Optimized coupling of a Gaussian beam into an optical waveguide with a grating coupler: comparison of experimental and theoretical results

The coupling efficiency of grating couplers is derived for a Gaussian incident beam. Its optimum value depends on the beam waist and on the position of a light spot with respect to the coupler edge for given grating parameters. The characteristic coupling length has been experimentally determined for the grating coupler studied. Relative measurements of the coupling efficiency as a function of incident beam characteristics are in good agreement with the numerical results.     

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.     

Realization of an all-optical triode and diode with a two-level-atom-loaded diffraction grating

A finite-difference time-domain full-wave vector Maxwell equation solver is coupled with a two-level-atom model to simulate the scattering of an ultrafast pulsed Gaussian beam from a finite-length, metallic lamellar grating loaded with two-level atoms. The atomic medium is taken to be resonant at or near the frequency of the incident optical radiation. The highly resonant material and grating behaviors are then combined to realize an all-optical triode at low powers and an all-optical diode at high powers. Simulation results demonstrate the operating characteristics of these triode and diode configurations.     

Scattering of the electromagnetic waves from a rough surface

The electromagnetic field scattered by a rough surface of a semi-infinite body is computed up to the second order of a perturbation scheme with the surface roughness as a perturbation parameter. The calculations are based on the equation of motion of the polarization within the Lorentz–Drude (plasma) model of polarizable, non-magnetic, homogeneous matter. The surface roughness contributes both to the main (specularly) reflected and refracted fields and diffuse scattering, or gives rise to secondary (second-order) diffraction peaks for a regular grating. The calculations are performed both for the s- and p-waves. Two-dimensional modes, resonant at certain frequencies, are identified, confined to and propagating only on the surface, as a consequence of the surface roughness.     

Transient Gratings Formed by Nonequilibrium Quasiparticles in YBa2Cu3O6.5

We report transient grating measurements of nonequilibrium quasiparticles in untwinned single crystals of YBa₂Cu₃O_6.5. By interfering two laser beams on the sample, we introduce a sinusoidally varying density of nonequilibrium quasiparticles. A third laser beam incident on this pattern is both reflected and diffracted due to the sinusoidally varying index change caused by photoinduced quasiparticles. In this paper, we focus on the low excitation density limit. In this limit, measuring the reflected and diffracted beams as a function of the time and grating period yields the diffusion constant and elastic scattering rate for these nonequilibrium quasiparticles.     

Transient Gratings Formed by Nonequilibrium Quasiparticles in YBa2Cu3O6.5

We report transient grating measurements of nonequilibrium quasiparticles in untwinned single crystals of YBa₂Cu₃O_6.5. By interfering two laser beams on the sample, we introduce a sinusoidally varying density of nonequilibrium quasiparticles. A third laser beam incident on this pattern is both reflected and diffracted due to the sinusoidally varying index change caused by photoinduced quasiparticles. In this paper, we focus on the low excitation density limit. In this limit, measuring the reflected and diffracted beams as a function of the time and grating period yields the diffusion constant and elastic scattering rate for these nonequilibrium quasiparticles.     

Ultrasonic wave scattering from rough,imperfect interfaces. Part II. Incoherent and coherent scattered fields

