Water wave diffraction by a small deformation of the ocean bottom for oblique incidence

Summary In this paper, the problem of oblique water wave diffraction by a small deformation of the bottom of a laterally unbounded ocean is considered using linear water wave theory. It is assumed that the fluid is incompressible and inviscid, and the flow irrotational. A perturbation analysis is employed to obtain the velocity potential, reflection and transmission coefficients up to the first order in terms of integrals involving the shape functions c(x) representing the bottom deformation by using Green's integral theorem. Two particular forms of the shape function are considered, and the integrals for the reflection and transmission coefficients are evaluated for these two different functions. Among those cases, for the particular case of a patch of sinusoidal ripples at the bottom, the reflection coefficient up to the first order is found to be an oscillatory function in the quotient of twice the wave number along the x-axis and the ripple wave number. When this quotient becomes one, the theory predicts a resonant interaction between the bed and free surface, and the reflection coefficient becomes a multiple of the number of ripples, and high reflection of the incident wave energy occurs if this number is large. Known results for the normal incidence are recovered as special cases. The numerical solutions for the reflection and transmission coefficients are also evaluated against wave numbers and angles of incidence.     

On diffraction of waves by the infinite grating of circular dielectric cylinders at oblique incidence: Floquet representation

Abstract

We investigate the diffraction of plane E-polarized electromagnetic waves by an infinite array of infinitely long circular dielectric cylinders for the most generalized case of oblique incidence. Employing the Sommerfeld integral representation of the Hankel function, and exploiting Poisson's summation formula in separation-of-variables solution, we have acquired a new representation for the diffraction of waves by the infinite grating of the circular dielectric cylinders at oblique incidence. The exact solutions for the external electric and magnetic field intensities have been derived in terms of the diffraction angles of the grating which are obtained by solving the grating equation. In addition, the transmitted and reflected fields of the infinite grating have been presented in terms of propagating and evanescent Floquet modes.     

Optical properties of a slightly absorbing film for oblique incidence

Approximate equations are derived for calculating the transmittance and reflectance of a slightly absorbing film when radiation is incident at an arbitrary angle. These formulas are compared with those derived from wave optics. Examination of the real and the imaginary parts of the complex phase change and the complex angle of refraction shows the simple equations to be consistent with the wave-optics formulation under the assumption that the imaginary part of the refractive index of the film is much smaller than its real counterpart.     

Mirrorless optical bistability in a semiconductor-doped-glass plate as a result of oblique incidence

A procedure to obtain optical bistability in a third-order nonlinear film (or parallel plate) of low refractive index without any external mirrors is investigated both theoretically and experimentally. If an s-polarized light is incident obliquely at a large angle of incidence on the film, the generation of optical bistability can be expected because of the resulting increase in the reflectivity at the surfaces. Arigorous analysis of the stationary transmission characteristics of the nonlinear film is done for both positive and negative nonlinear coefficients with a plane-wave model. In the experimental demonstration, a CdS(x)Se(1-x)doped glass (Hoya Y-52) plate and a cw Ar(+) laser are used as the nonlinear material and the light source, respectively. It is shown that three operations of optical bistability, optical limiting, and differential gain can be easily obtained through adjustment of the angle of incidence as an initial detuning. The measured nonlinearity is thermal, and the magnitude and sign of the nonlinear refractive index are determined.     

High-frequency ultrasonic cleaning tank utilizing oblique incidence

Transmission characteristics of a double-structured tank, used for high-frequency (1 MHz range) ultrasonic cleaning of semiconductor wafers and substrates, were improved by utilizing oblique incidence of ultrasonic waves. As the sound transmittivity through a plate in water varies with the angle of incidence, the bottom of the Pyrex glass inner container was slanted at the angle where strong transmission occurred. In the slant-bottom container, an intensive and uniform sound pressure distribution was measured with a polyvinylidene fluoride (PVDF) hydrophone probe. In comparison with the conventional horizontal-bottom container, it was shown that the distributions as well as amplitude of sound pressure were remarkably improved by slanting the bottom of the inner container at the proper angle     

