Nanofibers with Bragg gratings from equidistant holes

We study nanofibers with Bragg gratings from equidistant holes. We calculate analytically and numerically the reflection and transmission coefficients for a single grating and also for a cavity formed by two gratings. We show that the reflection and transmission coefficients of the gratings substantially depend on the number of holes, the hole length, the hole depth, the grating period, and the light wavelength. We find that the reflection and transmission coefficients of the gratings depend on the orientation of the polarization vector of light with respect to the holes. Such a dependence is a result of the fact that the cross-section of the gratings is not cylindrically symmetric.     

The reflection and transmission of elastic waves through a plane of spheres in periodic arrangement

The work presented in this paper focuses on the reflection and transmission coefficients of an incident plane wave which impinges obliquely a plane of identical spheres arranged periodically in a homogeneous host with infinite extension. The Bloch theorem of periodic structure and the addition theorem of spherical wave functions are used to obtain the total scattering wave from all spherical scatterers periodically arranged in a plane. The total scattering wave in series form of spherical wave functions is then transformed into plane wave form in order to derive the reflection and transmission coefficients. Some numerical examples are given for different size, material constants and array patterns of spherical scatterers, and their influences on the reflection and transmission coefficients of a plane of spheres are discussed based on the numerical results. This study implies that a plane of spheres can be elaborately designed to serve as a sound barrier at a certain frequency range.     

Polarization conversion from highly conducting,asymmetric trapezoidal gratings

The differences in the curves of the zeroth-order cross-polarization reflection coeffients (p --> s and s --> p) versus angle of incidence have remarkable potential for application in scatterometry because, if the differences are larger than the measurement error, they could contribute to a reliable nondestructive technique for detecting asymmetries in grating profiles. The cross-polarization efficiencies of highly conducting metallic gratings with asymmetric trapezoidal profiles are investigated theoretically by means of a rigorous electromagnetic code. The results show that the differences between p --> s and s --> p conversion tend to be undetectable for highly conducting materials, a fact that limits, in principle, the application of this potential detection technique.     

Effect of Columnar Grain Orientation on Ultrasonic Plane Wave Energy Reflection and Transmission Behaviour in Anisotropic Austenitic Weld Materials

This article describes a comprehensive quantitative analysis on effect of columnar grain orientation on ultrasonic plane wave energy reflection and transmission behaviour in acoustically anisotropic austenitic weld materials. The quantitative results are presented for following general interfaces (a) Isotropic-Anisotropic, (b) Anisotropic-Isotropic, (c) Fluid-Anisotropic, (d) Anisotropic-Fluid, (e) Anisotropic-Anisotropic, (f) Anisotropic-Free surface occur during the ultrasonic non destructive evaluation of austenitic weld materials. Explicit analytical expressions are presented for energy reflection and transmission coefficients at an interface between two arbitrarily oriented transversely isotropic materials. By applying explicit analytical expressions for energy reflection and transmission coefficients, numerical results are presented for several columnar grain orientations of the transverse isotropic austenitic weld material including both real and complex domain of the reflected and transmitted normal component of slowness vectors. Valid domains of incident wave vector angles, angular dependency of energy reflection and transmission coefficients and critical angles for reflected and transmitted waves are discussed. The existence of a reflected (or) transmitted second branch of quasi shear vertical waves and its consequence to the ultrasonic non destructive testing of austenitic weld materials are investigated. The presented comprehensive quantitative evaluation provides an overview on the effect of anisotropic properties on energy reflection and transmission coefficients in columnar grained austenitic weld materials.     

Explicit expressions for spectral remittances of axially excited chiral sculptured thin films

Abstract

A theory of reflection and transmission of normally incident plane waves to a chiral sculptured thin film (CSTF) is presented. It is based on a coupled wave approach, in which the handedness-reversing reflections at the medium's interfaces are combined with the handedness-preserving distributed reflection inside the CSTF. Explicit formulas for the various reflection and transmission coefficients are derived. The method is shown to provide acceptable quantitative agreement with the exact full electromagnetic analysis.     

二维金属光栅的矢量模式研究

用矢量模式场来描述二维金属光栅各层中的电磁场。由边界条件,推导出模式场方程组;借助反射透射系数阵递推算法,得出了方程组的解。这种矢量模式方法物理概念清晰且稳定收敛,可以处理任意偏振态平面波入射到二维亚波长金属光栅中的衍射问题。     

Transverse-electric/transverse-magnetic polarization converter using 1D finite biaxial photonic crystal

We show that by using a one-dimensional anisotropic photonic structure, it is possible to realize optical wave polarization conversion by reflection and transmission processes. Thus a single incident S(P) polarized plane wave can produce a single reflected P(S) polarized wave and a single transmitted P(S) polarized wave. This polarization conversion property can be fulfilled with a simple finite superlattice (SL) constituted of anisotropic dielectric materials. We discuss the appropriate choices of the material and geometrical properties to realize such structures. The transmission and reflection coefficients are calculated in the framework of the Green's function method. The amplitude and the polarization characteristics of reflected and transmitted waves are determined as functions of frequency, wave vector k(parallel) (parallel to the interface), and the orientations of the principal axes of the layers constituting the SL. Specific applications of these results are given for a SL consisting of alternating biaxial anisotropic layers NaNO(2)/SbSI sandwiched between two identical semi-infinite isotropic media.     

