Gaussian Schell-model Pulsed Beams Research Articles

Statistical properties of a spatiotemporally partially coherent vector cosine-Gaussian-correlated pulsed beam with radial polarization in atmospheric turbulence

In this study, we introduce a novel class of partially coherent vector sources, namely radially polarized spatiotemporally partially coherent cosine-Gaussian-correlated Schell-model pulsed (CGCSMP) beams, which are natural extensions of the scalar Gaussian Schell-model pulsed beams. The conditions for the physical realization of this source are established, and analytical formulae for the two-point, two-frequency cross-spectral density matrix elements of a beam propagating through turbulent atmosphere are derived within the framework of the extended Huygens–Fresnel principle and the atmospheric turbulence spectrum model. The behaviors of the spectral intensity, the spectral degree of polarization (DOP), and the spectral degree of coherence (DOC) of the beam during transmission are investigated numerically. Our work enriches the classical theory of propagating stochastic electromagnetic beams and may be useful for applications requiring a specified degree of beam coherence.

Hanbury Brown and Twiss effect in spatiotemporal domain.

Hanbury Brown and Twiss (HBT) effect has broad applications in optics and other branches of physics, and traditionally this effect is considered in pure spatial or temporal domain. Here we investigate the spatiotemporal HBT effect, extending this phenomenon from spatial or temporal to spatiotemporal domain. By assuming the Gaussian statistics of partially coherent spatiotemporal pulsed sources, we find the generalized analytical results for spatiotemporal HBT effect in the compact form, with the help of the matrix-optics method, which can consider the HBT effect in spatial and temporal domain simultaneously. Furthermore, for Gaussian Schell-model pulsed beams (GSMPBs) used as a spatiotemporal correlated source, we have obtained the generalized expression to calculate spatiotemporal HBT effect, which is useful for up to three-dimensional cases in any second-order linear dispersive medium. By taking a simple two-dimensional case and using air as an example of a linear dispersive medium, we numerically illustrate the properties of the spatiotemporal HBT effect by adjusting the spatial and temporal parameters of the GSMPB source, and reveal the influence of both the spatial and temporal parameters on the spatiotemporal HBT effect. This work paves the path towards the detailed study of HBT effect for a source containing spatiotemporal information with Gaussian statistics.

Anisotropic turbulence-induced statistical properties evolution of a radially polarized partially coherent pulsed beam on propagation

In this study, we introduce a new kind of partially coherent vector beam with Gaussian distribution in the spatial, temporal and correlation components named a radially polarized partially coherent Gaussian Schell-model pulsed (GSMP) beam as a natural extension of scalar Gaussian Schell-model pulsed beam. Analytical formulas for the two-frequency cross-spectral density matrix elements of this beam are derived based on the extended Huygens–Fresnel theory. Within the frame of extend anisotropic non-Kolmogorov spectrum, the effects of asymmetry anisotropic turbulence eddies on the statistical properties of a radially polarized partially coherent GSMP beam are investigated numerically. Our work improves the classical theory of stochastic electromagnetic beams on propagation and may be useful for applications involving free-space optical communications.

Turbulence-induced changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating through anisotropic turbulence

The changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating along a horizontal path through anisotropic turbulence are investigated. Unpolarized and partially polarized, partially coherent pulsed electromagnetic Gaussian Schell-model beams are compared in terms of the turbulence-induced changes in the spectral degree of polarization. Our analysis is focused on models pertaining to electromagnetic Gaussian Schell-model pulsed beams but can either be readily reduced to scalar or be readily generalized to other beam classes. Within the framework of the anisotropic generalized exponential spectrum, considering simultaneously the finite inner and outer scales of turbulence and the asymmetric property of turbulence eddies in the orthogonal x y -plane throughout the propagation path, we derive analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle, and degree of ellipticity. Finally, we study the effects of the anisotropic turbulence parameter on the spectral degree of polarization, orientation angle, and degree of ellipticity of the beams. Our results can be useful for applications involving partially polarized, partially coherent pulsed beams propagating through atmospheric turbulence.