Scattering by a dense finite layer of infinite cylinders at oblique incidence

This paper presents the scattering solution for a finite dense layer of cylinders irradiated by an arbitrarily polarized plane wave at a general incident direction. The theoretical formulation utilizes the effective field approach and quasi-crystalline approximation to derive the governing equations for the propagation constant and amplitudes of the effective waves. The finite layer thickness gives rise to effective waves propagating in both the forward and backward directions inside the dense medium. Formulas are developed for the far-field coherent and incoherent scattered intensities, as well as the extinction and scattering cross sections of the dense layer. The forward peak of the incoherent scattered intensity is shown to be shifted to the propagating direction of the effective waves. The influence of incident direction, layer thickness, and solid volume fraction on the scattering properties is illustrated by means of a numerical example.     

Angular tolerant resonant grating filters under oblique incidence

Resonant grating filters have been proposed as a promising alternative to multilayer stacks for narrowband free-space filtering. The efficiency of such filters under normal incidence has been demonstrated. Unfortunately, under oblique incidence, the limited angular tolerance of the resonance forbids any filtering applications with use of standard collimated incident beams. Using a multimode planar waveguide and a bi-atom grating, we show how to increase the angular tolerance up to the divergence of standard beams (0.2 deg) without modifying the spectral bandwidth (0.1 nm), under any oblique angle of incidence.     

Optical-fiber diameter determination by scattering at oblique incidence

A new nondestructive method for determination of the outer diameter of optical fibers is described. The principle of this technique is based on observing interference maxima in the scattered light from a fiber that is side illuminated by a laser beam at oblique incidence. This technique is easy to implement and can be applied to a fiber with an inhomogeneous and large core.     

Nonpolarizing guided-mode resonant grating filter for oblique incidence

A new type of guided-mode resonant grating filter is described. The filter is independent of polarization state for oblique incidence. The filter has a crossed grating structure, and the plane of incidence on the filter contains the symmetric axis of the grating structure. Theoretical considerations and numerical calculations using two-dimensional rigorous coupled-wave analysis show that a rhombic lattice structure is suitable to such filters. In this configuration an incident light wave is diffracted into the waveguide and is divided into two propagation modes whose directions are symmetric with respect to the plane of incidence. In particular, when the propagation directions of the two modes are perpendicular to each other, the fill factor of grating structure can be approximately 50%. The filter was designed for an incident angle of 45 degrees. Tolerances of setting errors and fabrication errors for this filter were estimated by numerical calculations.     

Broadband high-reflection multilayer coatings at oblique angles of incidence

The angular properties of various wideband high reflectors are investigated. The theory is developed for the design of high reflectors based on contiguous quarter-wave stacks for use at one oblique angle or for a range of angles of incidence. Numerical results are presented for several high reflectors designed to have a high reflectance in the 0.4-0.8-mum spectral region for use at 50 degrees and with angles of incidence ranging between 0 degrees and 50 degrees . A random error perturbation analysis shows that such layer systems can be produced experimentally.     

Water penetration fronts in thin films deposited at oblique incidence

Water penetration spots in thin films deposited at oblique incidence are shown to be nearly elliptical in shape. Water spreads laterally at greatest speed in the direction normal to the plane of incidence of the evaporant molecules. The ratio of the maximum and minimum speeds increases with the angle of incidence of the vapour and, for magnesium fluoride, is about 1.5 for an angle of 60°. The primary cause of the anisotropic water penetration effect is believed to be self-shadowing which occurs during the deposition of thin films, leading to a columnar microstructure with intermediate voids which act as sinks for penetrating liquids.     

4x4 ray matrix for a curved chirped grating at oblique incidence

The general 4x4 ray matrix of a grating is presented. This matrix suits the cases of transmission and reflection by a chirped grating with curved lines lying on a curved interface. The matrix presented applies to the general oblique incidence of the optical axis and therefore to nonorthogonal cases and to conical diffraction.     