Non-absorbing isotropic–uniaxial interfaces: refraction in ordinary and extraordinary total reflection

We study characteristics of refraction of plane waves in a non-absorbing isotropic–uniaxial interface in conditions of total and partial reflection when the incident wave has arbitrary direction with regard to the optical axis of the crystal and polarization. We analyse the ordinary and extraordinary fields and a phase shift that appears in the propagating wave which subsists in ordinary or extraordinary total reflection. We obtain that, unlike what happens in isotropic interfaces, under conditions of ordinary total reflection, the ordinary time-averaged Poynting vector changes its direction with the angle of incidence which does not depend on the existence of extraordinary total reflection. Extraordinary total reflection gives place to an analogous behaviour of the extraordinary time-averaged Poynting vector. In addition, we define and calculate in an explicit way complex coefficients of transmission for geometries with and without symmetry in partial and total reflection.     

Effect of Slab Interfaces on Diffraction of Visible Light by a Thick Volume Grating

Abstract

A theory of visible light diffraction by a volume grating is given for the case when reflection at slab interfaces cannot be neglected. A method of approximate solution of the second-order coupled-wave equations, applicable over a wide range of the grating vector orientation, is proposed. An appropriate boundary-value problem is discussed and solved in the two-wave approximation. The results are analytical and expressed in matrix notation suitable for both transmission and reflection diffraction gratings. Particular attention is given to the diffraction regime that arises in a slanted grating under the total internal reflection of the diffracted wave (TIRDW). Strong transmission anomalies occurring in the vicinity of the TIRDW threshold are established and analysed.     

Ultrasonic reflection by a planar distribution of cracks

Ultrasonic wave reflection and transmission by planar crack distributions is considered. General expressions for the reflection and transmission coefficients are derived for incident longitudinal and transverse time harmonic plane waves. For low frequencies, closed-form algebraic expressions are given in terms of the geometrical parameters, the material constants, and the incident wavefield. The results have been extended to statistical distributions, and reflection coefficients for equivalent statistical and deterministic distributions of penny-shaped cracks are compared. It is also shown that the Mode-I stress-intensity factor for a distribution of equal-sized cracks can be directly related to reflection data.     

Depolarization properties of a periodic sequence of chiral and material layers

We consider the electromagnetic field due to the reflection and transmission of a plane wave by a bounded periodic structure containing chiral layers. The problem is solved using the 2x2-block-representation transfer-matrix formulation. The frequency and angular dependences of the reflection and transmission coefficients are given. The boundaries of the passbands and stopbands are determined from the basic-element transfer-matrix eigenvalue analysis.     

Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork-shaped gratings

Expressions describing the vortex beams that are generated by the process of Fresnel diffraction of a Gaussian beam incident out of waist on fork-shaped gratings of arbitrary integer charge p, and vortex spots in the case of Fraunhofer diffraction by these gratings, are deduced. The common general transmission function of the gratings is defined and specialized for the cases of amplitude holograms, binary amplitude gratings, and their phase versions. Optical vortex beams, or carriers of phase singularity with charges mp and -mp, are the higher negative and positive diffraction-order beams. The radial part of their wave amplitudes is described by the product of the mpth-order Gauss-doughnut function and a Kummer function, or by the first-order Gauss-doughnut function and the difference of two modified Bessel functions whose orders do not match the singularity charge value. The wave amplitude and the intensity distributions are discussed for the near and far fields in the focal plane of a convergent lens, as well as the specialization of the results when the grating charge p=0; i.e., the grating turns from forked into rectilinear. The analytical expressions for the vortex radii are also discussed.     

Cross-polarization of light at a dielectric-biisotropic medium interface

The problem of reflection and refraction of TE- and TM-polarized electromagnetic waves at oblique incidence on a dielectric-biisotropic medium interface has been solved. Conditions for the Brewster angles, at which the reflected wave field contains only the cross-polarized component, are established and the influence of the chirality and nonreciprocity parameters on the reflection coefficients is analyzed. It is shown that the appearance of cross-polarization upon reflection from the biisotropic medium is caused by the presence of nonreciprocity in addition to chirality.     

