Diffraction Of Light Waves Research Articles

Modelling the diffraction of laser-cooled atoms from magnetic gratings

The diffraction of laser-cooled atoms from a spatially-periodic potential is modelled using rigorous coupled-wave analysis. This numerical technique, normally applied to light-diffraction, is adapted for use with atomic de Broglie waves incident on a reflecting diffraction grating. The technique approximates the potential by a large number of constant layers and successively solves the complex eigenvalue problem in each layer, propagating the solution up to the surface of the grating. The method enables the diffraction efficiencies to be calculated for any periodic potential. The results from the numerical model are compared with the thin phase-grating approximation formulae for evanescent light-wave diffraction gratings and idealised magnetic diffraction gratings. The model is applied to the problem of diffracting Rb atoms from a grating made from an array of permanent magnets.

Computer-simulated Fresnel holography

This paper presents a method of producing a computer-generated hologram for an object that has depth. It is a continuation of the author's previously published work on computer-simulated holography, which dealt with the generation of Fraunhofer holograms for planar objects. The technique is now extended to the case of Fresnel holograms for simple objects whose points do not lie in a single plane. The method utilizes the computer's ability, using packaged mathematical software, to compute the Fresnel diffraction pattern of a planar aperture by taking the Fourier transform of a modified aperture function. By adding a plane wave reference beam to the diffraction pattern, a hologram for each plane of the object is constructed, and the superposition of these holograms yields a resultant hologram whose reconstruction exhibits the depth of the object. Since computer-simulated holography is based on the interference and diffraction of light waves, the material presented in this paper could serve to enhance the understanding of these topics in a university course in optics.

Multiple light diffraction theory in volume gratings using perturbative integral expansion method

Light wave diffraction from multiple superposed volume gratings is inestigated using a perturbative iteration method of the integral equation of Maxwell's wave equation. The host material and index gratings are anisotropic and non-coplanar multiple volume gratings are considered. In this method, the paraxial approximation and lack of backward scattering in conventional coupled mode theory are not assumed. Systematic analysis of anisotropic wave diffraction due to multiple noncoplanar volume index gratings is performed in increasing level of diffraction orders corresponding to successive iterations.

Miniature semiconductor optical power splitterswith submicrometre wide aperture

The authors propose a miniature semiconductor optical power splitter with a submicrometre wide input aperture enhancing lightwave diffraction in a planar free-space region. They present its design and have demonstrated a GaInAs/GaAs quantum well laser with a miniature 1 × 20 power splitter inside the laser cavity.

Observation of light diffraction by time-resolved femtosecond correlation interferometry

We demonstrate time development of the diffraction of light waves from objects for what is to our knowledge the f irst time by using a new femtosecond correlation interferometry. This new dynamical optics method allows for the conversion of temporal information to space information with femtosecond resolution and has the potential to produce a time-resolved femtosecond movie for the visualization of light-wave propagation in space for scientific, biological, and medical applications.

Behavior of heated particle gas and light-wave diffraction by phase screen in warm-ray model

On the basis of the analogy between the density evolution of a heated gas of noninteracting particles and the diffraction of monochromatic optical waves by a random phase screen, a formula is derived for the correlation function of intensity fluctuations behind the screen. A hypothesis on the statistical splitting of the geometric and diffraction means allows the multiplicity of the integral that determines this function to be reduced by half.

Light diffraction by ultrasonic pulses: Analytical and numerical solutions of the extended Raman–Nath equations

Light diffraction by ultrasonic pulses at normal incidence is studied as well in the Raman–Nath region (low frequencies) as in the Bragg region (high frequencies). Based on a generating function method, an analytical expression for the Raman–Nath-like diffraction has been derived and compared with earlier work. Only small corrections within its validity region were observed. In order to extend these existing theories toward higher frequencies, numerical expressions for the intensity of the diffracted light waves are obtained by means of the Laplace transform theory. This powerful method leads to the same results for Raman–Nath-like diffraction and can easily be applied for much higher frequencies, too. Examples are provided showing the frequency dependence of the ultrasound, the influence of the Raman–Nath parameter v, and the spectral composition of the pulse on the diffraction pattern. When the pulse approaches a continuous wave, both theories converge to known results. A general condition concerning the symmetry properties of the diffraction spectrum has been derived.

