Experimental observations of the spectrum of light diffracted at a slit as a secondary source

In this paper, we investigated both theoretically and experimentally the normalized spectrum of partially coherent light radiated from a secondary source which is produced by an imaging system. The experimental results show that, if the imaging lens is achromatic, the normalized spectrum of the light radiated from a secondary source shifts either towards the red side or towards the blue side, compared to the spectrum of the source, and the spectral shifts change for different position of the observation points. It is found that the experimental results are consistent with the theoretical ones. A chromatic lens, acting as the imaging lens, is used to investigate the effect of the chromatic aberration on the normalized spectrum of the light field. The results show that the influence of the chromatic aberration on the normalized spectrum is considerable and cannot be neglected in high-precision spectral measurement experiments.     

The Imbert-Fedorov shift of paraxial light beams

We present a solution to the problem of reflection and transmission of a polarized paraxial light beam at an interface between two homogeneous media by using a two-form amplitude and an extension matrix to represent the vectorial angular spectrum of a three-dimensional (3D) light beam. We derive general formulas for the Imbert-Fedorov (IF) shift of the reflected and transmitted beams of a polarized paraxial light beam. The IF shift of two different types of polarized beams is calculated, and the influence of the polarization state and the polarization feature of the vectorial angular spectrum on the IF shift is discussed.     

Reflection of the light beam carrying orbital angular momentum from a lossy medium

It is shown that after reflection from a lossy medium the s- or p-polarized paraxial light beam carrying the orbital angular momentum suffers the 2D shift of the beam's centre of gravity relative the geometric optic axis. The direction as well as the length of the 2D vector, which describes the shift, change smoothly with the change of the angle of incidence.     

Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media

We study the coherence properties of the field generated by beam radiated from quasi-homogeneous (QH) electromagnetic source scattering on QH media. Formulas for the spectral density and spectral degree of coherence of the three dimensional scattered field are derived. The results show under assumption that the diagonal correlation coefficients of the source are proportional to each other, the far field of the scattered light satisfy two reciprocity relations analogous to that in the scalar case, that, the spectral density is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential; the spectral degree of coherence is proportional to the convolution of the diagonal correlation coefficients and the strength of the scattering potential.     

Cross spectral purity and its influence on ghost imaging experiments

Pseudo-thermal light has been widely used in ghost imaging experiments. In order to understand the differences between the pseudo-thermal source and thermal source, we propose a method to investigate whether a light source has cross spectral purity (CSP), and experimentally measure the cross spectral properties of the pseudo-thermal light source in near-field and far-field zones. Moreover we present a theoretical analysis of the cross spectral influence on ghost imaging.     

Observation of superluminal and slowdown light propagation in doped lithium niobate crystals

We investigate the group velocity of light in a one-dimensional volume grating inside lithium niobate crystals doped with different impurities. The superluminal and slowdown light propagations are both observed in the crystals. The relationships between the group refractive index and the grating amplitude and phase shift are presented and discussed.     

Analytical characterization of spectral anomalies in polychromatic apertured beams

The power spectrum of polychromatic apertured spherical waves changes strongly in the vicinity of phase singularities. A spectral shift effect is observed and, in some cases, a spectral switch occurs together with a broadening of the power spectrum. Low-order moments of the power spectrum are evaluated in points of the focal volume with spectral anomalies. First-order analytical expressions are proposed for the evaluation of the relative spectral shift and the relative spectral broadening in the transverse focal plane and along the optical axis. The influence of the fractional bandwidth and the selected singularity order is considered.     

Height distribution on a rough plane and specularly diffracted light amplitude are Fourier transform pair

In this report we show that the amplitude of specularly diffracted light from a plane rough surface as a function of incident angle cosine is Fourier transform of the height distribution on the surface. Therefore, an even height distribution function, which is the case for many rough surfaces, can be obtained by measuring the specularly diffracted light intensities. Also, it is observed that for polychromatic illumination the spectrum of the specularly diffracted light is modified and the modification depends on roughness, incident angle, and wavelength. It is also shown that, for a fixed incident angle, the height distribution on the rough plane is Fourier transform of the spectral modifying function. Experimental studies on some surfaces of different roughnesses, prepared by grinding sheet-glasses by powders of different grain sizes, show that the corresponding height distributions are Gaussian and the rms heights obtained by the two approaches are quite consistent.     

Positive and Negative Lateral Shifts from an Anisotropic Metamaterial Slab Backed by a Metal

The lateral shift of a light beam at the surface of an anisotropic metamaterial (AMM) slab backed by a metal is investigated. Analytical expressions of the lateral shifts are derived using the stationary-phase method, in the case that total reflection does and does not occur at the first interface. The sign of the lateral shift in two situations is discussed, and the necessary conditions for the lateral shift to be positive or negative are given. It is shown that the thickness and physical parameters of the AMM slab and the incident angle of the light beam strongly affect the properties of the lateral shift. Numerical results validate these conclusions. The lossy effect of the metamaterial on the lateral shift is also investigated.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

Giant positive and negative lateral shifts from the Kretschmann-Raether configuration with a weakly absorbing left-handed slab

The lateral shift of a TE-polarized beam reflected from the Kretschmann-Raether structure with a weakly absorbing left-handed slab is studied theoretically. It is shown that the lateral shift can be very large negative as well as positive near the resonant condition. These large negative and positive shifts can be one order of magnitude much larger than the shift from the corresponding nonabsorbing slab. As the absorption factor increases, the incident angle of producing largest lateral shift increases when the thickness is kept unchanged but the thickness of the slab of producing largest lateral shift decreases when the incident angle is kept unchanged.     

