The relay propagation of partially coherent cosh–Gaussian–Schell beams in turbulent atmosphere

We have studied the relay propagation of a partially coherent cosh–Gaussian–Schell beam in turbulent atmosphere. Analytical expressions for both the cross-spectral density at the relay system and average intensity at the target are derived. By using the analytical expressions some special cases are studied and some numerical simulation comparisons are made, especially the effects of the coherence of the beam, turbulence strength, aperture and its size on the relay propagation. Our study shows that the effects of diffraction and coherence of initial beam on the intensity profiles at the relay system are so small that they can be neglected when the effects due to turbulence are large enough. Even though the correction to the receiving beam at relay system is important, it is not necessary to improve the receiving beam when the effect of turbulence over the travel path is strong. A high peak intensity at target can be obtained by optimizing these factors, such as propagation distance, aperture and spatial correlation length.     

Relation between asymmetrical orbital angular momentum and irradiance-profile rotation for partially coherent beams

On the basis of the irradiance-moment formalism for describing general partially coherent beams, we investigate the relation between the spatial orientation of the transverse beam profile upon propagation and the asymmetrical part of its orbital angular momentum (OAM). More specifically, a necessary and sufficient condition (one-to-one correspondence) is shown between freely propagating non-rotating beams and vanishing asymmetrical OAM. As a corollary, it is obtained that any beam emerging from optical systems that transform a rotating field into a non-rotating beam exhibits vortex OAM only.     

Generation of partially coherent vortex bottle beams

Intensity distribution of the partially coherent Bessel vortex beams focused by an aperture lens is inves- tigated.It is found that the intensity distribution in the neighborhood of the geometrical focus is not only dependent on the topological charge and the radial frequency of the incident partially coherent Bessel vortex beam,but also on its coherence length.Based on this,the desired partially coherent vortex bottle beams can be obtained by choosing appropriate values of parameters.Because such bottle beams possess characteristics of low coherence and vortex,it may be used in microscopic particles guiding,trapping,and inducing rotation.     

Partially coherent vortex beams propagation in a turbulent atmosphere

Beam propagation through atmospheric turbulence is asubject of considerable importance in connection withfree-space optical communications, targeting systems,and remote sensing, and imaging systems[1,2]. Laserbeams are of special interest and employed due to theirhigh directionality. However, fully coherent laser beamsare very sensitive to the properties of the propagationmedia, as a consequence, the turbulence-induced spa-tial broadening of the beam is a limiting factor in mostapplications[1,…     

Scintillation calculations for partially coherent general beams via extended Huygens–Fresnel integral and self-designed Matlab function

We present scintillation calculations in weak atmospheric turbulence for partially coherent general beams based on the extended Huygens–Fresnel integral and a Matlab function designed to handle expressions both of the average intensity and the average squared intensity. This way, the integrations are performed in a semi-analytic manner by the associated Matlab function, and this avoids lengthy, time-consuming and error prone hand derivations. The results are obtained for the partially coherent fundamental and higher-order sinusoidal and annular Gaussian beams. By plotting the scintillation index against the propagation distance and source size, we illustrate the on-axis scintillation behaviors of these beams. Accordingly, it is found that within specific source and parameter ranges, partially coherent fundamental, higher-order sinusoidal and annular Gaussian beams are capable of offering less scintillations, in comparison to the fundamental Gaussian beam.     

Changes in the state of polarization of partially coherent flat-topped beam in turbulent atmosphere for different source conditions

The polarization states, i.e. the size, the shape and the orientation of the polarization ellipse of partially coherent flat-topped (PCFT) beams passing through atmospheric turbulence are studied in detail. The effects are studied of different source conditions on the polarization states of a PCFT beam propagating through atmospheric turbulence. Based on the unified theory of the polarization states for random electromagnetic beams, we have established the detailed formula for calculating the change of the polarization states of such beams. The polarization states behavior of PCFT beams passing through atmospheric turbulence for any arbitrary order of a flat-topped beam “N” under different source conditions were investigated.     

