Polarization changes in a partially coherent radially polarized doughnut beam through turbulent ocean

On the basis of the extended Huygens–Fresnel integral principle and unified theory of coherence and polarization of light, we studied the effects of oceanic turbulence on polarization properties of a partially coherent radially polarized doughnut (PCRPD) beam. The ocean-induced fluctuations in the refractive index are assumed be driven by temperature and salinity fluctuations. Numerical examples of changes in polarization properties, such as the degree of polarization, the degree of ellipticity, and the orientation angle in the oceanic turbulence for the PCRPD beam, are given. Our analysis demonstrates how polarization of the PCRPD beam is affected by statistical properties of the source and by several parameters of oceanic turbulence. We find that the propagation of the PCRPD beam is different from that of stochastic beams in oceanic turbulence. The degree of polarization for the PCRPD beam approaches a certain steady value, and the elliptical polarized state of the fully polarized portion of the beam will become fully linear in the far field.     

Analytical non-paraxial TM polarized Gaussian beam in the source region

The non-paraxial TM polarized Gaussian beam, which approximately reduces to be a Gaussian TEM₀₀ mode at the paraxial case, is the rigorous solution of Maxwell's equations for a confocal resonator. By means of mathematical techniques, the analytical expression in the source region has been derived without any approximation and expressed as a sum of the propagating part and the evanescent part. With some certain given values of the initial Gaussian half width w ₀, the distributions of the squared modulus of the propagating part, the evanescent part, and the whole beam are depicted in the reference plane close to the source. When w ₀ is small enough, the squared modulus of the non-paraxial TM polarized Gaussian beam is composed of two lobes, which results from the contribution of the evanescent wave. This research further reveals the difference of a non-paraxial TM polarized Gaussian beam from a non-paraxial Gaussian beam.     

Radiation forces of highly focused radially polarized hollow sinh-Gaussian beams on a Rayleigh metallic particle

Based on the vector diffraction theory, the tight focusing properties of radially polarized hollow sinh-Gaussian (HsG) beams are theoretically studied. It is found that the radially polarized HsG beams can form a longitudinally polarized sub-wavelength focal spot. Moreover, the radiation forces acting on a Rayleigh metallic particle are calculated for the case where the radially polarized HsG beams are applied. Compared with the use of conventional Gaussian beams, the high-order radially polarized HsG beams can largely enhance the radial trap stiffness and broaden the axial trap distance. The influence of the beam order m on the focusing properties and trap stiffness is investigated in detail.     

Nonparaxial propagation of spirally polarized optical beams

The free-propagation features of light beams whose transverse electric field lines are logarithmic spirals (namely, spirally polarized beams) are investigated in both the paraxial and the nonparaxial regime. The complete propagated electric field is considered, and some general properties are obtained regardless of the specific transverse distribution. Simple and significant analytical results are obtained when the transverse intensity profile is chosen as that pertinent to an axially symmetric Laguerre-Gaussian beam of order 1 (namely, spirally polarized donut beams). In particular, it is found that for such beams, the propagated longitudinal electric field can be expressed as a simple superposition of elegant Laguerre-Gaussian beams. Numerical results are presented for different values of the beam parameters and are compared with recently obtained experimental results.     

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.     

Propagation properties of partially coherent radially polarized beam in a turbulent atmosphere

Based on the Huygens–Fresnel principle and the unified theory of coherence and polarization of partially coherent beams, we investigate the propagation characteristics of a partially coherent radially polarized doughnut (PCRPD) beam in a turbulent atmosphere. It is found that, after propagating through a turbulent atmosphere, the doughnut beam spot is changed into a circular Gaussian beam. Moreover, the degree of coherence, the degree of polarization and the degree of cross-polarization of the beam will change on propagation, and this change is dependent upon the degree of coherence of the source and atmospheric turbulence.     

Statistical properties of a radially polarized twisted Gaussian Schell-model beam in a uniaxial crystal

We derive the analytical formulas for the elements of the cross-spectral density matrix of a radially polarized partially coherent beam with a twist phase named radially polarized twisted Gaussian Schell-model (RPTGSM) beam propagating in a uniaxial crystal, and explore the statistical properties, such as the intensity distribution, the degree of polarization (DOP) and the state of polarization (SOP) of such beam in a uniaxial crystal with the help of the derived formulas. It is found that the statistical properties of a RPTGSM beam are closely related with the twist phase and the anisotropy of the uniaxial crystal, e.g. the twist phase leads to the rotation of the intensity, DOP and SOP distributions, and the anisotropy of the uniaxial crystal leads to the asymmetry distributions of these statistical properties. Our results will be useful for designing light field with prescribed intensity, DOP and SOP distributions, and may be useful in optical manipulations and free-space optical communications.     

