Average intensity and spreading of an elegant Hermite-Gaussian beam in turbulent atmosphere

Experimental realization of modulated Hermite-Gaussian laser modes: a maximum number of highly intense lobes

Here, we present an experimental method that redistributes the optical energy among the lobes of high-order standard Hermite-Gaussian (SHG) laser modes in a controlled manner. We numerically designed diffractive optical elements, displayed over a spatial light modulator for redistribution of optical energy that converts low and moderate intense lobes into all highly intense lobes and vice versa at the Fourier plane. Such precise generation of modulated HG (MHG) laser modes offers a maximum number of highly intense lobes compared to SHG modes. Hence, we envisage that MHG beams may surpass SHG beams in many applications, such as particle manipulation and optical lithography, where highly intense lobes play a significant role.

Generation of an Adjustable Optical Cage through Focusing an Apertured Bessel-Gaussian Correlated Schell-Model Beam

An adjustable optical cage generated by focusing a partially coherent beam with nonconventional correlation function named the Bessel–Gaussian correlated Schell-model (BGCSM) beam is investigated in detail. With the help of the generalized Huygens–Fresnel integral and complex Gaussian function expansion, the analytical formula of the BGCSM beam passing through an apertured ABCD optical system was derived. Our numerical results show that the generated optical cage can be moderately adjusted by the aperture radius, the spatial coherence width, and the parameter β of the BGCSM beam. Furthermore, the effect of these parameters on the effective beam size and the spectral degree of coherence were also analyzed. The optical cage with adjustable size can be applied for particle trapping and material thermal processing.

Evolution properties of partially coherent standard and elegant Hermite-Gaussian beams in uniaxial crystals

The propagation properties of a partially coherent elegant Hermite-Gaussian beam (EHGB) and a partially coherent standard Hermite-Gaussian beam (SHGB) in uniaxial crystals orthogonal to the optical axis are studied. The propagation expression for the cross-spectral density of the partially coherent EHGB and SHGB propagating in a uniaxial crystal is derived. With the help of the derived formula, some analyses are illustrated by numerical examples related to the evolution properties of the spectral density, the spectral degree of coherence, and the effective beam width of the partially coherent EHGB and SHGB in a uniaxial crystal. It is shown that propagation properties of the partially coherent EHGB and SHGB in an isotropic crystal are much different from the evolution properties in an anisotropic crystal. The evolution behavior of spectral density and the spectral degree of coherence depends on the parameters of the uniaxial crystals (the ratio of extraordinary and ordinary refractive indices), and beam parameters including the coherence length and the beam order, as well as the propagation distance.

Circularly symmetric cusped random beams in free space and atmospheric turbulence

A class of random stationary, scalar sources producing cusped average intensity profiles (i.e. profiles with concave curvature) in the far field is introduced by modeling the source degree of coherence as a Fractional Multi-Gaussian-correlated Schell-Model (FMGSM) function with rotational symmetry. The average intensity (spectral density) generated by such sources is investigated on propagation in free space and isotropic and homogeneous atmospheric turbulence. It is found that the FMGSM beam can retain the cusped shape on propagation at least in weak or moderate turbulence regimes; however, strong turbulence completely suppresses the cusped intensity profile. Under the same atmospheric conditions the spectral density of the FMGSM beam at the receiver is found to be much higher than that of the conventional Gaussian Schell-model (GSM) beam within the narrow central area, implying that for relatively small collecting apertures the power-in-bucket of the FMGSM beam is higher than that of the GSM beam. Our results are of importance to energy delivery, Free-Space Optical communications and imaging in the atmosphere.

Far-zone polarization distribution properties of partially coherent beams with non-uniform source polarization distributions in turbulent atmosphere

It has already been found that, in turbulent atmosphere, many partially coherent electromagnetic beams with uniform source polarization distributions can regain these distribution patterns in the far field. However, the far-zone polarization properties of beams with non-uniform source polarization distributions are not sufficiently studied and the condition for an electromagnetic beam to reconstruct its source polarization distribution in the far zone is not established. Using a type of electromagnetic anisotropic Gaussian Schell-model (GSM) beams which can have non-uniform polarization distributions on the source plane, we find that, under the influence of turbulent atmosphere, the transverse polarization distribution will finally become uniform starting with a non-uniform source polarization distribution, and the far-field degree of polarization is affected by the source intensity parameters, but not by the source spatial coherence parameters. We also find that, electromagnetic anisotropic GSM beams can regain their source polarization patterns in the far field when propagating through atmospheric turbulence if and only if, the two intensity distributions corresponding to the two orthogonal field components on the source plane are the same, or are different only for a constant parameter. The validity of this condition is unaffected by the intensity and spatial coherence profiles on the source plane.