Propagation properties of partially coherent Hermite–cosh-Gaussian beams through atmospheric turbulence

The analytical expression of partially coherent Hermite–cosh-Gaussian (HChG) beams propagating through atmospheric turbulence is derived and used to study their propagation properties through atmospheric turbulence. It is shown that partially coherent HChG beams propagating through atmospheric turbulence undergo several stages of evolution and a decrease of the spatial correlation length speeds up the evolution process. The smaller the spatial correlation length and the larger the beam orders are, the less the beam-width spreading of partially coherent HChG beams is affected by turbulence. At a sufficiently long propagation distance the beam-width spreading of partially coherent HChG beams with smaller Ch-part parameter and smaller waist width is less affected by turbulence. The results are illustrated by numerical examples, and the validity of the results is interpreted physically.     

Polarization properties of partially coherent electromagnetic elegant Laguerre–Gaussian beams in turbulent atmosphere

Based on the extended Huygens–Fresnel Principle and the unified theory of coherence and polarization, the analytical formulas for the polarization degree and spectral coherence degree of partially coherent electromagnetic elegant Laguerre–Gaussian (PCEELG) beams through turbulent atmosphere are obtained theoretically in detail. It is found that the polarization degree of PCEELG beams tends to the value of its source plane after a sufficiently long propagation distance in turbulent atmosphere. Furthermore, this value is independent of the beam orders, the correlation length in the source plane and the structure constant of the turbulent atmosphere ( $C_{n}^{2}$ ). The polarization degree of PCEELG beams also acquires a particular value at a certain distance in free space, which is different from the value in the source plane. The spectral coherence degree of PCEELG beams has an oscillatory behavior for different propagation distance, beam orders and  $C_{n}^{2}$ .     

Polarization fluctuations of partially coherent Hermite–Gaussian beams in a slant turbulent channel

The propagation of a partially coherent Hermite–Gaussian beam in a slant turbulent channel is studied. The analytical formula for the quantum degree of polarization of a partially coherent Hermite–Gaussian beam is derived based on the quantum Stokes operators and the generalized Huygens–Fresnel principle. It is shown that the zenith angle slightly affects the polarization degree of partially coherent Hermite–Gaussian beams, and the changes of polarization degree are affected by the coherence length, the detection photon-number and the ground refractive index structure parameter. Furthermore, the numerical simulations show that a partially coherent Hermite–Gaussian beam with bigger coherence length, higher photon-number level, lower beam order, shorter wavelength is less affected by the turbulence. These results indicate that one can choose the partially coherent Hermite–Gaussian beam with bigger coherence length, lower beam order, shorter wavelength, higher detection photon-number and set the size of transmitting aperture w₀$w_0$ as about 0.065 m to improve the performance of a polarization-encoded free-space quantum communication system.     

Ghost imaging with partially coherent light radiation through turbulent atmosphere

Based on the classical optical coherent theory and the extended Huygens-Fresnel integral, ghost imaging with partially coherent light radiation through turbulent atmosphere has been studied. The analytical ghost-imaging formulas have been derived. Based on these formulas and the numerical calculation results, we find that the image quality is influenced by the turbulence strength, the propagation distance, and the coherent parameters of the partially coherent light.     

Scintillation of partially coherent Gaussian–Schell model beam propagation in slant atmospheric turbulence considering inner- and outer-scale effects

Based on the modified Rytov theory and the international telecommunication union-radio （ITU-R） slant atmospheric structure constant model, the uniform scintillation index of partially coherent Gaussian-Schell model （GSM） beam propa- gation in the slant path is derived from weak- to strong-turbulence regions considering inner- and outer-scale effects. The effects of wavelength of beams and inner- and outer-scale of turbulence on scintillation are analyzed numerically. Compar- ison between the scintillation of GSM beams under the von Karman spectrum and that of beams under the modified Hill spectrum is made. The results obtained show that the scintillation index obtained under the von Karman spectrum is smaller than that under the modified Hill spectrum. This study can find theory bases for the experiments of the partially coherent GSM beam propagation through atmospheric turbulence.     