Simple interferometric technique for generation of a radially polarized light beam

We present a theoretical and experimental investigation of an interferometric technique for converting a linearly polarized Gaussian beam into a radially polarized doughnut beam. The experimental setup accomplishes the coherent summation of two orthogonally polarized TEM01 and TEM10 beams that are obtained from the transformation of a TEM00 beam by use of a simple binary diffractive optical element. We have shown that the degree of radial polarization is maximum at a given distance from the interferometer output port that depends on the diameter of the incident beam at the interferometer input port.     

Gaussian laser beam transformation into an optical vortex beam by helical lens

In this article, we investigate the Fresnel diffraction characteristics of the hybrid optical element which is a combination of a spiral phase plate (SPP) with topological charge p and a thin lens with focal length f, named the helical lens (HL). As incident a Gaussian laser beam is treated, having its waist a distance ζ from the HL plane and its axis passing through the centre of the HL. It is shown that the SPP introduces a phase singularity of pth order to the incident beam, while the lens transforms the beam characteristic parameters. The output light beam is analyzed in detail: its characteristic parameters and focusing properties, amplitude and intensity distributions and the vortex rings profiles, and radii, at any z distance behind the HL plane, as well as in the near and far field.     

Global beam shaping with nonuniformly polarized beams: a proposal

A procedure for global beam shaping by modifying some global spatial parameters characteristic of the beam is proposed. This method is based on the generation of a nonuniformly polarized beam using a Mach-Zehnder system with two suitably shaped intensity transmittances and orthogonal linear polarizers. The changes in beam quality and kurtosis parameters after a linear polarizer placed at the output of the system are investigated.     

Phase compensation of azimuthally polarized j(1) bessel-gaussian laser beams

As other semiconductor lasers, concentric-circle-grating, surface-emitting lasers are compact, light, and efficient. However, unlike other semiconductor lasers, they emit high-power, low-divergence azimuthally polarized J(1) Bessel-Gaussian beams. Because of their azimuthal polarization, they have a null at the center of the beam that makes them undesirable for certain applications. Binary phase compensation, a lossless technique previously used to improve the far-field profile of linearly polarized Hermite-Gaussian beams, is adapted to these azimuthally polarized beams to rid them of their axial nulls and improve their beam profile.     

Stable isotope ratio analysis at trace concentrations using degenerate four-wave mixing with a circularly polarized pulsed probe beam

Stable isotope analysis based on vectorial optical-phase conjugation by resonant degenerate four-wave mixing (D4WM) is reported by using a D4WM method with vertically polarized pump beams and a circularly polarized probe beam. Since the polarization of the signal beam is different from that of the pump beams, the background radiation is suppressed more effectively. Excellent sensitivity, high spectral resolution, and efficient optical detection make this an effective and unusually convenient nonlinear spectrometric method for the analysis of trace amounts of stable isotopes. Using an excimer-pumped pulsed dye laser, the fine structures of lithium are examined. A detection limit of 2.5 ng/mL lithium is observed while a Doppler-free resolution is maintained by using transient "coherent-grating" based D4WM spectroscopy.     

Influence of laser array performance on spectrally combined beam

Abstract

Incoherent spectral beam combining (SBC) of multiple laser beams is accomplished along the emitters’ arraying direction. Considering that the output beams from a laser array (LA) usually have deflection angles, positional displacements and divergence angles even after being collimated, a propagation model of SBC systems based on multilayer dielectric gratings has been built up. On the basis, properties of the spectrally combined beam affected by parameters of the LA have been discussed in detail. Simulation results show that with the increase in the deflection angle, both the power and the beam quality of the combined beam degrade dramatically. The positional displacement has little impact on the intensity distribution and the beam quality of combined beam but change the wavelength composition of the combined beam. The divergence angle strongly affects the intensity distribution and the beam quality of the combined beam. Additionally, the effect of the deflection angle on the output beam quality is more obvious and may shift the beam spot when comparing with that of the divergence angle.     

A four-variable refined shear-deformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities

