Rigorous theory of the diffraction of Gaussian beams by finite gratings: TM polarization

Diffraction of TM-polarized Gaussian beams by N equally spaced slits (finite grating) in a planar perfectly conducting thick screen is treated. We extend to the TM polarization case the results of a previous paper where the TE polarization was considered. The far-field diffraction patterns, the transmission coefficient tau, and the normally diffracted energy E as a function of several optogeometrical parameters are analyzed within the so-called vectorial region. The existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits is shown. In addition, the property E=Ntau/lambda, valid in the scalar region, is extended to the TM polarization case in the vectorial region, lambda being the wavelength. The coupling between slits is analyzed, giving an oscillating amplitude-decreasing function as the separation between slits increases, where the period for these oscillations is the wavelength lambda. Finally, the extraordinary optical transmission phenomena that appear when the wavelength is larger than the slit width (subwavelength regime) are analyzed.     

Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions.     

Transmission of an inhomogeneous plane wave through an electrically small aperture in a perfectly conducting plane screen

Most solutions for electromagnetic diffraction by a circular aperture in a perfectly conducting plane screen are for an incident homogeneous (propagating) plane wave. When the aperture is electrically small (dimensions small compared to the wavelength), the well-known transmission coefficient behaves as the fourth power of the diameter/wavelength. We consider the case in which the incident field is an inhomogeneous (evanescent) plane wave. Numerical calculations for the electrically small circular aperture show that the transmission coefficient for an inhomogeneous plane wave can be substantially greater than for a homogeneous plane wave at the same frequency. This observation may be helpful in explaining the increased transmission recently reported for electrically small apertures in plane screens with modifications. The numerical calculations for the electrically small aperture are in agreement with results from approximate analytical expressions that are based on the equivalent electric and magnetic dipole moments for the electrically small complementary disk.     

Wideband two-port beam splitter of a binary fused-silica phase grating

The usual beam splitter of multilayer-coated film with a wideband spectrum is not easy to achieve. We describe the realization of a wideband transmission two-port beam splitter based on a binary fused-silica phase grating. To achieve high efficiency and equality in the diffracted 0th and -1st orders, the grating profile parameters are optimized using rigorous coupled-wave analysis at a wavelength of 1550 nm. Holographic recording and the inductively coupled plasma dry etching technique are used to fabricate the fused-silica beam splitter grating. The measured efficiency of (45% x 2) = 90% diffracted into the both orders can be obtained with the fabricated grating under Littrow mounting. The physical mechanism of such a wideband two-port beam splitter grating can be well explained by the modal method based on two-beam interference of the modes excited by the incident wave. With the high damage threshold, low coefficient of thermal expansion, and wideband high efficiency, the presented beam splitter etched in fused silica should be a useful optical element for a variety of practical applications.     

Observation of high voltage resonances in one-dimensional arrays

Dynamic states in parallel one-dimensional arrays of small Josephson tunnel junctions are experimentally investigated in the presence of an external magnetic field H. In addition to conventional Fiske modes and flux-flow branches, the current-voltage characteristics exhibit a new type of resonances which appear in higher voltage regions as additional groups of resonant steps. These resonances can be explained in terms of a simple kinematic model, in the limit where the fluxon frequency is higher than the maximum linear wave frequency. The model is in good agreement with reported experiments.     

Properties of TM resonances on metallic slit gratings

Electromagnetic resonances on metallic slit gratings induced by TM polarized incident light have been investigated and physically interpreted. We have developed an electromagnetic model imposing surface impedance boundary conditions on the metallic grating surface from which we derive simple formulas explaining all physical properties of these resonances. It is demonstrated that Fabry-Perot (or cavity) resonances are generated by the zeroth slit mode yielding extraordinary transmission. For very narrow slits, the resonant H-field is squeezed to the slit walls and causes enhanced power losses. The excitation of surface plasmon polaritons (SPPs), however, is generated by two mode coupling. SPPs are linked to sharp absorption peaks and dips in transmittance. It is shown that these phenomena are primarily caused by the interaction of the electromagnetic fields with the finite conducting slit walls. These findings have been confirmed by measured transmittance data of gold gratings with periods of 0.5 μm, 1 μm, and 2 μm.     