Nonparaxial propagation of linearly polarized modified Bessel–Gaussian beams and phase singularities of the electromagnetic field components

Based on an operator transformation technique and the nonparaxial propagation results of linearly polarized Gaussian beams, the nonparaxial propagation formulas of linearly polarized modified Bessel–Gaussian beams with optical vortices are constructed. Numerical investigations indicate that electromagnetic field components associated with the beams exhibit different phase singularities.     

Partially coherent elegant Hermite–Gaussian beams

Elegant Hermite–Gaussian beams (EHGBs) are extended to the partially coherent case. An explicit and analytical formula is derived for the cross-spectral density of a partially coherent EHGB propagating through an aligned or misaligned paraxial ABCD optical system. The propagation properties of a partially coherent EHGB in free space and its focusing properties through a thin lens are studied numerically, and are compared to those of a partially coherent standard Hermite–Gaussian beam (SHGB). It is found that the propagation and focusing properties of a partially coherent EHGB are closely related to its initial coherence. A partially coherent EHGB spreads slower than a partially coherent SHGB in free-space propagation. A partially coherent EHGB can be focused more tightly than a partially coherent SHGB.     

M 2-factor of a partially coherent Lorentz–Gauss beam in a turbulent atmosphere

Based on the second-order moments of partially coherent beams in atmospheric turbulence, the analytical beam propagation factor of a partially coherent Lorentz–Gauss beam in a turbulent atmosphere is derived. As a special case of the general formula, the beam propagation factor of a partially coherent Lorentz beam in a turbulent atmosphere is also presented. By using the derived analytical expression, the beam propagation factor is illustrated and analyzed with numerical examples, and the influences of the beam parameters a _j and w _0j , the coherent parameter τ _j , the axial propagation distance z, the structure constant C_n²C_{n}^{2}, and the inner scale turbulence l ₀ on the beam propagation factor are also discussed in detail.     

Can two partially coherent cosh-Gaussian beams generate far fields with the same spectral degree of coherence？

Taking partially coherent cosh--Gaussian (ChG) beams as an example of more general partially coherent beams, we have studied the spectral degree of coherence of partially coherent ChG beams in the far field. It is shown that, unlike Gaussian Schell-model (GSM) beams, in the strict sense there do not exist two partially coherent ChG beams which can generate far fields with the same spectral degree of coherence. However, under certain conditions it is possible to find two partially coherent ChG beams with the same spectral degree of coherence in the far field.     

Dynamic behavior of composite spectral Stokes singularities in?superimposed partially coherent beams beyond the paraxial approximation

The composite spectral Stokes singularities are introduced to describe polarization singularities in superimposed partially coherent beams beyond the paraxial approximation. Based on the vector Rayleigh–Sommerfeld diffraction integrals, the dynamic behavior of composite spectral Stokes singularities in the free-space propagation is studied and illustrated by numerical examples. A comparison with the previous work is also made.     

Dense laser-driven electron sheets as relativistic mirrors for coherent production of brilliant X-ray and γ-ray beams

Several techniques exist to obtain brilliant X-ray beams by coherent reflection from relativistic electrons (E _e=γ mc ²) with Doppler frequency upshift of 4γ ². We describe a new approach starting with an ultra-thin solid target. Larger ‘driver’-laser intensities with high contrast are required to produce dense electron sheets. Their acceleration in vacuum results in a transverse momentum component besides the dominant longitudinal momentum component. The counter-propagating ‘production’ laser for optimum Doppler boost in X-ray production by reflection has to be injected opposite to the electron direction and not opposite to the driver laser. Different measures to increase the reflectivity of the electron sheet via laser trapping or free-electron-laser-like micro-bunching are discussed, extending the photon energy into the MeV range. Here, first-order estimates are given.