Twisted Anisotropic Gaussian Schell-model Beam Research Articles

Orbital angular moment of a partially coherent beam propagating through an astigmatic ABCD optical system with loss or gain

We derive the general expression for the orbital angular momentum (OAM) flux of an astigmatic partially coherent beam carrying twist phase [i.e., twisted anisotropic Gaussian-Schell model (TAGSM) beam] propagating through an astigmatic ABCD optical system with loss or gain. The evolution properties of the OAM flux of a TAGSM beam in a Gaussian cavity or propagating through a cylindrical thin lens are illustrated numerically with the help of the derived formula. It is found that we can modulate the OAM of a partially coherent beam by varying the parameters of the cavity or the orientation angle of the cylindrical thin lens, which will be useful in some applications, such as free-space optical communications and particle trapping.

Propagation of a twisted anisotropic Gaussian Schell-model beam beyond the paraxial approximation

With the help of a tensor method, an analytical nonparaxial propagation formula for a twisted anisotropic Gaussian Schell-model (GSM) beam in free space is derived based on the generalized Raleigh-Sommerfeld diffraction integral. The far-field nonparaxial propagation expression for a twisted anisotropic GSM beam is also derived. The paraxial approximation is dealt with as a special case of our general result. Our numerical results show that the nonparaxial propagation properties of a twisted anisotropic GSM beam are closely related to the initial beam parameters (i.e., twist factor, transverse spot width matrix, coherence width matrix and wavelength) and the propagation distance. Our formulae provide a convenient and powerful way for studying the paraxial and nonparaxial propagation of an isotropic or anisotropic GSM beam with or without twist phase in free space.

Propagation of a decentered astigmatic partially coherent beam in a turbulent atmosphere

Propagation properties of a decentered general astigmatic partially coherent beam (i.e., decentered twisted anisotropic Gaussian Schell-model beam) in a turbulent atmosphere are investigated. Analytical formulas for the cross-spectral density and decentered parameter of a decentered astigmatic partially coherent beam propagating in a turbulent atmosphere are derived. Irradiance properties of a decentered astigmatic partially coherent beam in a turbulent atmosphere are studied graphically, and are found to be quite different from its properties in free space.

Propagation of a partially coherent twisted anisotropic Gaussian Schell-model beam in a turbulent atmosphere

Analytical formulas are derived for the propagation of a partially coherent twisted anisotropic Gaussian Schell-model (TAGSM) beam in a turbulent atmosphere. Propagation properties of a TAGSM beam in a turbulent atmosphere are investigated in detail. It is found that a TAGSM beam will become a circular beam in a turbulent atmosphere, and low coherence and larger twist have an effect of anticircularization of the beam spot. The beam spot spreads more rapidly for lower coherence, larger twist, or stronger turbulence.

Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through an apertured astigmatic optical system

By expanding the hard-aperture function into a finite sum of complex Gaussian functions, we derived an approximate analytical formula for a partially coherent twisted anisotropic Gaussian Schell-model (AGSM) beam propagating through an apertured paraxial general astigmatic (GA) optical system by use of a tensor method. The results obtained by using the approximate analytical formula are in good agreement with those obtained by using the numerical integral calculation. Our formulas avoid time-consuming numerical integration and provide a convenient and effective way for studying the propagation and transformation of a partially coherent twisted AGSM beam through an apertured paraxial GA optical system.

Fractional Fourier transform for partially coherent beam in spatial-frequency domain

By using Fourier transform and the tensor analysis method, the fractional Fourier transform (FRT) in the spatial-frequency domain for partially coherent beams is derived. Based on the FRT in the spatial-frequency domain, an analytical transform formula is derived for a partially coherent twisted anisotropic Gaussian–Schell model (GSM) beam passing through the FRT system. The connections between the FRT formula and the generalized diffraction integral formulae for partially coherent beams through an aligned optical system and a misaligned optical system in the spatial-frequency domain are discussed, separately. By using the derived formula, the intensity distribution of partially coherent twisted anisotropic GSM beams in the FRT plane are studied in detail. The formula derived provide a convenient tool for analysing and calculating the FRTs of the partially coherent beams in spatial-frequency domain.

Application of the Wigner distribution function to studying spectral changes of twisted anisotropic Gaussian Schell-Model beams

Summary By using the Wigner distribution function (WDF), a general closed-form expression for the spectrum of twisted anisotropic Gaussian Schell-model (AGSM) beams in passage through a first-order ABCD system is derived. The spectral changes of twisted AGSM beams propagating in free space and through a thin lens, and the spectral changes of conversional Gaussian-Schell model (GSM) beams are treated as special cases of our general expression. Our theoretical and numerical results show that the WDF provides a powerful and simple tool in analyzing propagation properties of general AGSM beams. Specifically, the spectral behavior of twisted AGSM beams and conventional GSM beams can be treated in a unified and analytical way.

Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane.

