Visual-Width of an Ultrasonic Gaussian Beam on the Schlieren Photograph and Explanation to the Nonspecularly Reflected Sound Field

On the Schlieren photograph,a continuous ultrasonic Gaussian beam and its nonspecularly reflected beams [Chin.Phys.Lett.16 (1999)819] always have limited visual-width,although the theoretical spatial distribution of the sound field is a continuous function.To study this problem,the first step is to investigate the visual-width of the beam on the photograph related to the sound pressure at the centre of the beam by the threshold of the optical system caused by the refraction of light;the second step is to explain the visual-width of nonspecularly reflected field.By applying a relevant threshold,checked by the visual width of the incident beam,to cut the theoretical curves of the reflected sound field,one can find the visual-width of the two reflected beams and the gap between them correspond to that on the Schlieren photograph.     

Mean—Field Calculations for the Three—Dimensional Holstein Model

The electron-phonon Holstein model is studied in three spatial dimensions.It is argued that this model can be used to account for major features of the high-Tc BaPb1-xBixO3 and BaxK1-xBiO3 systems.Mean-field calculations are performed via a path integral representation of the model.Charge-density-wave order parameters and transition temperatures are obtained.     

Characterization of Nonparaxial Truncated Cosine-Gaussian Beams and the Beam Quality in the Far Field

The analytical expression characterizing the propagation of nonparaxial truncated cosine-Gaussian （COG） beams in free space is derived, and some special cases are discussed. The extended power in the bucket （PIB） is proposed to characterize the beam quality of nonparaxial truncated beams in the far field. It is shown that the extended PIB is applicable to nonparaxial truncated beams, and the PIB of nonparaxial truncated CoG beams depends on the decentred parameter, waist-width-to-wavelength ratio, truncation parameter, and bucket size chosen.     

Reversible Decoherence of a Mesoscopic Superposition Driven by a Time—Dependent External Field

By using the normal-ordering technique in the coherent state representation,we discuss the dynamical evolution of the coherence of a Schrodinger cat state in a high Q cavity coupled to another resonator in the presence of external fields.During the progression of the coherence,we pay particular attention to the effect of the external fields,as well as to the initial phase of the Schrodinger cat state.     

A Simple Calculation Approach for the Second－Harmonic Sound Beam Generated by an Arbitrary Distribution Source

We present a simple calculation approach for the fundamental and second-harmonic sound beams with an arbitrary distribution source in the quasilinear approximation. The analysis is based on the assumption that the source function with an arbitrary geometry and distribution is expanded into the sum of a set of two-dimensional Gaussian functions. The two- and five-dimensional integral solutions for the fundamental and second-harmonic fields are, respectively, reduced in terms of Gaussian functions and simple one-dimensional integrals. The numerical evaluation of field distributions is then greatly simplified.     

Propagation of Partially Coherent Twisted Anisotropic Gaussian—Schell Model Beams in the Spatial—Frequency Domain

The generalized Collins formula for partially coherent beams through axially non-symmetrical optical systems in the spatial-frequency domain is derived by means of the tensor method.Based on this formula,the tensor ABCD law in the spatial-frequency domain for partially coherent twisted anisotropic Gaussian-Schell model (GSM) beams is derived,which governs the transformation of the twisted anisotropic GSM beams in the spatialfrequency domain.An example of an application is provided.     

A Pseudospectral Time—Domain Algorithm for Calculating the Band Structure of a Two—Dimensional Photonic Crystal

A pseudospectral time-domain (PSTD) method is developed for calculating the band structure of a two-dimensional photonic crystal.Maxwell‘s equations are rewritten in terms of period fields by using the Bloch theorem.Instead of spatial finite differences,the fast Fourier transform is used to calculate the spatial derivatives.To reach a similar accuracy,fewer sample points are required in the present PSTD method as compared to the conventional finite-difference time-domain methods.Our numerical simulation shows that the present PSTD method is an efficient and accurate method for calculating the band structure of a photonic crystal.