Bistable reflection and plane transverse magnetic wave passage in a dimensionally quantized film

The self-consistent problem of the interaction of a plane transverse magnetic wave with a dimensionally quantized semiconductor film is studied. At grazing incidence of the wave on the film, the conditions for hysteresis (i.e. bistable) reflection and transmission, with variation in the incident field intensity, are obtained. Bistable reflection and transmission by the film are determined by the non-linear resonant dependence of the film permittivity on the electromagnetic field intensity. A detailed analysis for a GaAs film in an IR field (CO₂ laser) is carried out.     

Three-dimensional electromagnetic diffraction of a Gaussian beam by a perfectly conducting half-plane

Formulas are derived for the diffraction of a three-dimensional electromagnetic Gaussian beam by a perfectly conducting half-plane. The beam can be incident from any direction, and the main component of the electric field can point in any direction on the plane of the beam waist. The center of the beam waist is on the edge of the half-plane. The incident beam is constructed as a superposition of plane waves, and the total diffracted field is obtained from a superposition of the diffracted fields that are due to each plane wave. Physical constraints that limit the size and direction of the beam relative to the half-plane are described and incorporated into the theory. The scattered field in the far zone is obtained by asymptotic evaluation of the general formulas. Graphical results for the near-field as well as far-field patterns are presented and discussed.     

Relativistic Cherenkov microwave oscillator without a guiding magnetic field

A relativistic Cherenkov microwave oscillator without a guiding magnetic field has been designed, constructed, and tested in which a continuous cylindrical electron beam propagates in a short (L ≈ 3λ, λ being the radiation wavelength) resonant slow-wave structure. The electron beam is energy-modulated at the input of the interaction space, which provides conditions for the energy exchange at a wave phase velocity exceeding the particle velocity. The effective beam-wave coupling is provided by a nearly homogeneous profile of the longitudinal electric field component of the synchronous wave in the interaction space cross section. The efficiency of power conversion from high-current electron beam to electromagnetic radiation at E₀₁ mode is about 8% at a maximum output pulse radiation power of 1.2 ± 0.3 GW and a working frequency of 4.05 GHz.     

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.     

Diffraction Grating Anomalies: An Experimental Study of Phase Shifts and Resonances

The diffracted intensities at the different orders were measured for both polarization components as a function of the wavelength. The phase difference was also obtained. Certain anomalies show clearly a resonant behaviour in phase and intensity. In the plots of the polarization properties we have included the Rayleigh wavelengths and also the wavelengths for which resonances of surface plasma oscillations are expected. Some of the observed resonances are far from these wavelengths. Among certain orders a similar behaviour was observed, except for a wavelength shift.     

Effects of Arbitrary Phase Shift on the Higher-order Self-diffraction in Absorptive Photorefractive Medium

Abstract

Interactions between optical beams incident upon and two higher-order self-diffracted beams generated within an absorptive photorefractive material are investigated by solving a set of coupled differential equations. The medium is assumed to be free of linear and circular birefringence. Arbitrary phase shift between the light grating and the refractive index grating is considered. It is shown that under favourable conditions, a significant amount of power may be transferred to the newly generated waves. Investigated are the effects of phase shift, thickness and absorption of the crystal, coupling constant and off-Bragg parameter on energy transfer to the higher-order diffracted beams. It is shown that in the case of phase-shift other than π/2, higher-order self-diffracted beams can be generated on both sides of the input beams. Coupled wave equations are solved numerically by a fourth-order Runge-Kutta method and results are presented in graphical form. This analysis is valid for the near collinear interacting beam geometry, i.e. in the case of large grating spacing.     

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.     

Vp×B electron linear accelerator with TE-wave assisted by plasma for beam stabilization

The V_p × B acceleration scheme with the use of a transverse electromagnetic wave is demonstrated experimentally, in which a pre-ionized plasma is supplemented for obtaining a stable electron beam. The slow wave structure employed here is a dielectric loaded waveguide, and an electron beam in the accelerator induces surfaces charges on the dielectric. The electron beam on account of acceleration also produces a dilute plasma to neutralize the surface charges. An initial energy gain of 2.5 keV for the electron beam is observed from an incident energy of 60 keV without any external vertical magnetic field. When an external vertical magnetic field of 1.5 G is applied under the same conditions for performing the V_p × B scheme, an additional 1.5 keV energy gain is observed.     