This article proposes a four-variable shear deformation refined beam theory for thermo-mechanical vibration characteristics of porous, functionally graded (FG) beams exposed to various kinds of thermal loadings by using an analytical method. Thermo-mechanical properties of functionally graded material (FGM) beams are supposed to vary through the thickness direction, and are estimated through the modified power-law rule in which the porosities with even and uneven types are approximated. The material properties of FGM beams are supposed to be temperature dependent. Porosities possibly occur inside FGMs during fabrication because of technical problems that lead to the creation of microvoids in these materials. The variation of pores along the thickness direction influences the mechanical properties. Thus, it is incumbent to predict the effect of porosities on the thermo-mechanical vibration behavior of FG beam in the present study. Four types of thermal loading, namely, uniform, linear, nonlinear, and sinusoidal temperature rises through the z-axis direction are discussed. The governing differential equations and boundary conditions of FG porous beams subjected to thermal loadings are formulated through Hamilton's principle, based on a four-variable refined theory that considers a constant transverse displacement and higher order variation of axial displacement through the depth of the beam without the need of any shear correction factors. An analytical solution procedure is used to achieve the natural frequencies of porous FG beams subjected to various temperature fields. The impact of several specific parameters such as power-law exponent, porosity volume fraction, different porosity distribution, and thermal effect on the vibration of the porous FG beams is perused and discussed in detail. It is deduced that these parameters play a notable role on the thermo-dynamic behavior of porous FG beams. Presented numerical results can serve as benchmarks for the future analyses of FG beams with porosity phases.     

余弦-高斯光束通过光阑-透镜分离系统的焦移

利用Collins公式,研究了余弦-高斯光束通过光阑-透镜分离系统时的轴上光强分布和聚焦特性。研究表明轴上光强分布和相对焦移是光学系统参数、光束参数 、菲涅尔数和光阑尺寸的函数。通过选择适当的光学系统和光束参数,焦移现象消失或反转。     

Focusing of radially polarized Lorentz–Gauss beams with the power–exponent–phase vortex

Using the vector diffraction theory, the optical field of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex is derived. The normalized intensity distributions of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex are numerically demonstrated. The influences of the power order n and the topological charge m on the normalized intensity distribution are examined. The beam centre and the effective beam size, which are defined by the first- and the second-order moments of the intensity distribution, are the important parameters for focus. Therefore, the quantitative effects of the power order n and the topological charge m on the beam centre and the effective beam size are further investigated. This research is beneficial to the optical manipulation which is involved in the radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex.     

Thermally induced birefringence in nonsymmetrically pumped laser rods and its implications for attainment of good beam quality in high-power, radially polarized lasers

The ability to generate and then amplify radially polarized light opens up the possibility of achieving very high-power, near diffraction-limited beams from rod-based solid-state lasers. Residual bifocusing rapidly degrades beam quality. Residual bifocusing results from nonradially symmetric pump distributions. We analyze how a nonradially symmetric pump distribution induces a nonradially symmetric stress map. This manifests itself as nonradially symmetric birefringence, and as depolarization to radially/azimuthally polarized beams (or as deterioration in birefringence compensated linearly polarized lasers). Here we analytically describe the birefringence terms of a nonradially symmetric strain map. The model results are supported by radial-depolarization measurements in our 2 kW Nd:YAG pump chambers. For the current level of depolarization, beam quality degradation per rod is DeltaM(2)=4 because of bifocusing alone. The degradation per rod can be reduced substantially by improving pump uniformity.     

A comparative study of standard and elegant Hermite–Gaussian beams propagating through turbulent atmosphere

Based on the extended Huygens–Fresnel principle and the definition of the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the root-mean-square (rms) beam width and far-field divergence angle, curvature radius and M ²-factor of standard Hermite–Gaussian (SHG) and elegant Hermite–Gaussian (EHG) beams passing through turbulent atmosphere are derived and compared. It is shown that in turbulent atmosphere the far-field divergence angle of SHG and EHG beams is equal under the same conditions, but the rms beam width, curvature radius and the M ²-factor of SHG and EHG beams are different except for beam orders m?=?0 and m?=?1. The relative rms beam width, relative curvature radius and relative M ²-factor of SHG beams are less than those of EHG beams. Therefore, the conclusion that SHG beams are less influenced by turbulence than EHG beams can be drawn if we examine one of the above three relative beam parameters.     

Cyano azobenzene polymer films: Photo-induced reorientation and birefringence behaviors with linear and circular polarized light

Photo-induced behavior of polymethacrylate polymer, with cyano azobenzene side group, was studied. The photoisomerization process occurs in cyano azo polymer, by illumination of a film with polarized and unpolarized light. The illumination of the polymer film with light results in color change, the color of film gets darker. This is in opposition to common azo polymers in which the result of illumination is a photo-bleaching. Study of spectrum changes of a dilute polymer solution shows that the color change under pump beam illumination is not due to interaction between dye molecules. Time evaluation of probe beam absorption induced by Ar⁺ laser pump beam shows the fast change in population of isomers at higher light powers. Light induced birefringence (LIB) experiments with high power pump beams shows uncommon new features. A high long-term stability of LIB is demonstrated when the polymer film is kept in the dark. Not only a circular polarized light cannot erase the birefringence but it also induces anisotropy in polymer film. It appears that this is relevant of a phase transition in the polymer film.