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.     

Optical Diffraction in Close Proximity to Plane Apertures. I. Boundary-Value Solutions for Circular Apertures and Slits

In this paper the classical Rayleigh-Sommerfeld and Kirchhoff boundary-value diffraction integrals are solved in closed form for circular apertures and slits illuminated by normally incident plane waves. The mathematical expressions obtained involve no simplifying approximations and are free of singularities, except in the aperture plane itself. Their use for numerical computations was straightforward and provided new insight into the nature of diffraction in the near zone where the Fresnel approximation does not apply. The Rayleigh-Sommerfeld integrals were found to be very similar to each other, so that polarization effects appear to be negligibly small. On the other hand, they differ substantially at sub-wavelength differences from the aperture plane and do not correctly describe the diffracted field as an analytical continuation of the incident geometrical field.     

The theory of the boundary diffraction wave for wedge diffraction

A new potential function, line integration which gives the edge diffracted fields, is constructed for wedge diffraction by using the method of modified theory of physical optics. The surface integrals are transformed into line integrals by the technique of asymptotic reduction. As an application of the novel potential function, the diffracted field is obtained for the geometry of a wedge for arbitrary incidence of plane waves.     

Diffraction of evanescent plane waves by a resistive half-plane

Diffraction of evanescent plane waves by a resistive half-plane is examined. The scattering integrals are constructed with the modified theory of physical optics. These integrals are evaluated uniformly by using an unusual method. The scattered fields of evanescent waves are obtained by giving the angle of incidence a complex value. The diffracted waves are plotted numerically for different parameters of the incident field.     

Rib Waveguide Theory by the Spectral Index Method

The geometric theory of diffraction is a well known and very successful asymptotic technique in electromagnetics for the evaluation of scattered fields from objects that are large compared to the wavelength. Our recent work has produced approximate diffraction coefficients for diffracted rays from edges and corners in planar conducting or dielectric surfaces. These diffraction coefficients are tested here by comparing theoretical predictions with experimental measurements made at 30 GHz of the diffracted field from a conducting quarter plane. Very good agreement is found between this asymptotic approach and experimental results for a linearly polarised incident field, with the E field aligned with one of the edges of the quarter plane. The incident field direction is varied from 5° to 54° to the normal to the quarter plane and the total field is measured over a plane behind the target. Average agreement for intensity values is found to be around 95%.     

Scattering of inhomogeneous plane waves by a truncated cylindrical cap

Scattered fields of the inhomogeneous plane waves from a truncated cylindrical cap are obtained. Also the uniform diffracted fields are performed in terms of the Fresnel functions. Reflected and diffracted fields are obtained by using the physical optics and the geometrical theory of diffraction methods, respectively. All the mentioned results are plotted numerically for various numerical parameters.     

Readout signals calculated for near-field optical pickups with land and groove recording

Optical disk readout signals with a solid immersion lens (SIL) and the land-groove recording technique are calculated by use of a simplified vector-diffraction theory. In this method the full vector-diffraction theory is applied to calculate the diffracted light from the initial state of the disk, and the light scattered from the recorded marks is regarded as a perturbation. Using this method, we confirmed that the land-groove recording technique is effective as a means of cross-talk reduction even when the numerical aperture is more than 1. However, the top surface of the disk under the SIL must be flat, or the readout signal from marks recorded on a groove decays when the optical depth of the groove is greater than lambda/8.     

Aberrations of diffracted wave fields. I. Optical imaging

The concept of aberrations of diffracted waves is revisited by using the Rayleigh-Sommerfeld theory of diffraction, and it is pointed out that these aberrations are in a class by themselves; they are only deceptively similar to the aberrations of a rotationally symmetric imaging system. Although an exact Fourier-transform expression can be written for the diffracted wave field, its numerical calculation is cumbersome because of the dependence of the aberrations of the diffracted wave on the observation point. This is true regardless of whether the diffracted wave field is observed on a plane or a hemisphere. It is shown that the Fresnel and Fraunhofer approximations, which neglect these aberrations and thereby simplify the calculations, are valid in imaging applications.     

