Laser backscattering analytical model of Doppler power spectra about rotating convex quadric bodies of revolution

We propose an analytical model of Doppler power spectra in backscatter from arbitrary rough convex quadric bodies of revolution (whose lateral surface is a quadric) rotating around axes. In the global Cartesian coordinate system, the analytical model deduced is suitable for general convex quadric body of revolution. Based on this analytical model, the Doppler power spectra of cones, cylinders, paraboloids of revolution, and sphere–cones combination are proposed. We analyze numerically the influence of geometric parameters, aspect angle, wavelength and reflectance of rough surface of the objects on the broadened spectra because of the Doppler effect. This analytical solution may contribute to laser Doppler velocimetry, and remote sensing of ballistic missile that spin.     

转动圆柱和圆锥的激光距离多普勒像分析模型

提出了一个新的转动圆柱和圆锥的激光距离多普勒像分析模型.该模型能分析圆柱和圆锥的几何参量、表面材料、姿态和脉冲宽度对这两种目标的距离多普勒像的影响,并能退化到平面波下的圆柱和圆锥的多普勒谱分析模型.数值分析了几何参量、表面材料、姿态和脉冲宽度对距离多普勒像的影响.理论和测量相结合,这个分析模型能用来进行圆柱和圆锥参量的识别.这个分析模型的解析表达式对于多普勒速度计和激光雷达应用有着重要的意义. 关键词： 光散射 双向反射分布函数 距离多普勒 目标识别     

Modified hollow Gaussian beam and its paraxial propagation

A model named modified hollow Gaussian beam (HGB) is proposed to describe a dark hollow beam with adjustable beam spot size, central dark size and darkness factor. In this modified model, both the beam spot size and the central dark size will be convergent to finite constants as the beam order approaches infinity, which are much different from that of the previous unmodified model, where the beam spot size and the central dark size will not be convergent as the beam order approaches infinity. The dependences of the propagation factor of modified and unmodified HGBs on the beam order are found to be the same. Based on the Collins integral, analytical formulas for the modified HGB propagating through aligned and misaligned optical system are derived. Some numerical examples are given.     

Superluminal propagation in resonant dissipative media

We analyse the superluminal propagation of optical narrow-band pulses at resonances in dissipative media. We find that, for a broad class of optical systems holding this type of lossy faster-than-light transmission capability, the output waveform is an attenuated, time-advanced version of the input which can be interpreted as the result of the interference of two scaled replicas of the input having a positive relative delay. This analysis is shown to apply, among other scenarios, both in the propagation in a passive bulk medium at an electronic resonance and in a dielectric waveguide coupled to a lossy micro-ring resonator.     

Experimental determination of the band structure of photonic crystals of colloidal silica spheres

A photonic band structure of colloidal crystals of silica spheres is analytically determined by a band model with three fitting parameters: the sphere size, the effective refractive index, and the band-gap. Optical properties of the crystals annealed at various temperatures were characterized by a procedure similar to X-ray diffraction technique, and the width of photonic band-gap measured from the transmission spectra experimentally servers as an additional check on the validation of the model. The photonic band structures defined by the band-gap, the refractive index, and the Brillouin zone are obviously superior to the use of the Bragg's expression involving simple zone folding.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

Between right- and left-handed media

We report analytical calculations for the propagation of electromagnetic radiation through an inhomogeneous layer whose refractive index varies in one-dimension situated between bulk right- and left-handed media. Significant field localization is generated in the layer that is caused by the coherent superposition of evanescent waves. The strength of the field localization and the transmission properties of the layer are investigated as a function of the layer width, losses and defects in the refractive index; the former two being modelled by continuous changes, and the latter by discontinuous changes, in the index profile.     

Depolarization characteristics of incompletely polarized and partially coherent laser beams in slant atmospheric turbulence

Based on the cross-spectral density function of transmission theory and the unified theory of coherence and polarization, the depolarization characteristics of incompletely polarized and partially coherent laser propagation in slant atmospheric turbulence are investigated. According to extended Huygens–Fresnel principle, the analytical expressions for intensity and degree of polarization in the slant path are derived. The effects of the wavelength, the initial spot size and the transmission distance on the intensity and degree of polarization are described. The results show that a more stable distribution of the degree of polarization at the receiver is obtained with increasing wavelength for a certain receiver height. The conclusions play an important role in optical communications and target recognition.     

Focal field computation of an arbitrarily polarized beam using fast Fourier transforms

In this work the vectorial diffraction theory of Richards and Wolf is extended to compute the focal field components of an arbitrarily polarized beam using fast Fourier transform (FFT) operations. Here the arbitrarily polarized pupil function is written as the vector sum of two mutually perpendicularly polarized pupil functions. The FFT based focal field expressions are particularly useful to compute the focal field components of pupil functions without a simple analytical form. We have then applied these expressions to simulate the effects of Zernike mode aberrations on the point spread functions of a number of important cylindrical-vector beam profiles such as radially and azimuthally polarized and helical light beams.     

