Stochastic Electromagnetic Gaussian Schell-model Research Articles

Kurtosis parameter K of arbitrary electromagnetic beams propagating through non-Kolmogorov turbulence

General analytical formulae for the kurtosis parameters K (K parameters) of the arbitrary electromagnetic (AE) beams propagating through non-Kolmogorov turbulence are derived, and according to the unified theory of polarization and coherence, the effect of degree of polarization (DOP) of an electromagnetic beam on the K parameter is studied. The analytical formulae can be given by the second-order moments and fourth-order moments of the Wigner distribution function for AE beams at source plane, the two turbulence quantities relating to the spatial power spectrum, and the propagation distance. Our results can also be extended to the arbitrary beams and the arbitrary spatial power spectra of Kolmogorov turbulence or non-Kolmogorov turbulence. Taking the stochastic electromagnetic Gaussian Schell-model (SEGSM) beam as an example, the numerical examples indicate that the K parameters of a SEGSM beam in non-Kolmogorov turbulence depend on propagation distance, the beam parameters and turbulence parameters. The K parameter of a SEGM beam is more sensitive to effect of turbulence with smaller inner scale and generalized exponent parameter. A non-polarized light has the strongest ability of resisting turbulence (ART), however, a fully polarized SEGSM beam has the poorest ART.

Correlations between intensity fluctuations in stochastic electromagnetic Gaussian Schell-model beams

Recent researches about the vector theory of the Hanbury Brown–Twiss effect at optical frequencies have shown that a new statistical quantity, called the degree of cross-polarization, is needed to predict the correlations between intensity fluctuations in stochastic electromagnetic beams. This note is devoted to an investigation of the variations of the degree of cross-polarization and then to a comparison of the distributions of degree of coherence and the correlations between intensity fluctuations across the cross-section of stochastic electromagnetic Gaussian Schell-model (GSM) beams. Analysis leads to a generalization of scalar theory of the degree of global coherence that describes the GSM sources that generate the electromagnetic GSM beams of either spatially very coherent or spatially very incoherent in the global sense.

Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber

We demonstrate experimentally the procedure of coupling of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam into a single-mode optical fiber. We find that the coupling efficiency depends closely on the coherence and polarization properties of the EGSM beam, which is consistent with theoretical prediction. Our results may find applications in connection with free-space optical communications and LIDARs, where coupling of a stochastic beam into an optical fiber is inevitable encountered.

Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam

Based on classical theory of optical coherence and polarization, coincidence fractional Fourier transform (FRT) with a stochastic electromagnetic Gaussian Schell-model (EGSM) beam is investigated. Dependences of the quality and visibility of the coincidence FRT pattern of an object on the degree of polarization and correlation coefficients of the EGSM beam are studied numerically. It is shown that the quality and visibility of the coincidence FRT pattern of an object are determined by the polarization and coherence of the EGSM beam together.

Polarization ellipse and Stokes parameters of a stochastic electromagnetic Gaussian Schell-model beam propagating through a polarization grating

An analytical propagation formula for the cross-spectral density matrix of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam after propagating through a polarization grating is derived with the help of a tensor method. The statistics properties, particularly the degree of polarization, polarization ellipse and Stokes parameters, of the EGSM beam on propagation after passing through a polarization grating are studied numerically. Our results clearly show that the statistics properties of the EGSM beam on propagation are closely determined by the initial parameters of the EGSM beam and the parameter of the polarization grating. The polarization grating provides one way for modulating the polarization properties of an EGSM beam.

Modulation of spectral intensity, polarization and coherence of a stochastic electromagnetic beam

Analytical formula for the cross-spectral density matrix of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam truncated by a circular phase aperture propagating in free space is derived with the help of a tensor method, which provides a reliable and fast way for studying the propagation and transformation of a truncated EGSM beam. Statistics properties, such as the spectral intensity, the degree of coherence, the degree of polarization and the polarization ellipse of a truncated EGSM beam in free space are studied numerically. The propagation factor of a truncated EGSM beam is also analyzed. Our numerical results show that we can modulate the spectral intensity, the polarization, the coherence and the propagation factor of an EGSM beam by a circular phase aperture. It is found that the phase aperture can be used to shape the beam profile of an EGSM beam and generate electromagnetic partially coherent dark hollow or flat-topped beam, which is useful in some applications, such as optical trapping, material processing, free-space optical communications.