Flat-topped spectrum obtained from partially coherent hollow Gaussian Schell-model beams passing through a slit

The anomalous spectral behaviors of partially coherent polychromatic hollow Gaussian Schell-model beams (HGSMBs) diffracted by a slit are investigated. Besides spectral switches, asymmetrical dual-peak spectral split and multi-peak spectral split are observed. In the vicinity of the positions where spectral switches occur, flat-topped spectrum can be obtained, the bandwidth of which is adjustable by changing the transverse coherence width and the observation position. The flat-topped spectrum has potential application for creating probe beams in optical metrology systems and generating broadband optical sources in fiber optic sensor interface systems.     

A Novel Method for Enhancing Goos-Hänchen Shift in Total Internal Reflection

Due to the tiny shift in order of optical wavelength for Goos-Hǎnchen （GH） shift, it is very difficult to directly measure and apply the GH shift. We develop a new method for enhancing GH shift of both TE and TM polarized waves. The method is based on a total reflection prism made of BK9 glass combined with a precise measurement of the resulting spatial displacement with a one-dimensional charge coupled device （CCD）. Measurements are performed to examine the validity of the method. Experimental and theoretical results indicate the feasibility of the method with an enhancement in optical wavelenghth shift at millimetre scale. The method is advantageous to application the GH shift in the optical domain, and is also meaningful for measuring even smaller changes in the refractive index of a liquid.     

Statistical properties of correlated radial stochastic electromagnetic array beams on propagation

A kind of array beam named the correlated radial stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by use of tensor method. The analytical expression for the cross-spectral density matrix of this array beam propagating through the turbulent atmosphere and in free space is obtained after performing vector integration. Some typical numerical calculations are illustrated for the changes in the spectral density, spectral degree of polarization, and spectral degree of coherence of the beam on propagation. We find that the atmospheric turbulence can destroy the correlated effect among the beamlets.     

A temporal-coherence anisotropy of unpolarized light

We analyze the anisotropic behavior of unpolarized, temporally partially coherent light. We demonstrate that unpolarized light with different intrinsic degrees of coherence can present an anisotropic behavior which is experimentally observable while it is not the case if both intrinsic degrees are equal. This behavior is analyzed in comparison with the standard anisotropy property of partially polarized light.     

Giant and negative bistable shifts for one-dimensional photonic crystal containing a nonlinear metamaterial defect

In this Letter, we investigate giant and negative bistable lateral shifts for a light beam transmitted through a one-dimensional photonic crystal containing a nonlinear metamaterial defect. It is shown that there exists a typical S-shaped curve of the normalized input-output intensity. The hysteresis of lateral shift, resulting from the reshaping effect (constructive and destructive interferences of each plane wave components undergoing different phase shifts) is dependent on the nonlinear defect, the incident intensity and incidence angle. Numerical simulations are also made for the validity of stationary phase approach. All these phenomena lead to potential applications in integrated optics and optical switches.     

Wavelength dependence of the phase retardation of a quarter-wave plate

We describe an optical heterodyne polarization interferometer that can be efficiently used for the precision measurement of the change in the state of polarization of a light wave induced by polarizing optical devices. This technique is used to measure the change with wavelength of the phase retardation of a quarter-wave plate. A theoretical derivation is presented to permit computation of the wavelength dependence of the phase shift induced by a quarter-wave plate.     

Theory of the partially coherent temporal Talbot effect

The behaviour of the temporal Talbot effect under carrier partial coherence is analysed. This effect finds application as a passive method for multiplying the repetition rate of the intensity of pulse trains in first-order dispersive media. The study is based on the representation of the average intensity of partially coherent modulated light after first order dispersion as a coherence-dependent low pass filter acting on the intensity distribution obtained with a monochromatic carrier. The resulting coherence limitations are more restrictive in Talbot devices with high indices, due to the necessity of highly coherent carriers to produce a faithful reconstruction of trains by multiple pulse-to-pulse interference. Coherence limitations for architectures composed of externally modulated cw sources are analysed. Generalizations of the theory to several spectral lines, and its relation with the Collett-Wolf theorem are also reported.     

Experimental observation of focal shifts in focused partially coherent beams

We report the experimental observation of focal shifts in partially coherent beams of Gaussian Schell-model (GSM) type focused by a circularly apertured thin lens. The relative focal shift increases as the aperture radius or the state of coherence of the GSM source decrease. The experimental results agree well with theoretical predictions.     

Effect of cross-polarization of electromagnetic source on the degree of polarization of generated beam

In this paper we study the degree of cross-polarization of a beam-like field whose cross-spectral density matrix is symmetric with respect to the permutation of its spatial arguments. Formulas were derived expressing the degree of cross-polarization in terms of the generalized Stokes parameters. With the help of an uniformly polarized quasi-homogeneous model source, the effect of degree of cross-polarization of a source on the degree of polarization of the radiated beam was demonstrated, that, two sources with same spectral degrees of coherence and polarization but with different degrees of cross-polarization can generate beams that have different spectral degrees of polarization in the far field.