Modelling the magnetorefractive effect in giant magnetoresistive granular and layered materials

The Zhang–Levy–Granovskii (Z–L–G) model of the magnetorefractive effect (MRE) in granular films and the Jacquet–Valet (J–V) model, originally developed for magnetic multilayers, are compared and their common origin demonstrated. Simulations in an extended Hagen–Rubens (H–R) model give new insight into the variation with wavelength of the MRE, and the relative dependence of giant magnetoresistance (GMR) and the MRE to material and experimental parameters such as bulk and interface scattering parameters, mean free paths, grain diameter, polarisation and reflection geometry is explored. The sensitivity of the size, wavelength dependence and the position of the depth of the minimum in the MRE spectra to the different parameters is verified. We establish powerful new equations to correlate the MRE and GMR, and we analyse their validity for a variety of film parameters. This suggests a new approach to the use of the MRE in sensing GMR in the films.     

Height-dependence of spatio-temporal spectra of wall-bounded turbulence – LES results and model predictions

Wavenumber–frequency spectra of the streamwise velocity component obtained from large-eddy simulations (LES) are presented. Following recent work we show that the main features, a Doppler shift and a Doppler broadening of frequencies, are captured by an advection model based on the Tennekes–Kraichnan random-sweeping hypothesis with additional mean flow. In this paper, we focus on the height-dependence of the spectra within the logarithmic layer of the flow. We furthermore benchmark an analytical model spectrum that takes the predictions of the random-sweeping model as a starting point and find good agreement with the LES data. We also quantify the influence of the LES grid resolution on the wavenumber–frequency spectra.     

Communication modes in scalar diffraction

The communication modes are a useful concept in studies of optical resolution, wave propagation, and image synthesis. We present an overview of earlier results on the communication modes in scalar diffraction theory. Besides the general theory, the modes are reviewed for the far-field and Fresnel regimes, and new eigenequations are derived for wide-angle diffraction. We prove a conjugate relationship between the transmitting and receiving modes in a general symmetric system. We also suggest an approximate method for far-field and Fresnel domain propagation, in which propagation amounts to a rotation of each mode in the complex plane. The main focus is on the near-field communication modes, where we present numerical examples of the modes and coupling strengths for a near-field geometry with a sub-wavelength size receiving domain. These results provide insights, for example, into the understanding of near-field scanning probe techniques.     

Optical coherence of planar microcavity emission

An analytical expression for the self-coherence function of a microcavity and a partially coherent source is derived. Excellent agreement is found between the model and the experimental measurements from two resonant-cavity light-emitting diodes. The variation of coherence length as a function of numerical aperture is examined and indicates that the variable coherence properties of planar microcavities are determined by the underlying coherences of the microcavity and the source. Furthermore, coherence-length variations approaching a factor of five can be achieved by engineering the cavity finesse.     

Talbot effect in cylindrical waveguides

We extend the theory of Talbot revivals for planar or rectangular geometry to the case of cylindrical waveguides. We derive a list of conditions that are necessary to obtain revivals in cylindrical geometry. A phase space approach based on the Wigner and the Kirkwood-Rihaczek functions provides a pictorial representation of interference phenomena that lead to the Talbot effect.     

Monte Carlo simulation and optical transmission studies of lattice-tunable column arrays composed of ferrofluids

The aggregation and rearrangement of nanoparticles embedded in a thin cell of ferrofluid at various applied magnetic fields was studied by Monte Carlo simulation. Regular microcolumns with the axis parallel to the magnetic field were observed with column size and spacing depending on the ramp speed of the applied field. Our model successfully simulated the reported experimental results that the column size decreases as the ramp speed increases, which is attributed to the diminishing time to achieve the final assembled state at a given final magnetic field. Column arrays of tunable lattice constants characterizing various spectroscopic dispersions are elucidated. The hexagonal structure of the aggregation of magnetic nanoparticles and optical dispersion were observed through an optical microscope. The transmission diffraction spectra depending on column spacings and sizes of the column array are simulated to yield results comparable to the experiment.     

A Monte Carlo study of penetration depth and sampling volume of polarized light in turbid media

Detection depth and sampling volume of polarized light in highly turbid, cylindrically-shaped samples are estimated using pathlength distributions calculated from a polarization-sensitive Monte Carlo model. Due to defined ranges of the polarized light pathlength distribution, the estimated penetration depth and the interrogated volume of the polarization-maintaining photon subpopulation are smaller than those of the whole collected photon population, the latter exhibiting a wider pathlength distribution resulting from multiple scattering. It is also demonstrated that the spatial interrogation extent of polarized light in turbid media is greatly affected by the experimental detection geometry.     

Statistical properties of correlated radial stochastic electromagnetic array beams on propagation

A kind of array beam named the correlated radial stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by use of tensor method. The analytical expression for the cross-spectral density matrix of this array beam propagating through the turbulent atmosphere and in free space is obtained after performing vector integration. Some typical numerical calculations are illustrated for the changes in the spectral density, spectral degree of polarization, and spectral degree of coherence of the beam on propagation. We find that the atmospheric turbulence can destroy the correlated effect among the beamlets.     

Rubinowicz transform of the MTPO surface integrals

The surface integral of the modified theory of physical optics is reduced to a line integral by using the Rubinowicz transform for the incident scattered fields by an arbitrary aperture in a black surface. The integral theorem of Kirchhoff is applied to the scattering geometry and the diffracted fields are expressed in terms of a line integral along the contour of the diffracting edge.