A theoretical model for ultrasonic wave scattering for geometrically irregular and imperfectly bonded interfaces is presented. Part I presents the stochastic interface characterization and a model for its mechanical response based on a micromechanics model of asperity contact. Part II uses this interface representation to write the well used quasi-static boundary conditions for scattering from a.flat imperfect interface¹ directly on the irregular interface profile. The boundary conditions are then expanded in an asymptotic series in the roughness parameter (standard deviation of the surface height) which is small compared to wavelength. The slope of the profile must also be everywhere small. These equations are solved exactly for the zero-th and second order terms, which are the flat coherent solution and its' first coherent correction, and the first order term, which is the first term in the expansion for the incoherently scattered solution. Results for obliquely incident longitudinal and shear waves show a strong dependence on the roughness in both the coherent and incoherent reflected fields, but little if any dependence on the roughness in the transmitted fields. In particular, the reflected coherent fields show markedly increasing attenuation compared to the flat compliant interface with increasing roughness and increasing ultrasonic frequency, the latter result being in qualitative agreement with results for scattering from an inhomogeneous array of individual scatterers.² There is evidence in the incoherent reflected fields for the existence of an incoherent leaky interface disturbance which manifests itself as a bulk incoherent shear wave at a scattering angle equal to the critical longitudinal angle. A coherent true interface wave is also supported by the rough interface which is shown to further attenuate the coherent reflected fields compared to the flat compliant interface solution.     

Scattering from cylinders using the two-dimensional vector plane wave spectrum

The two-dimensional vector plane wave spectrum (VPWS) is scattered from parallel circular cylinders using a boundary value solution with the T-matrix formalism. The VPWS allows us to define the incident, two-dimensional electromagnetic field with an arbitrary distribution and polarization, including both radiative and evanescent components. Using the fast Fourier transform, we can quickly compute the multiple scattering of fields that have any particular functional or numerical form. We perform numerical simulations to investigate a grating of cylinders that is capable of converting an evanescent field into a set of propagating beams. The direction of propagation of each beam is directly related to a spatial frequency component of the incident evanescent field.     

Finite-element model for phase-change recording

The finite-element method is applied to model phase-change recording in a grooved recording stack. A rigorous model for the scattering of a three-dimensional focused spot by a one-dimensional periodic grating is used to determine the absorbed light in a three-dimensional region inside the phase-change layer. The optical model is combined with a three-dimensional thermal model to compute the temperature distribution. Land and groove recording and polarization dependence are studied, and the model is applied to the Blu-ray Disc.     

Wave characteristics in gratings by linear superposition of retarded fields

We present a formalism for the wave characteristics in gratings and periodic dielectrics based on the linear superposition of retarded fields. The idea is based on the physical picture that an incident field affects the charges in the material forming the gratings and hence leads to oscillating current and charge densities, which in turn generate more fields via the retarded potential. A set of self-consistent equations for the electric field and current and charge densities is derived. Expressions for the electric field everywhere, including the reflected and transmitted fields, are derived. The formalism is then applied to the calculation of diffraction efficiency so as to illustrate its application and to establish its validity by comparing results with the rigorous coupled-wave method. We further generalize the formalism to include possible anisotropy and nonlinearity in the response of the material forming the grating.     

Nonadditivity of poynting vector within opaque media

The energy flux within an opaque medium near an interface is not the sum of an incident plus a reflected term, as there is a synergistic contribution to the time-averaged Poynting vector that involves simultaneously both the incident and reflected fields. Therefore, the well-known formula R + T = 1, where R is the reflectance and T the transmittance, does not hold, and furthermore, R and T lose their accepted meanings. We illustrate the perils of assuming energy flux additivity by calculating the transmission and reflection spectrum of a film over a substrate normally illuminated by incoherent light at frequencies in the neighborhood of an optical resonance. We also show that the usual relation between the scattering, absorption, and extinction cross sections for particles immersed within a dissipative host have to be modified to account for the nonadditivity.     

The Reciprocity Theorem for Corrugated Surfaces Used in Conical Diffraction Mountings

The reciprocity theorem, well known for gratings used in classical diffraction, is generalized to the case where the incident wave propagates outside the cross-section plane of the grating (conical diffraction). The authors establish relations on the components of the electric and magnetic fields, for dielectric or conducting periodic structures utilized either in reflexion or in transmission. Symmetry properties of the scattering matrix are derived, from which relations on the efficiencies in natural light are established. All the relations are illustrated by numerical computations based on the electromagnetic theory of gratings.     

