Spectral Degree Of Coherence Research Articles

The influence of atmospheric turbulence on the spatial correlation property of partially coherent Hermite-Gaussian beams

Based on the extended Huygens-Fresnel principle, the expression for the spectral degree of coherence of the partially coherent Hermite-Gaussian (H-G) beams propagating through atmospheric turbulence is derived by using the quadratic approximation of Rytov's phase structure function, and the influence of atmospheric turbulence on the spatial correlation is studied. It is shown that the oscillatory behavior and phase singularities of the degree of spectral coherence may appear when partially coherent H-G beams propagate through atmospheric turbulence, which is very different from the behavior of Gaussian-Schell-model beams. But, the oscillatory behavior becomes weaker with increasing turbulence, and even disappears when the turbulence is strong enough. The smaller the coherence parameter, the less the spatial correlation property of partially coherent H-G beams is affected by the turbulence. In addition, a comparison between the mean-squared width of the spectral degree of coherence and the mean-squared width of the spectral intensity is also given. Some interesting results are obtained, and are explained with regard to their physical nature.

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.

The far-field spatial coherence of Gaussian Schell-model beam in turbulence in terms of position vectors

Spatial coherence properties of beam produced by Gaussian Schell-model source when the beam is propagating through atmosphere have been analyzed in terms of position vectors. New expressions for cross-spectral density of optical field and spectral degree of coherence as well as radiant intensity have been developed. Numerical results illustrated in this paper indicate the coherence degradation suffered from atmospheric turbulence and their directional dependence.

Control of the coherence of light scattered from a one-dimensional randomly rough surface that acts as a Schell-model source

We present an approach to the design of a one-dimensional perfectly conducting randomly rough surface that when illuminated at normal incidence by a laser beam produces a partially coherent scattered beam with a Gaussian dependence of its mean intensity in the mean scattering surface and with a specified spectral degree of coherence in that surface that can have a nearly arbitrary form. The approach is validated by the results of computer simulations.

Partially coherent nonparaxial modified Bessel–Gauss beams

The concept of partially coherent nonparaxial modified Bessel–Gauss (MBG) beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order m, ξ and f parameters and to compare the difference between the paraxial and nonparaxial results.

Effect of absorption on the spatial coherence in scalar fields generated by statistically homogeneous and isotropic sources

We investigate the behavior of the spectral degree of coherence of fluctuating scalar wave fields generated by statistically homogeneous and isotropic sources within absorbing media. In the limit of negligible losses, the degree of coherence is shown to be of a known universal form (sinc function), whereas in the limit of infinite losses it is shown to asymptotically approach the degree of coherence of the source. The intermediate cases are studied for fields produced by sources with Gaussian and sinc-type coherence functions. These studies show that the concept of negligible losses is meaningful only when defined with respect to specific source distribution statistics, and that even for arbitrarily small nonzero losses, the coherence length of the field can be arbitrarily short.

Coherence and polarization properties of far fields generated by quasi-homogeneous planar electromagnetic sources

In studies of radiation from partially coherent sources the so-called quasi-homogeneous (QH) model sources have been very useful, for instance in elucidating the behavior of fields produced by thermal sources. The analysis of the fields generated by such sources has, however, been largely carried out in the framework of scalar wave theory. In this paper we generalize the concept of the QH source to the domain of the electromagnetic theory, and we derive expressions for the elements of the cross-spectral density matrix, for the spectral density, the spectral degree of coherence, the degree of polarization, and the Stokes parameters of the far field generated by planar QH sources of uniform states of polarization. We then derive reciprocity relations analogous to those familiar in connection with the QH scalar sources. We illustrate the results by determining the properties of the far field produced by transmission of an electromagnetic beam through a system of spatial light modulators.

Spectrally partially coherent pulse trains in dispersive media

A general theory is presented for the propagation and spreading of spectrally partially coherent plane-wave pulse trains in dispersive media. The theory is applied to chirped pulse trains with Gaussian distributions of the spectrum and the degree of spectral coherence, propagating in linearly dispersive media. Analytic expressions are derived for both the cross-spectral density function and the mutual coherence function associated with such pulse trains. Some general physical interpretations concerning the optical coherence properties of pulse trains are given.

The effect of a moving diffuser on a random electromagnetic beam

The effects of a moving diffuser on the spectrum, on the spectral degree of polarization, and on the spectral degree of coherence of a random electromagnetic beam are investigated. It is found that while the spectrum and the spectral degree of coherence change on transmission, the degree of polarization does not.

Propagation properties of partially coherent modified Bessel–Gauss beams

Starting from the propagation law of partially coherent light, the analytical propagation equations of partially coherent modified Bessel–Gauss beams (MBGBs) through a paraxial optical ABCD system are derived and illustrated with typical application examples. Furthermore, by using the intensity moments method and integral transformation technique, the important characteristic parameters, including the beam width, far-field divergence angle, M 2 factor and kurtosis parameter of partially coherent MBGBs, are expressed in a closed and simple form. As a result, some basic properties of MBGBs and the dependence of the M 2 factor and kurtosis parameter on the spectral degree of coherence and beam order are illustrated both analytically and numerically.

Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes on propagation in free space

The spectral degree of coherence and of polarization of some model electromagnetic beams modulated by a polarization-dependent phase-modulating device, such as a liquid-crystal spatial light modulator, acting as a random phase screen are examined on the basis of the recent theory formulated in terms of the 2 x 2 cross-spectral density matrix of the beam. The phase-modulating device is assumed to have strong polarization dependence that modulates only one of the orthogonal components of the electric vector, and the phase of the phase-modulating device is assumed to be a random function of position imitating a random phase screen and is assumed to obey Gaussian statistics with zero mean. The propagation of the modulated beam is also examined to show how the spectral degrees of coherence and of polarization of the beam change on propagation, even in free space. The results are illustrated by numerical examples.

Coherence effects in the near-field

Expressions are derived for the cross-spectral density and for the spectral degree of coherence of the near-field generated by a planar, secondary, homogeneous source of any spectral distribution and of any state of spatial coherence. The behaviour of the spectral degree of coherence and the spectral intensity in the immediate vicinity of the source are illustrated by computed examples.

Effect of spectral correlations on spectral switches in the diffraction of partially coherent light.

The subject is the spectral characteristics of partially coherent light whose spectral degree of coherence satisfies or violates the scaling law in diffraction by a circular aperture. Three kinds of spectral correlations of the incident light are considered. It is shown that no matter whether the partially coherent light satisfies or violates the scaling law, a spectral switch defined as a rapid transition of spectral shifts is always found in the diffraction field. Different spectral correlations of the incident field in the aperture result in different points at which the spectral switch occurs. With an increment in the correlations, the position at which the spectral switch takes place moves toward the point at which the phase of the center frequency component omega0 becomes singular for illumination by spatially fully coherent light. For light that satisfies the scaling law, the spectral switch is attributed to the diffraction-induced spectral changes; for partially coherent light that violates the scaling law, the spectral switch is attributed to both the diffraction-induced spectral changes and the correlation-induced spectral changes.

Reconstruction of optical source-profile from spectral measurements in Young's interference experiment

An improved technique is described for determining the optical source-intensity-profile. The spectral degree of coherence produced by a quasi-homogeneous source masked with an amplitude grating, on the plane of a double slit of fixed baseline length, over the accessible frequencies in the visible range of the electromagnetic spectrum, is determined by measuring the single slit spectra and the superposed spectrum by applying the spectral interference law. The masking of the source by the amplitude grating enables to map the degree of coherence obtained experimentally over zero spatial frequency. The Fourier-inversion of the spectral degree of coherence over the mapped spatial frequencies is used to determine the source intensity-profile. This technique may have some practical applications namely automated inspection.

Determining field correlations produced by stars from the study of spectral changes in double slit experiment

Experiments are performed to determine the coherence properties of wave fields, produced by the broadband stellar sources on the earth surface, from the study of spectral changes produced on interference in the Young's double slit experiment. The spectral degree of coherence obtained experimentally in this study for four bright stars in the wavelength range from 325 nm to 660 nm is in close agreement with the value that is expected theoretically from the known angular diameter of the stars. It is shown that the spectral degree of coherence obtained experimentally by this spectral interferometric technique could be used to determine the angular diameter of stars.

Two-beam interference experiments in the frequency-domain to measure the complex degree of spectral coherence

Two-beam interference experiments in the frequency-domain to measure the complex degree of spectral coherence

Two-beam interference experiments in the frequencydomain to measure the complex degree of spectral coherence

Correlation-induced spectral changes in two-beam interference experiments in the space-frequency domain are used to determine the amplitude and phase of the complex degree of spectral coherence. The spectral modifications are observed either as a shift in the peak wavelength or as sinusoidal modulations within the bandwidth of the white light spectrum due to the complex degree of spectral coherence of the secondary source and the path difference between the interfering beams. These correlation-induced spectral changes were analysed using a theoretical model to establish the behaviour of the real and imaginary parts of the complex degree of spectral coherence over the entire visible region of the spectrum.

Transformation of coherence and of the spectrum of light by a moving diffuser

Effects of a diffuser on the spectral degree of coherence and on the spectrum of light produced by transmitting light through the diffuser are described. Both stationary and uniformly moving diffusers are considered and the analysis applies to dielectric as well as to absorbing diffusers. The results are illustrated by numerical examples.

Angular separation and spectra of two point sources determined from measured spectral coherence

The theoretical foundation is described not only of how to determine the angular separation of two point spectral sources, but also on how to recover each spectral profile from the measured complex degree of spectral coherence. It is shown that the so-called space-frequency equivalence law is not always required. A simple simulation experiment is done by incorporating paired superluminescent diodes as the two point sources with different broadband spectra. The experimental results verify the validity of the theoretical prediction.

Determination of the angular separation and the spectra of two-point sources from spectral coherence measurements

We present a novel method not only for determining the angular separation of unknown two-point spectral sources but also for obtaining each of their spectral profiles from measurements of both their complex degree of spectral coherence and their spectra across an observation area in the space-frequency domain. The theoretical predictions are fully proved by an experimental demonstration with a pair of uncorrelated two-point spectral sources.