M^2-factor of a stochastic electromagnetic beam in a Gaussian cavity

With the help of a tensor method, an explicit expression for the M2-factor of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in a Gaussian cavity is derived. Evolution properties of the M2-factor of an EGSM beam in a Gaussian cavity are studied numerically in detail. It is found that the behavior of the M2-factor of an EGSM beam in a Gaussian cavity is determined by the statistical properties of the source beam and the parameters of the cavity. Thermal lens effect induced changes of the M2-factor of an EGSM beam in a Gaussian cavity is also investigated. Our results will be useful in many applications, such as free-space optical communications, laser radar system, optical trapping and optical imaging, where stochastic electromagnetic beams are required.

Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam

The concept of the degree of paraxiality introduced recently for monochromatic fields is extended to the domain of stochastic electromagnetic fields. Analytical expression for the degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam is derived. Numerical results show that the degree of paraxiality of an EGSM beam is determined by the degree of polarization, r.m.s. widths of the spectral densities and of the correlation functions of its source. Degree of paraxiality of an EGSM beam after passing through a linear polarizer is also analyzed. Our results show that one can modulate the degree of paraxiality of an EGSM beam by a linear polarizer.

Thermal-lens effect induced changes of polarization, coherence and spectrum of a stochastic electromagnetic beam in a Gaussian cavity

Based on the unified theory of coherence and polarization, the interaction of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam with a Gaussian cavity containing thermal-lens medium is analyzed. In particular, the effect of the thermal medium of the lens on the evolution properties of the degree of polarization, the degree of coherence and the spectral shift are investigated in detail. It is shown that the thermal-lens medium has a strong influence on the behavior of the EGSM beam especially in unstable resonators, thus it is necessary for us to take the thermal-lens effect into consideration in practice.

Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam

Analytical formula is derived for the propagation factor (known asM(2)-factor) of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in free space and in turbulent atmosphere. In free space, the M(2)-factor of an EGSM beam is mainly determined by its initial degree of polarization, r.m.s. widths of the spectral densities and correlation coefficients, and its value remains invariant on propagation. In turbulent atmosphere, the M(2)-factor of an EGSM beam is also determined by the parameters of the turbulent atmosphere, and its value increases on propagation. The relative M(2)-factor of an EGSM beam with lower correlation factors, larger r.m.s. widths of the spectral densities and longer wavelength is less affected by the atmospheric turbulence. Under suitable conditions, an EGSM beam is less affected by the atmospheric turbulence than a scalar GSM beam (i.e. fully polarized GSM beam). Our results will be useful in long-distance free-space optical communications.

Spectral shift of a stochastic electromagnetic Gaussian Schell-model beam in a Gaussian cavity

Spectral changes of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam interacting with a Gaussian cavity are investigated. It is shown that the spectral shift is mainly determined by the degree of polarization of the initial beam and by the parameters of the cavity. Generically the blue shift occurs at on-axis points, while the red shift can occur at off-axis points. The condition under which the relative spectral shift is independent of the degree of polarization of the initial beam is analyzed.

Effect of polarization on spectral switches in the diffraction of stochastic electromagnetic beams

We consider the stochastic electromagnetic Gaussian Schell-model (EGSM) beam and show that the polarization of stochastic electromagnetic EGSM beams in the source plane affect spectral switches of diffracted stochastic electromagnetic EGSM beams in the far field. For two cases of fully coherent and partially coherent δxx=δyy the behavior of spectral switches are same in different degrees of polarization of the source.

Effects of astigmatism on spectra, coherence and polarization of stochastic electromagnetic beams passing through an astigmatic optical system

Analytical formulas for the cross-spectral density matrix of stochastic electromagnetic Gaussian Schell-model (EGSM) beams passing through an astigmatic optical system are derived. We show both analytically and by numerical examples the effects of astigmatism on spectra, coherence and polarization of stochastic electromagnetic EGSM beams propagating through an astigmatic lens. A comparison with the aberration-free case is made, and shows that the astigmatism has significant effect on the spectra, coherence and polarization.