Ray optics calculation of the radiation forces exerted on a dielectric sphere in an evanescent field

A ray optics approach was used to calculate the forces and the torque exerted on a dielectric sphere in the evanescent field produced by a linearly polarized Gaussian beam. The particle was assumed to be immersed in a dielectric fluid next to a solid dielectric plate with the evanescent field produced at the solid-fluid interface. Comparisons with calculations performed by use of more rigorous electromagnetic wave theory show that the ray optics results agree to within a factor of 2 even for particle radii as small as twice the incident wavelength. Calculation of the forces for conditions typical of a total internal reflection microscopy experiment show that the evanescent field has a negligible effect on either the net forces exerted on the particle or the particle motion (i.e., rotation or translation parallel to the interface). By our modifying the parameters of the experiment, however-namely, the incident beam power, radius of incident beam, and evanescent wave penetration depth-forces that are comparable with the net particle weight and capable of translating the particle several micrometers per second, as well as rotating the particle several revolutions per second, can be produced. The ability to micromanipulate a particle in this fashion could offer useful applications for studying particle and surface interactions.     

Diffraction effects in the propagation of radiation in polarizable layers

The very low transmission of light through holes smaller than the wavelength has been found to be enhanced for subwavelength apertures in metallic surfaces with periodic corrugations. This effect has been attributed to the interaction of light with surface plasmons. Similar effects obtained subsequently for non-metallic surfaces have been attributed to evanescent waves on the surface produced by the diffracted Bloch waves from different points in the array. We present an exact solution of Maxwell's equations in the discrete dipole approximation (DDA) for a periodic array of polarizable point dipoles in a layer. Metallic as well as non metallic layers are described. When the wavelength is smaller than the lattice period there is a Bragg's scattered wave, while for subwavelength conditions an evanescent wave on the surface appears. The transmission/reflection coefficients are found to oscillate as a function of frequency, with resonances occurring in a broad range of frequencies depending on the polarizability, at which the evanescent field is enhanced. A detailed study is presented for nanostructured arrays. We find that this model agrees with features observed in experiments through hole arrays supporting the role played by diffraction during light transmission through such arrays without invoking surface plasmons and providing a base to analyze more complex geometries.     

不同应力波穿过多条非线性变形节理时的透射特性

基于节理非线性位移不连续模型,分析不同弹性纵波正向入射多条节理时的透射规律。利用半解析半数值解法得到透射初至波质点振动速度一维数值差分解,进而研究不同类型、不同振幅的入射纵波穿过多条节理时,初至波质点速度幅值、能量、频谱及时间延迟的变化特性。研究表明,透射能力由大到小的顺序为:矩形波、半正弦波、三角形波。速度透射系数、能量透射系数、透射波中高谐波频域幅值均随入射脉冲幅值增大而增大;延迟时间随入射波振幅的增大而减小,且三角波入射时的时间延迟大于半正弦波。随着节理条数的增加,速度和能量透射系数逐渐降低,且下降速度逐渐减慢;高谐波频域幅值先增大后下降,且下降速度逐渐减慢;时间延迟增大的速度逐渐加快。     

Comment on ‘Two-state Description of Total Polarization by Means of Singular Eigenvalue Problems’

We derive a formulation that can be used to determine the electromagnetic field distribution in the focal region of a wide-angle spherical mirror illuminated by an obliquely incident and linearly polarized plane monochromatic wave. The integrals representing the diffracted fields derived in part 1 [1] for the two cases of polarization of the incident field are first suitably expanded in series form. The integrals with respect to the azimuth 0 are then evaluated analytically with the help of some new integration formulae developed in this paper. The diffracted field components for the two cases of incident polarization are finally expressed in forms suitable for numerical computation. Our formulae can be used to determine the three-dimensional field distribution in the caustic region of the mirror for any obliquity of the incident beam. Simpler expressions for the field components for a few special cases of interest are also derived. In particular, it is shown that the series solution obtained for the case of oblique incidence reduces to the simpler results found by previous authors for the case of normal incidence.     

Scattering of inhomogeneous plane waves by a slit formed with impedance and perfectly electric conducting half planes

Scattering of an inhomogeneous plane wave with an arbitrary angle of incidence travelling through a slit made of perfectly electric conducting and impedance half planes is investigated. For the investigation of the scattering phenomena evaluation of the modified theory of physical optics integrals are evaluated asymptotically. An inhomogeneous plane wave is taken into consideration by assuming the incident angle of a homogeneous plane wave as a complex parameter. Uniform asymptotic results will be employed for the correct solution of an incoming inhomogeneous plane wave scattering problem. Asymptotic evaluation is carried out for the reflected and diffracted fields. Diffracted fields are uniformly expressed in terms of the Fresnel functions. To obtain correct plots of the diffracted fields, complex detour parameter decomposition method is applied. Obtained resultant fields are plotted numerically.