An analytical and concise formula is derived for the fractional Fourier transform (FRT) of partially coherent beams that is based on the tensorial propagation formula of the cross-spectral density of partially coherent twisted anisotropic Gaussian-Schell-model (GSM) beams. The corresponding tensor ABCD law performing the FRT is obtained. The connections between the FRT formula and the generalized diffraction integral formulas for partially coherent beams passing through aligned optical systems and misaligned optical systems are discussed. With use of the derived formula, the transformation and spectrum properties of partially coherent GSM beams in the FRT plane are studied in detail. The results show that the fractional order of the FRT has strong effects on the transformation properties and the spectrum properties of partially coherent GSM beams. Our method provides a simple and convenient way to study the FRT of twisted anisotropic GSM beams.

Spectral shift of partially coherent twisted anisotropic Gaussian–Schell-model beams focused by a thin lens

The spectral shift of partially coherent twisted anisotropic Gaussian–Schell-model (GSM) beams focused by a thin lens is treated analytically by using the tensor method. This method allows us to avoid time-consuming numerical integration that has been commonly used in previous study of spectral shift problems. The dependence of the relative frequency shift on the beam's initial parameters is demonstrated numerically in detail. The results show that the spectral shift of twisted anisotropic GSM beams is closely related to the initial transverse coherence width matrix and the twist factor. The spectral shift changes from blue-shift to red-shift with the increase of the transverse coordinate.

Focusing properties of partially coherent twisted anisotropic Gaussian–Schell model beams

Abstract The focusing properties of partially coherent twisted anisotropic Gaussian–Schell model (GSM) beams by a thin astigmatic lens are studied in detail by using the newly derived tensor ABCD law. The intensity distribution, the evolutions of the beam spot area and the twisted factor of the focused anisotropic GSM beams are calculated and illustrated graphically. The results show that the focusing properties of twisted anisotropic GSM beams are closely related with the spatial coherence of the beams.

Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams in dispersive and absorbing media.

By adopting a new tensor method, we derived an analytical propagation formula for the cross-spectral density of partially coherent twisted anisotropic Gaussian Schell-model (GSM) beams through dispersive and absorbing media. Using the derived formula, we studied the evolution properties and spectrum properties of twisted anisotropic GSM beams in dispersive and absorbing media. The results show that the dispersive and absorbing media have strong influences on the propagation properties of twisted anisotropic GSM beams and their spectrum evolution. Our method provides a simple and convenient way to study the propagation of twisted anisotropic GSM beams in media with complex refractive index.

Fractional Fourier transform for partially coherent Gaussian–Schell model beams

The fractional Fourier transform (FRT) is applied to partially coherent twisted anisotropic Gaussian-Schell model (GSM) beams based directly on the cross-spectral density. An analytical and concise formula is derived for the cross-spectral density of partially coherent twisted anisotropic GSM beams passing through a FRT system in terms of the tensor method. The corresponding tensor ABCD law for performing a FRT is obtained. The connection between the FRT formula and the generalized Collins formula for partially coherent beams is discussed. The formulas derived provide a powerful tool for analyzing and calculating the FRTs of partially coherent beams.

Propagation of partially coherent twisted anisotropic Gaussian–Schell model beams through misaligned optical systems

The generalized diffraction integral formulae for partially coherent beams through misaligned optical systems are derived in both spatial and spatial-frequency domain. Based on these formulae, the analytical propagation formulae for partially coherent twisted anisotropic Gaussian–Schell model (GSM) beams through misaligned optical systems are derived. The derived formulae provide a powerful and convenient tool for treating the propagation and transformation of partially coherent twisted anisotropic GSM beams through misaligned optical systems in spatial domain and spatial-frequency domain. As an application example, the intensity distribution properties of partially coherent twisted GSM beams through a misaligned thin lens are studied.

Spectral shift of partially coherent twisted anisotropic Gaussian Schell-model beams in free space

The spectral shift of partially coherent twisted anisotropic Gaussian Schell-model (GSM) beams in free space is treated analytically by using the newly derived tensor ABCD law for partially coherent twisted anisotropic GSM beams. This representation generalizes the previous results for isotropic GSM beams into anisotropic and twisted cases. It can avoid numerical integral that is time consuming and commonly used in the previous study of spectral shift problems. The results show that the spectral shift of twisted anisotropic GSM beams is closely related with the degree of coherence, wavefront curvature and the twist factor. The spectral shift changes from blueshift to redshift with the increase of the transverse coordinate.

Tensor ABCD law for partially coherent twisted anisotropic Gaussian–Schell model beams

A 4 x 4 complex curvature tensor M>(-1) is introduced to describe partially coherent anisotropic Gaussian-Schell model (GSM) beams. An analytical propagation formula for the cross-spectral density of partially coherent anisotropic GSM beams is derived. The propagation law of M(-1) that is also derived may be called partially coherent tensor ABCD law. The analytical formulas presented here are useful in treating the propagation and transformation of partially coherent anisotropic GSM beams, which include previous results for completely coherent Gaussian beams as special cases.