Superresolution Near-field Readout in Phase-Change Optical Disk Data Storage

Readout of a phase-change optical disk with a superresolution (SR) near-field structure (Super-RENS) is theoretically examined on the basis of three-dimensional, full-wave vector diffraction theory. Calculations have demonstrated that Super-RENS has a high spatial resolution beyond the diffraction limit in readout. The read signal is dependent on the nature of SR, the layer structure of the disk, and the state of polarization of the incident laser beam. For the Super-RENS in which antimony is used for SR readout, the readout signal is quite small, and the estimated carrier-to-noise ratio (CNR) is only ~30 dB for marks of 300 nm. For the Super-RENS in which a metallic region is formed during readout, the read signal is large, and the CNR can be as high as 50 dB in reading 300-nm marks.     

Optimization of the parallelogrammic grating diffraction efficiency for normally incident waves

The diffraction directivity of parallelogrammic gratings with second-order pitch is examined for a plane wave normally incident upon a corrugated waveguide structure. The three diffracted components are assumed to be in the form of guided waves, which permits a self-consistent calculation. The efficiencies of diffraction into the horizontal components are obtained. Also, the dependence of efficiency on grating thickness, waveguide thickness, grating pitch, and angle of inclination is determined. The approach provides a useful simulation tool for optimizing the design parameters for waveguide couplers with an orthogonal source.     

Vector diffraction and polarization effects in an optical disk system

The track pitch of current optical disks is comparable with the wavelength of the laser source. In this domain of the pitch-to-wavelength ratio, the complex-diffraction amplitudes are different for different incident polarization states, and the validity of the scalar diffraction theory is questionable. Furthermore, the use of multilayer coatings and high-numerical-aperture beams in modern optical disk technology inevitably entails the excitation of surface waves, which can disturb the baseball pattern significantly. To describe the interaction of a focused beam with a grooved multilayer system fully, it is necessary to have a rigorous vector theory. We use a rigorous vector theory to model the diffraction of light at the optical disk. We present the simulation and the experimental results and demonstrate the ability of this approach to predict or model accurately all essential features of beam-disk interaction, including the polarization effects and the excitation of surface waves.     

The interaction of two inclined cracks with dynamic stress wave loadings

To gain insight into the phenomenon of the interaction of stress waves with material defects and the linkage of two cracks, the transient response of two semi-infinite inclined cracks subjected to dynamic loading is examined. The solutions are obtained by the linear superposition of fundamental solutions in the Laplace transform domain. The fundamental solution is the exponentially distributed traction on crack faces proposed by Tsai and Ma [1]. The exact closed form solutions of stress intensity factor histories for these two inclined cracks subjected to incident plane waves and diffracted waves are obtained explicitly. These solutions are valid for the time interval from initial loading until the first wave scattered at one crack tip returns to the same crack tip after being diffracted by another crack tip. The result shows that the contribution of diffracted waves to stress intensity factors is much less than the incident waves. The probable crack propagation direction is predicted from the fracture criterion of maximum circumferential tensile stress. The linkage of these two cracks is also investigated in detail.     

Effect of surface plasmon excitations on the irradiance pattern of the return beam in optical disk data storage

The excitation of surface plasmons at a dielectric-metal interface is responsible for dips in the zeroth order diffraction efficiency of a metal grating at certain angles of incidence. The dips appear as dark bands in the returning irradiance pattern in an optical disk system and are seen only when there is a component of incident polarization that lies perpendicular to the tracks. The location of these bands is derived from theoretical considerations and is shown to depend on the track pitch and the materials involved, but not on the groove depth or width. The band locations are confirmed by zeroth order diffraction efficiency measurements as a function of incident angle. A possible negative effect of these bands on an optical disk system is the introduction of additional fluctuations and noise into the focusing and push-pull tracking signals.     