Partial polarization theory of pulsed optical beams

We introduce a consistent matrix formalism for the characterization of partial polarization and coherence of random, nonstationary electromagnetic beams in time and frequency domains. We derive the temporal and spectral degrees of polarization and the Stokes parameters in terms of the time-domain and frequency-domain polarization matrices. The connections between temporal polarization and spectral coherence on the one hand and spectral polarization and temporal coherence on the other hand are discussed. Additionally, we establish equivalence theorems for fields with different temporal coherence properties to have the same spectral polarization states and for fields with different spectral coherence properties to possess identical temporal polarization. The theory is illustrated by analyzing specific examples of time-domain and frequency-domain electromagnetic Gaussian Schell-model pulsed beams.

Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic Cosh-Gaussian pulsed beams

Based on the generalized Rayleigh–Sommerfeld diffraction integral, the analytical expression for 3×3 cross-spectral density matrix of nonparaxial spatially and spectrally partially coherent electromagnetic Cosh-Gaussian (ChG) pulsed beams propagating in free space is derived, and used to formulate the spectral density and spectral degree of polarization of electromagnetic pulsed beams at the z-plane. It is found that the parameters f and fαα are the key parameters in determining the nonparaxiality of spatially and spectrally partially coherent electromagnetic ChG pulsed beams. And the decentered parameter, pulse duration and temporal coherence length can change the nonparaxial behavior of the electromagnetic ChG pulsed beams. The effect of decentered parameter, pulse duration and temporal coherence length on the spectral density and spectral degree of polarization of electromagnetic ChG pulsed beams is illustrated through numerical calculations. Propagation of nonparaxial spatially and spectrally partially coherent electromagnetic Gaussian Schell-model pulsed beams can be treated as a special case when the decentered parameter of electromagnetic ChG pulsed beams approaches to zero.

Second-order statistics of Gaussian Schell-model pulsed beams propagating through atmospheric turbulence

Novel analytical expressions for the cross-spectral density function of a Gaussian Schell-model pulsed (GSMP) beam propagating through atmospheric turbulence are derived. Based on the cross-spectral density function, the average spectral density and the spectral degree of coherence of a GSMP beam in atmospheric turbulence are in turn examined. The dependence of the spectral degree of coherence on the turbulence strength measured by the atmospheric spatial coherence length is calculated numerically and analyzed in depth. The results obtained are useful for applications involving spatially and spectrally partially coherent pulsed beams propagating through atmospheric turbulence.

Influence of Turbulent Atmosphere on Polarization Properties of Stochastic Electromagnetic Pulsed Beams

Using the coherence theory of non-stationary fields and the characterization of stochastic electromagnetic pulsed beams, the analytical expression for the spectral degree of polarization of stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beams in turbulent atmosphere is derived and is used to study the polarization properties of stochastic electromagnetic GSMP beams propagating through turbulent atmosphere. The results of numerical calculation are given to illustrate the dependence of spectral degree of polarization on the pulse frequency, refraction index structure constant and spatial correlation length. It is shown that, compared with free-space case, in turbulent atmosphere propagation there are two positions at which the on-axis spectral degree of polarization P is equal to zero. The position change depends on the pulse frequency, refraction index structure constant and spatial correlation length.

Spectral Properties of Spatially and Spectrally Partially Coherent Pulsed Beams in Fused-Silica Glass Medium

Using the coherence theory of non-stationary fields and the method of Fourier transform, the spectral properties of spatially and spectrally partially coherent Gaussian Schell-model pulsed (GSMP) beams in fused-silica glass medium are studied and analyzed numerically. It is shown that the spectral shift takes place, which depends on the position of the field point, spatial correlation length, temporal coherence length and dispersive property of medium, as GSMP beams propagate in fused-silica glass medium. The on-axis spectrum is blue-shifted, and the relative spectral shift increases with increasing propagation distance, and decreases as the spatial correlation length and temporal coherence length increases, and then approaches an asymptotic value. The dispersive property of medium plays an important role in the spectral properties of spatially and spectrally partially coherent beams.

Influence of Polarization on the Spectral Changes of Stochastic Electromagnetic Pulsed Beams

An analytical expression for the spectrum of stochastic spatially and temporally partially coherent electromagnetic Gaussian Schell-model pulsed (GSMP) beams is derived, and used to study the spectral changes of electromagnetic GSMP beams in free space. The influence of polarization on the on-axis relative spectral shift is emphasized. It is shown that the on-axis relative spectral shift increases with increasing the degree of polarization of source P0 for the case of δxx≠δyy, i.e. the spatial coherence length δxx of x component of the electric field at the source is not equal to that of y component. For δxx=δyy or δxx→∞ and δyy→∞, the on-axis relative spectral shift is independent of P0.