Acoustooptic interferometric nonreciprocal element

A considerable increase in the amplitude and phase nonreciprocity of acoustooptic elements due to formation of an interferometer for diffracted light waves is demonstrated theoretically and experimentally. The optimal conditions for unidirectional single-frequency operation of ring lasers with an acoustooptic interferometric nonreciprocal element are determined. A new frequency decoupling system is proposed for counterpropagating waves in a ring laser.

Theoretical study of the anisotropic diffraction of light waves by acoustic waves in lithium niobate crystals

The anisotropic diffraction of light by high frequency longitudinal ultrasonic waves in the tangential phase matching configuration may present some definite advantages over the same interaction using transverse acoustic waves. A systematic search for favorable crystal cuts in lithium niobate was worked out. The main results of this study are reported here; they enable the choice of the best configuration for a given operating center frequency.

Anisotropic Bragg diffraction in photorefractive crystals

Abstract Light diffraction from photoinduced gratings recorded in anisotropic materials is discussed. In particular anisotropic diffraction in which the diffracted light wave has an orthogonal polarization to the incident wave can be used for optically controllable light deflectors and spatial light modulators. A noncritical configuration has been found which allows light deflection of a He-Ne laser beam at fixed incidence angle within a range of 5.67 deg. by changing the wavelength of the steering Ar+ Laser beam λr using for recording the photorefractive grating (wavelength tuning range: 457.9nm < λr < 514, 5 nm).

Light diffraction by a sound beam in circularly birefringent crystals with extreme acoustooptic coupling

A solution is obtained for the self-consistent problem of Bragg acoustooptic interaction (AOI) of circularly polarized light waves in transparent gyrotropic crystals with extreme acoustooptic coupling or a long interaction zone. It is shown that the polarization parameters of the diffracted field differ very little from the corresponding parameters of the incident light wave in AOI with identical circular polarization vectors, and the natural circular birefringence of the medium for the diffracted light wave is compensated in the case of interaction between waves with different circular polarizations. It is confirmed that the laws governing the variation of the polarization azimuth of a given wave coincide with the corresponding AOI laws in optically isotropic media. The diffracted field and the corresponding polarization characteristics are determined for Raman-Nath AOI in gyrotropic crystals.

Image processing adapted to the atmosphere speckle. I. Speckle formation in turbulent atmosphere. Statistical properties

Reviews the theory of the production of speckle by the diffraction of light waves through turbulent layers seen as phase screens. Different atmospheric situations allow the authors to show the influence of the distance between the diffuser and the observer on the speckle geometry. The small perturbation approximation is experimentally justified and it is shown that the speckle pattern is still contrasted even with broadband photoelectric receivers. Image processing by means of spatiotemporal analysis of a single or multiple star could give one a variety of geophysical information.

Diffraction of Light Waves in an Inhomogeneous and Anisotropic Medium

Approximate solutions of Maxwell's equations in an anisotropic medium with the weak inhomogeneity are shown when monochromatic plane light waves are incident. One group of approximate solutions including the Raman-Nath diffraction in an anisotropic medium is derived by using the phase function method under the condition that the spatial variation of the medium is sufficiently small compared with that of the incident light waves. Another group of solutions derived by The use of the Born approximation includes both the normal Bragg diffraction and the abnormal one. The two solution types hold only in the neighbourhood of the boundary plane because of the conditions under which they are applicable.

Diffraction of light waves by dynamic gratings in waveguides made of semiconductor materials

A theoretical study is made of the diffraction of light waves by dynamic grating structures formed as a result of one-photon absorption of the recording radiation in the waveguide material. The characteristics of diffraction in waveguides with step and exponential refractive index profiles are considered. The results are given of an experimental investigation of the diffraction of traveling waves by dynamic gratings in GaAs0.15P0.85 and CdS1–ySey waveguides. A satisfactory agreement between the calculated and experimental results is reported.