Uniform theory for the diffraction of evanescent plane waves

A uniform diffracted field is obtained in terms of Fresnel functions with complex argument by subtracting the unit step function from the Fresnel integral. The method is applied to the problem of diffraction of inhomogeneous plane waves by a perfectly conducting half-plane and wedge. The results are plotted numerically and compared with results reported in the literature.     

High-resolution optical diffraction microscopy

In an optical diffraction microscopy experiment, one measures the phase and amplitude of the field diffracted by the sample and uses an inversion algorithm to reconstruct its map of permittivity. We show that with an iterative procedure accounting for multiple scattering, it is possible to visualize details smaller than lambda/4 with relatively few illumination and observation angles. The roles of incident evanescent waves and noise are also investigated.     

Scattering of waves by a planar junction between resistive half-screen and perfectly electric conducting wedge

The diffraction of plane waves by a planar junction between a resistive half-plane and perfectly conducting wedge is investigated. First of all, the relation between the scattered geometrical optics waves and diffracted fields by a wedge is outlined. Then the scattered GO fields of the planar junction are obtained by subtracting the initial fields from the total geometrical optics waves. The diffracted waves by the junction is derived with the aid of the scattered GO waves’ structure. The behaviour of the fields is analysed numerically.     

Integral representation of the edge diffracted waves along the ray path of the transition region

The expression of the edge diffracted fields, in terms of the Fresnel integral, is transformed into a path integral. The obtained integral considers the integration of the incident field along the ray path of the transition region. The similarities of the path integral with Kirchhoff's theory of diffraction and the modified theory of physical optics are examined.     

Self-pumped phase-conjugate interferometer with a photorefractive iron-doped lithium-niobate crystal

A single object wave is amplitude divided by a beam splitter into two waves of equal intensity that are made to interfere at the back surface of an iron-doped lithium-niobate crystal so that the normal to the back surface is the angular bisector of the input waves. The interference results in the formation of a phase grating (Bragg grating) in the volume of the crystal. These waves are diffracted at the Bragg grating on both the front focal plane and the back focal plane of the crystal. The wave diffracted in the back focal plane from the Bragg grating and counterpropagating to the incident wave is observed to be the phase conjugate of the input object wave. The wave diffracted in the front focal plane of the Bragg grating is incorporated into the design of an interferometer to measure a specific in-plane displacement of the object wave. It is theoretically evaluated and experimentally demonstrated that interferometers such as those that incorporate conjugate-wave pairs are highly sensitive.     

Polarizationally Non-sensitive Pseudo-holographic Computer Reconstruction of Random Rough Surface

Abstract

The function, describing a profile of a random rough surface (RRS) is expanded in a Fourier series, i.e. the surface is considered as a composition of sinusoidal gratings. The total diffracted optical field from this RRS is a sum of the fields due to all harmonic gratings, since Kirchhoff's condition for ‘locally flat surface’ is realized for each harmonic grating at a given light wavelength and at an appropriate choice of the basic grating period. The registered s and p components of the diffracted (+1 diffraction orders of each harmonic gratings), incident and mixed optic fields are separated with an optical analyser. These fields are experimentally measured and from these values the phase and the amplitude of each grating are determined. The profile of the surface is reconstructed for s and p polarization of the light scattered field, when the electric vector of the incident light concludes an arbitrary angle with the incidence plane. The mean roughness is determined in both cases. It is shown, that both reconstructions of the profile and the determination of the mean roughness are not dependent on the polarization of the incident light. The separation of the s and p components is of great importance at the two-dimensional reconstruction, when independent of incident light polarization (s or p), the scattered optical field is always depolarized. In this case the profile of the two-dimensional surface can be easily reconstructed with s or p component of the mixing and diffracted fields.     

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.