The laws of plane defect wave propagation across the interface between two viscoplastic media

Relations determining the laws of reflection and refraction of a plane wave in the defect field at an interface between two viscoplastic media are obtained based on the dynamic equations of the continuum theory of defects. The reflection and transmission coefficients relating the amplitudes of reflected and transmitted waves to the incident wave amplitude are determined. The obtained relations are applied to a particular case of media with weakly decaying waves.     

Reflection and transmission of ultrasound by a region of damaged material

Reflection and transmission of ultrasonic waves by a layer-like region of distributed microcracks in a bulk material has been investigated. It has been assumed that for sufficiently low frequencies and far away from the damaged layer, the reflected and transmitted waves are plane waves. By applying the Betti reciprocal theorem to a cell containingN cracks, and by choosing one elastodynamic state as the actual wave state and the other as a suitably chosen auxiliary wave state, the reflection and transmission coefficients have been expressed in terms of integrals over theN cracks. Simple expressions have been obtained for the case that all cracks are identical and parallel to each other. For the case that the cracks do not interact with each other, numerical results for the reflection and transmission coefficients are presented for a distribution of penny-shaped cracks. The variation of these coefficients with frequency, relative layer thickness and angle of incidence has been displayed in graphs.     

Beam-width-dependent filtering properties of strong volume holographic gratings

The finite dimension of the incident beam used to read out volume holographic gratings has interesting effects on their filtering properties. As the readout beam gets narrower, there is more deviation from the ideal response predicted for monochromatic plane waves. In this paper we experimentally explore beam-width-dependent phenomena such as wavelength selectivities, angular selectivities, and diffracted beam profiles. Volume gratings in both reflection and transmission geometries are investigated near 1550 nm. Numerical simulations utilizing the technique of Fourier decomposition provide a satisfactory explanation and confirm that the spread of spatial harmonics is the main contributing factor.     

Effects of Cross-polarization Coupling in DFWM in Photorefractive Compound Semiconductor Crystals: Transmission Geometry

Abstract

Effects of cross-polarization coupling have been investigated in the case of degenerate four-wave mixing (DFWM) in absorbing semi-insulating compound semiconductor photorefractive (PR) crystals in transmission geometry. Considering pump beam depletion, and the slowly varying approximation, nonlinear coupled wave equations are obtained and have been solved numerically by a shooting method. Numerical results obtained from computer calculation are presented in graphical form. It is seen that if all the input beams are of the same polarization, cross-polarization coupling generates a phase-conjugate beam which is polarized in a plane orthogonal to that of the input beam.     

The Properties of Holographic Overlap Gratings

The analysis of a holographic beam expander which can, under perfect lossless conditions, convert a plane input beam into a plane diffracted beam, with a specified diffraction efficiency and beam width expansion ratio, is presented. Using solutions of the coupled-wave differential equations of [2], the effects of average loss, and both constant and spatially dependent dephasing are studied. These solutions are also used to compare the properties of overlap gratings with Kogelnik's [1] results for infinite gratings, and to extend the analysis of [4] to lossy, dephased cases. The maximum possible diffraction efficiency of an absorption overlap grating is shown to depend on its shape and also to lie between the values for Kogelnik's reflection and transmission cases.     

Reflection and transmission properties of holographic mirrors and holographic Fabry-Perot filters. I. Holographic mirrors with monochromatic light

The reflection and transmission coefficients of holographic mirrors (HM's) and holographic Fabry-Perot filters (HFPF's) are studied. The diffraction efficiencies, the angular selectivities, and the wavelength sensitivities of HM's and HFPF's and their effects on the spectrum and on the coherence properties of the incident light are investigated. The results show that holographic techniques can indeed be used to construct high-quality reflecting mirrors and Fabry-Perot filters. HM's illuminated by a monochromatic plane wave are investigated in detail. The reflection and transmission coefficients are first studied as functions of frequency (wavelength) of the incident light and also as functions of the angle of incidence. It is shown that HM's can be used as highly reflecting mirrors around their Bragg angle of incidences. Their reflectivity curves have fairly wide angular- and frequency-selectivity ranges.     

Transmission and reflection coefficients for surface transverse waves propagating under shorted metal strip gratings

Coupled-mode theory is used for the analysis of surface transverse waves (STWs) propagating under metal-strip gratings in the YZ plane of quartz. Analytical expressions are obtained for the reflection and transmission coefficients of waves propagating on rotated Y-cut substrates of weakly piezoelectric trigonal, tetragonal, or hexagonal crystals. A quadratic dependence of the stopband width on the height-to-period ratio of the electrodes is found. This is an agreement with stopband width measurements. The results can be used in the analysis of STW grating structures, particularly the two-port resonator filter.