Generalized Stokes parameters of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams

The analytical expressions for the generalized (two-point) Stokes parameters of stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beams propagating in free space are obtained. The changes in the spectral Stokes parameters in free space propagation are studied. The dependence of on-axis and transverse spectral Stokes parameters of stochastic electromagnetic GSMP beams on the pulse parameters including pulse duration and temporal coherence length is stressed and illustrated numerically. The results are interpreted physically.

Effect of turbulence on the spectral switches of diffracted spatially and spectrally partially coherent pulsed beams in atmospheric turbulence

Taking the spectrally partially coherent Gaussian Schell-model pulsed (GSMP) beam as a typical example of spatially and spectrally partially coherent pulsed beams, an analytical expression for the spectrum of diffracted spectrally partially coherent GSMP beams propagating through atmospheric turbulence is derived by using the method of the complex Gaussian function expansion, and used to study the spectral switches of spectrally partially coherent GSMP beams in atmospheric turbulence. Numerical calculation results are given to illustrate the dependence of spectral switches on the refraction index structure constant and temporal coherent length. The results are interpreted physically.

Characterization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams

The unified theory of coherence and polarization proposed by Wolf is extended from stochastic stationary electromagnetic beams to stochastic spatially and spectrally partially coherent electromagnetic pulsed beams. Taking the stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the expressions for the spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic GSMP beams propagating in free space are derived. Some special cases are analyzed. The illustrative examples are given and the results are interpreted physically.

Spectral shifts and spectral switches of spatially and spectrally partially coherent pulsed beams in Young’s interference experiment

Taking the Gaussian Schell-model pulsed (GSMP) beam as a typical example of spatially and spectrally partially coherent pulsed beams, an analytical expression for the far-field spectrum of diffracted GSMP beams in Young’s interference experiment is derived, and used to study the spectral shifts and spectral switches of GSMP beams in the far field. Numerical calculation results are given to illustrate the dependence of spectral shifts and spectral switches on the obscuration ratio ε, temporal coherent length T c, spatial correlation parameter β and diffraction angle α. It is shown that the critical angle α c of the first- and second-order spectral switches moves away from the z axis with increasing T c, but α c of the third-order spectral switch moves towards the z axis with increasing T c. The spectral transition height Δ decreases and spectral minimum S min increases as T c increases. α c decreases, Δ increases and S min decreases as β increases. The potential application of spectral switches of spatially and spectrally partially coherent pulsed beams in information encoding and transmission is proposed.

Spectral shifts and spectral switches of diffracted spatially and spectrally partially coherent pulsed beams in the far field

Taking the Gaussian Schell-model pulsed (GSMP) beam as a typical example of spatially and spectrally partially coherent pulsed beams, an analytical expression for the far-field spectrum of diffracted GSMP beams in the space–frequency domain is derived by using the method of the complex Gaussian function expansion, and used to study the spectral shifts and spectral switches of GSMP beams in the far field. Numerical calculation results are given to illustrate the dependence of spectral shifts and spectral switches on the temporal coherence length, spatial correlation parameter, truncation parameter and diffraction angle.

The M2 factor of partially coherent ultrashort pulsed beams

Starting from the space-time Wigner distribution function and taking the Gaussian Schell-model pulsed beam as a typical example, the M 2 factor of partially coherent ultrashort pulsed beams is studied. It is shown that the M 2 factor increases with increasing bandwidth and decreases with increasing spatial correlation. Furthermore, for chirped pulse, the M 2 factor increases as the chirp parameter increases.

Theory of spatially and spectrally partially coherent pulses

A coherent-mode representation for spatially and spectrally partially coherent pulses is derived both in the space-frequency domain and in the space-time domain. It is shown that both the cross-spectral density and the mutual coherence function of partially coherent pulses can be expressed as a sum of spatially and spectrally and temporally completely coherent modes. The concept of the effective degree of coherence for nonstationary fields is introduced. As an application of the theory, the propagation of Gaussian Schell-model pulsed beams in the space-frequency domain is considered and their coherent-mode representation is presented.