Modification of the structure of Bessel beams under oblique incidence

The stability of a Bessel beam generated via an annular slit on the focal plane of a convergent lens as a function of the angle of incidence of a plane wave into the slit was measured. Although the paraxial approximation, along with an infinite lens assumption, predicts that the only change in the Bessel beam should be a displacement, experimental results showed that other slight changes were present. It was shown numerically that the way to take into account those changes is to abandon the quadratic phase approximation for the lens. Good agreement was then found between the experimental data and the numerical simulation.     

Wave forces on steeply-sloping sea walls: oblique incidence

Previous work, [3], studying the forces exerted by non-breaking, normally-incident water waves of small amplitude on a sloping sea wall is here extended to the case of oblique incidence. The range of applicability of the Galerkin solutions is increased by means of the Shanks transform. Results are presented for a planar, outward-sloping sea wall. In shallow water, the total normal wave force per unit span is found to decrease as the wall slope increases, except for extremely obliquely incident waves. In deep water, it increases. Regarded as a function of the angle of incidence , the wave force in shallow water is virtually independent of , except for very oblique waves. In deep water, by contrast, the force first increases with and then decreases. In this case, the maximum wave force does not occur for normally incident waves.     

Tunable, oblique incidence resonant grating filter for telecommunications

We have designed a tunable, oblique-incidence resonant grating filter that covers the C band as an add-drop device for incident TE-polarized light. We tune the filter by tilting a microelectromechanical systems platform onto which the filter is attached. The fabrication tolerances as well as the role of finite incident-beam size and limited device size were addressed. The maximum achievable efficiency of a finite-area device as well as a scaling law that relates the resonance peak width and the minimum device size is derived. In good agreement with simulations, measurements indicate a negligible change in shape of the resonance peak from 1526 nm at a 45 degrees angle of incidence to 1573 nm at a 53 degrees angle with a full width at half-maximum of 0.4 nm. In this range the shift of the peak wavelength is linear with respect to changes in the angle of incidence.     

Light scattering at oblique incidence on two coaxial cylinders

A solution for the problem of a plane wave at oblique incidence on two coaxial cylinders is presented. The solution of the wave equation is determined for various geometric regions, and boundary conditions are applied at the material interfaces. The resulting solution consists of a system of eight equations in eight unknown coefficients. Expressions for two of the Mueller-scattering matrix elements (S(11) and S(12)) and the extinction, scattering, and backscattering cross sections are derived. A numerical algorithm for the solution is developed and implemented. The algorithm is tested for several limiting cases: homogeneous, hollow, and metal-core cylinders at various angles of incidence for TM and TE waves. Comparisons of the results of the algorithm with the results of studies reported in the literature are made. The comparisons are favorable, achieving good agreement with published work. For two coaxial cylinders, the numerical calculations show that if one is to use light scattering as a diagnostic tool, both of the Mueller-scattering matrix elements S(11) and S(12) must be measured simultaneously. In addition, the backscattering cross section is very sensitive for monitoring change in the radii of the cylinders.     

斜入射光束时电光和旋光晶体的相移

提出了电光和旋光晶体中相移的精确计算方法。计算了电光和旋光效应中,当外界电场方向和传播方向任意时晶体的折射率。用作者建立的斜入射时晶体的相移公式研究了相移随入射角和方位角的改变。如果选择适当的方位角,相移对准直的灵敏度将有所改进。     

Polarization properties of oblique incidence scanning tunneling microscopy-tip-enhanced Raman spectroscopy

We used scanning tunneling microscopy-tip-enhanced Raman spectroscopy (STM-TERS) to study the polarization properties of near-field scattering on a crystalline material as well as on a dye adsorbate. The measurements on a (111)-oriented c-Si sample were found to be well described by a recently proposed model for TERS and allowed for a characterization of the polarization properties of the tips used. The tip enhancement was stronger for excitation radiation having a field component along the tip axis for both types of samples. A non-negligible enhancement was also found for the field component perpendicular to the tip axis.