Investigation of light wave diffraction in a waveguide plane by optically induced dynamic gratings

An investigation is made of the feasibility of controlling radiation propagating in a planar waveguide by using dynamic diffraction gratings formed by nonequilibrium charge carriers induced by light inside the waveguide as a result of one- and two-photon absorption of optical power. A diffraction efficiency of 45% is reported for the TM0 mode in a GaAs1–xPx waveguide.

Amplitude modulation of diffracted light waves caused by adjacent ultrasonic beams of frequency ratio 1: n

A study has been made of the influence of the phase-difference of two ultrasonic beams, a fundamental and its nth harmonic, on the intensities or amplitudes of diffracted lightwaves. After showing the similarity between superposed and adjacent ultrasound in the Raman-Nath region ρ ⪡ 1, simplified expressions for the intensities have been set up to draw conclusions concerning the symmetry of the diffracted pattern, the amplitude modulation, and the numerical calculation of the factor α n , from the intensities in which α n represents the ratio of the ultrasonic pressures. All results are illustrated in the case of a fundamental and its second or third harmonic.

Theory of Bragg diffraction by limited-aperture gratings in a planar optical waveguide

An analysis is made of Bragg diffraction of light waves in a planar optical waveguide by diffraction gratings of finite aperture and length used as waveguide couplers in integrated optics. In the asymptotic coupled-wave approximation, the complex amplitude of an inhomogeneous diffracted wave is described by a hyperbolic partial differential equation with boundary conditions determined by the profile of the grating and the incident optical beam. The interaction constant of the coupled waves is calculated and its dependence on the diffraction angle is determined for the electric and magnetic modes of a planar optical waveguide. Examples are given of calculations of the diffraction field in the near-field zone for gratings having the configurations of a characteristic parallelogram and trapezium.

The diffraction of light by progressive supersonic waves. Oblique incidence of the light: III. The special case ϱ ⪢ 1

Approximate expressions for the intensities of the diffracted light waves, in the case ϱ ⪢ 1 are derived from the formulae of the intensities, established by the exact solution of the system of difference-differential equations of Raman-Nath for the amplitudes of the diffracted light waves. Two cases are considered: (1) the angle of incidence φ is a Bragg angle; (2) φ is neither a Bragg angle, nor zero. In order to facilitate the computations in the latter case, a new notation is introduced for the coefficients of the Mathieu functions of fractional order and their characteristic numbers. From the obtained formulae, symmetry or asymmetry properties of the diffraction spectrum are derived; periodicity properties as well as extremal values for the diffraction lines are established, which are in agreement with experiments of Nomoto. The approximate solutions of Phariseau, Bhatia and Noble and David have been found.

General symmetry properties of the diffraction pattern in the diffraction of light by parallel adjacent ultrasonic beams

The system of difference-differential equations for the amplitudes of a diffracted light wave, caused by parallel partly adjacent and partly superposed ultrasonic beams, respectively of the n1th and the n2th harmonic of the same fundamental tone, is derived. The general symmetry properties of the diffraction pattern are discussed.

The diffraction of light by progressive supersonic waves. Oblique incidence of light: II. Exact solution of the Raman-Nath equations

The partial differential equation associated with the system of difference-differential equations of Raman-Nath for the amplitude of the diffracted light waves, in the case of oblique incidence of light, is solved exactly by the method of separation of variables. The complete solution is presented as an infinite series containing Mathieu functions of integral order, if the angle of incidence corresponds with a Bragg angle, of fractional order, otherwise. Considering those solutions as Laurent series in one of the variables, the Laurent coefficients immediately give the exact expressions for the amplitudes of the diffracted light waves, from which the intensities may be calculated. From the obtained formulae, asymmetry and symmetry properties of the spectrum may be derived. It is also found that the nth order intensity has an extremum for the corresponding nth order Bragg angle. Numerical calculations show that those extrema can be maxima as well as minima. For ϱ ⪢ 1 the approximate solutions of David, Bhatia and Noble and Phariseau are found.