Propagation of a radial phased-locked Lorentz beam array in turbulent atmosphere

A radial phased-locked (PL) Lorentz beam array provides an appropriate theoretical model to describe a coherent diode laser array, which is an efficient radiation source for high-power beaming use. The propagation of a radial PL Lorentz beam array in turbulent atmosphere is investigated. Based on the extended Huygens-Fresnel integral and some mathematical techniques, analytical formulae for the average intensity and the effective beam size of a radial PL Lorentz beam array are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of a radial PL Lorentz beam array in turbulent atmosphere are numerically calculated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of a radial PL Lorentz beam array in turbulent atmosphere are discussed in detail.

Propagation of elegant Laguerre-Gaussian beam in non-Kolmogorov turbulence

The analytical formulas for the average intensity and the beam width of the elegant Laguerre-Gaussian beam (ELGB) in non-Kolmogorov turbulence have been derived based on the extended Huygens-Fresnel principle. Numerical results reveal that the ELGB converts to Gaussian form quicker for smaller values of beam order and for smaller wavelengths. The root-mean-square (rms) beam width of ELGB increases markedly with the propagation distance for higher beam order, smaller waist width, and larger wavelength. Furthermore, discussions of the influence of ELGB by the non-Kolmogorov turbulence reveal that the normalized intensity distribution of ELGB converts into Gaussian form more quickly and that the rms beam width of ELGB increases more rapidly in non-Kolmogorov turbulence with smaller parameter α, larger outer scale, smaller inner scale and larger structure constant.

Evolution properties of the intensity distribution of an anisotropic Gaussian Schell-model beam in a turbulent atmosphere

An analytical expression for the cross-spectral density of an anisotropic Gaussian Schell-model (AGSM) beam propagating in a turbulent atmosphere is derived, which is featured by its clear physical meaning. The evolution properties of the intensity distribution of an AGSM beam in a turbulent atmosphere are studied thoroughly. It is found that owing to the anisotropy of the source coherence, the intensity distribution can have many different evolution processes; but under the influence of the turbulent atmosphere, it will finally take on a circular shape. The effects of lowering the source coherence on the circularization speed of the intensity distribution are also investigated. It is found that, when the anisotropy of the source coherence is taken into account, lowering the source coherence can accelerate or decelerate the circularization of the intensity distribution. We propose and demonstrate five kinds of conditions, and, under each condition, lowering the source coherence has a unique and definite effect on the circularization speed of the intensity distribution. In particular, we give an analysis about the equivalence between the problem studied in one of our five conditions and that in the work of Cai and He [Appl. Phys. Lett. 89, 041117 (2006)] and show that their relevant conclusion is incorrect.

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.

Propagation of a partially coherent Lorentz-Gauss beam through a paraxial ABCD optical system

Based on the generalized Huygens-Fresnel integral and the Hermite-Gaussian expansion of a Lorentz distribution, analytical expressions for the mutual coherence function, the effective beam size, and the spatial complex degree of coherence of a partially coherent Lorentz-Gauss beam through a paraxial and real ABCD optical system are derived, respectively. As a numerical example, the focusing of a partially coherent Lorentz-Gauss beam is considered. The normalized intensity distribution, the effective beam size, and the spatial complex degree of coherence for the focused partially coherent Lorentz-Gauss beam are numerically demonstrated in the focal plane. The influence of the spatial coherence length on the normalized intensity distribution, the effective beam size, and the spatial complex degree of coherence is mainly discussed.

Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere

The propagation of a Lorentz-Gauss beam in turbulent atmosphere is investigated. Based on the extended Huygens-Fresnel integral and the Hermite-Gaussian expansion of a Lorentz function, analytical formulae for the average intensity and the effective beam size of a Lorentz-Gauss beam are derived in turbulent atmosphere. The average intensity distribution and the spreading properties of a Lorentz-Gauss beam in turbulent atmosphere are numerically demonstrated. The influences of the beam parameters and the structure constant of the atmospheric turbulence on the propagation of a Lorentz-Gauss beam in turbulent atmosphere are also discussed in detail.

Propagation of vector vortex beams through a turbulent atmosphere

We numerically study the propagation properties of vector vortex beams through a turbulent atmosphere. The irradiance pattern, degree of polarization, and scintillation index of radially polarized beam are computed for different propagation distances in an atmosphere with weak and strong turbulences. Corresponding properties of a fundamental Gaussian beam and a scalar vortex beam with topological charge of + 1 propagating through the same atmospheric turbulence conditions are calculated for comparison. With the same initial intensity profile, the vector vortex beam shows substantially lower scintillation than the scalar vortex. The existence of the vectorial vortex can be identified with longer propagation distance than the scalar vortex even with vanishing characteristic vortex structure in the irradiance images. This indicates the potential advantages of using a vector vortex beam to mitigate atmospheric effects and enable a more robust free space communication channel with longer link distance.