A Simple Model for a Microrough Diffraction Grating That Predicts Diffuse Light Bands

Abstract

A real diffraction grating is simulated by a plane boundary with a coordinate-dependent surface impedance. This surface impedance is constructed as the sum of two complex functions: a perfectly periodic function representing a grating without defects, plus a randomly varying, spatially localized function that represents the microroughness or defects of a real grating. This alternative scattering problem is solved in a rigorous electromagnetic manner for two polarizations of the incident field. Our results show that when the magnetic field is parallel to the grooves the scattered light pattern exhibits intensity maxima. The behaviour of these peaks reproduces that reported for the diffuse light bands observed in the spectrum of a real grating.     

Electromagnetic field calculations for a sphere illuminated by a higher-order Gaussian beam. II. Far-field scattering

A previously developed theoretical procedure for determination of electromagnetic fields associated with the interaction of a higher-order Gaussian beam with a homogeneous spherical particle is used to investigate the effects of incident beam type on far-field scattering. Far-field scattering patterns are calculated for (0,0), (0,1), and (1,1) mode Hermite-Gaussian beams and for the helix doughnut mode beam. The effects of incident beam type on the angular distribution of far-field scattering, for both on-sphere-center and off-sphere-center focusing, are examined.     

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.     

Reflection and refraction of an arbitrary electromagnetic wave at a plane interface separating an isotropic and a biaxial medium.

Exact solutions are obtained for the reflected and transmitted fields resulting when an arbitrary electromagnetic field is incident on a plane interface separating an isotropic medium and a biaxially anisotropic medium in which one of the principal axes is along the interface normal. From our exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component. This gives a change in polarization that can be utilized to determine the properties of the biaxial medium. The time-harmonic solution for the reflected field is in the form of two quadruple integrals, one of which is a superposition of plane waves polarized perpendicular to the plane of incidence and the other a superposition of plane waves polarized parallel to the plane of incidence. The time-harmonic solution for the transmitted field is also in the form of two quadruple integrals. Each of these is a superposition of extraordinary plane waves with displacement vectors that are perpendicular to the direction of phase propagation.     

Diffraction by a microrelief grating

A model is proposed that describes diffraction by a microrelief grating. A microrelief grating is a grating of large period with grooves containing a periodic microrelief with a period considerably smaller than the period of the grating. In the model the interaction of the incident wave with the fine structure is taken into account rigorously while features of the grating that are large compared with the wavelength are modeled as phase or amplitude objects.     

Time-domain analysis of bandgap characteristics of two-dimensional periodic structures by use of a source-model technique

We introduce a time-domain source-model technique for analysis of two-dimensional, transverse-magnetic, plane-wave scattering by a photonic crystal slab composed of a finite number of identical layers, each comprising a linear periodic array of dielectric cylinders. The proposed technique takes advantage of the periodicity of the slab by solving the problem within a unit cell of the periodic structure. A spectral analysis of the temporal behavior of the fields scattered by the slab shows a clear agreement between frequency bands where the spectral density of the transmitted energy is low and the bandgaps of the corresponding two-dimensionally infinite periodic structure. The effect of the bandwidth of the incident pulse and its center frequency on the manner it is transmitted through and reflected by the slab is studied via numerical examples.     

Field control of magneto-optic gratings

The Faraday or Kerr rotation of the plane of polarization of light incident on adjacent magnetic domains has opposite sense. Thus light transmitted through a film containing stripe domains or reflected from it is diffracted, as by a grating. The period of such a grating can be controlled by the application of a uniform magnetic field. We report on experimental and theoretical work that explores the range of grating field control under quasistatic conditions, using real films, specifically     

A computational inverse diffraction grating problem

Consider the diffraction of a time-harmonic plane wave incident on a perfectly reflecting periodic surface. A continuation method on the wavenumber is developed for the inverse diffraction grating problem, which reconstructs the grating profile from measured reflected waves a constant distance away from the structure. Numerical examples are presented to show the validity and efficiency of the proposed method.