left-handed frequency region by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Using the multiple scattering theory, numerical simulations demonstrate that the left-handed mode and the right-handed mode are excited simultaneously by a point source and result in two kinds of transmitted waves. Impacted by the evanescent waves, superposition of these transmitted waves brings on complicated near field distributions such as the so-called imaging and its disappearance.

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.

Analytical vectorial structure of hollow Gaussian beams in the far field

The analytical vectorial structure of HGB is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HGB in the far-field, which is composed of TE term and TM term, are demonstrated. The physics pictures of HGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HGB propagation. (c) 2008 Optical Society of America.

Flexoelectro-optic properties of chiral nematic liquid crystals in the uniform standing helix configuration.

The flexoelectro-optic effect describes the rotation of the optic axis of a short-pitch chiral nematic liquid crystal under the application of an electric field. We investigate the effect in the uniform standing helix, or "Grandjean" configuration. An in-plane electric field is applied. The director profile is determined numerically using a static one-dimensional continuum model with strong surface anchoring. The Berreman method is used to solve for plane-wave solutions to Maxwell's equations, and predict the optical properties of the resulting structure in general cases. By using a chiral nematic with short pitch between crossed polarizers an optical switch may be generated. With no applied field the configuration is nontransmissive at normal incidence, but becomes transmissive with an applied field. For this case, numerical results using the Berreman method are supplemented with an analytic theory and found to be in good agreement. The transmitted intensity as a function of tilt, the contrast ratio, and the tilt required for full intensity modulation are presented. The angular dependence of the transmission is calculated and the isocontrast curves are plotted. For typical material and cell parameters a switching speed of 0.017 ms and contrast ratio of 1500:1 at normal incidence are predicted, at a switch-on tilt of 41.5 degrees. Experimental verification of the analytic and numerical models is provided.

Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane

This paper provides a review of important results concerning the Geometrical Theory of Diffraction and Geometrical Optics. It also reviews the properties of the existing solution for the problem of diffraction of a time harmonic plane wave by a half-plane. New mathematical expressions are derived for the wave fields involved in the problem of diffraction of a time harmonic plane wave by a quarter-plane, including the secondary radiated waves. This leads to a precise representation of the diffraction coefficient describing the diffraction occurring at the corner of the quarter-plane. Our results for the secondary radiated waves are an important step towards finding a formula giving the corner diffraction coefficient everywhere. © 2012 The authors.

Aeroacoustic source measurement methods for characterizing the sound generated by ducted flow devices with higher-order modes.

The International Organization for Standardization (ISO) method 5136 is widely used in industry and academia to determine the sound power radiated into a duct by fans and other flow devices. The method involves placing the device at the center of a long cylindrical duct with anechoic terminations at each end to eliminate reflections. A single off-axis microphone is used on the inlet and outlet sides that can theoretically capture the plane-wave mode amplitudes but this does not provide enough information to fully account for higher-order modes. In this study, the "two-port" source model is formulated to include higher-order modes and applied for the first three modes. This requires six independent surface pressure measurements on each side or "port." The resulting experimental set-up is much shorter than the ISO rig and does not require anechoic terminations. An array of six external loudspeaker sources is used to characterize the passive part of the two-port model and the set-up provides a framework to account for transmission of higher-order modes through a fan. The relative importance of the higher-order modes has been considered and their effect on inaccuracies when using the ISO method to find source sound power has been analyzed.

Design of novel polarization beam splitter in two-dimensional photonic crystal

We present the design and the simulation of an ultracompact high efficiency polarization beam splitter (PBS) based on the properties of the light waves propagating in straight waveguide and composite structure photonic crystal. The splitting properties of the PBS are numerically simulated and analyzed by using the plane wave expansion (PWE) method and finite difference time domain (FDTD) method. The PBS consists of three parts, namely, input waveguide, beam structure and output waveguide. It is shown that a high efficiency and a large separating angle for TE mode and TM mode can be achieved. Owing to these excellent features, including small size and high rate, the PBS makes a promising candidate in the future photonic integrated circuits.

Electronic structure and optical properties of GaN with Mn-doping

Calculations of the electronic structure and the density of states of GaN with Mn are carried out by means of first-principles plane-wave pesudopotential method based on density functional theory. The results reveal a 100% spin polarized impurity band in band structure of Ga1-xMnxN due to hybridization of Mn 3d and N 2p orbitals. The material is half metallic and suited for spin injectors. In addition, a peak of refractive index can be observed near the energy gap. The absorption coefficient increases in the UV region with the increase of the Mn content.

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.