Spectral properties of partially coherent azimuthally polarized beam in a turbulent atmosphere

In this paper, based on the extended Huygens–Fresnel integral formula, the analytical expression for the beam coherence-polarization (BCP) matrix of the partially coherent azimuthally polarized (PCAP) beams propagating in turbulent atmosphere has been derived. The distribution of the spectral density, the spectral degree of polarization, the spectral degree of coherence and the spectral degree of cross-polarization of the PCAP beams propagating in turbulent atmosphere with different coherences in the source are investigated in detail. It is shown by numerical results and analysis that the distribution of the spectral properties of the PCAP beam will change on propagation in a turbulent atmosphere, and this change is dependent upon the degree of coherence of the source beam and atmospheric turbulence. It is also shown that even through the source beam is chosen as δ_gxx ≠ δ_gyy the distribution of the spectral density, the spectral degree of polarization, the spectral degree of coherence and the spectral degree of cross-polarization in the far field tends to symmetrical profile.     

Propagation of a polarised polychromatic beam through a birefringent plate

The effect of propagation of a polarised polychromatic beam having a truncated gaussian spectral profile has been studied. The degree of polarisation of the output beam is seen to be less than of the of the standard deviation of the profile on the degree of polarisation of the output has been considered. Finally, the special case of a flat-top spectral profile has been discussed.     

Propagation Characteristics of a Partially Coherent Gaussian Schell-model Array Vortex Beam in the Joint Turbulence Effect of a Jet Engine and Atmosphere

This work investigates the joint effects of jet engine exhaust-induced turbulence and atmospheric turbulence on the propagation of a partially coherent Gaussian Schell-model Array (GSMA) vortex beam. Using the two-process propagation method, analytical formulae are derived for the cross-spectral density, spectral density, degree of coherence, and beam width of the considered beam. The results show that the considered beam takes different shapes; when the spatial coherence is large, the spectral density of the GSMA vortex beam takes an elliptical shape, whereas when the spatial coherence is smaller, the spectral density remains a Gaussian shape. The evolution profile of the degree of coherence weakens gradually when the propagation distance, topological charge, and turbulence strength increase. Moreover, the profile of the degree of coherence takes the Gaussian profile when the propagation distance is longer or turbulence atmospheric is stronger. Furthermore, the results reveal that the corresponding beam spreads faster with a larger propagation distance, lower spatial coherence, and high-strength turbulence. This study also concludes from the results that the beam is affected more when its propagation is near the jet engine exhaust, which means that this latter has a significant impact.     

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.     

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.     

The statistical properties of anisotropic electromagnetic beams passing through the biological tissues

We report the analytic formula of an electromagnetic Gaussian–Schell-model (EGSM) beam propagating through the turbulent biological tissues. With the help of this formula, the changes in characteristics of the beam such as the spectral density, the spectral degree of coherence, the spectral degree of polarization, and the spectral degree of cross-polarization of the EGSM beam passing through the biological tissues are illustrated and compared by numerical examples. The changes in anisotropic and isotropic EGSM beams are indicated. Necessary comparisons and analyses of the beams generated by the anisotropic source and the isotropic source through the turbulent biological tissues are given. Moreover, the influence of the light source and turbulence of tissues on the changes of the spectral degree of cross-polarization of the EGSM beam passing through the biological tissues are compared in the near-field and the far-field.     

Effects of a modified spectral model on the spatial coherence of a laser beam

The influence of a modified (bump) spectrum of refractive index fluctuations on the spatial coherence of an optical wave is studied here and compared with that based on a von Karman spectrum. Analytical expressions are derived for the mutual coherence function (MCF) and wave structure function (WSF) of a lowest-order Gaussian beam wave from which the beam spot size and degree of coherence are deduced. The qualitative behaviour of beam spreading and coherence length is basically the same for both spectral models. Also, when the radius of the Fresnel zone and initial beam radius are of comparable size, the presence of a spectral bump appears to have minimal effect on spatial coherence for all beams. However, the choice of spectral model is important for certain ranges of parameters. In particular, the implied spatial coherence length for a collimated beam based on the modified spectrum is significantly smaller than that based on the von Karman spectrum whenever the Fresnel zone is either much larger or much smaller than the initial beam radius, whereas for a focused beam the predicted coherence length based on the modified spectrum is slightly larger when the Fresnel zone size is much smaller than the initial beam radius.     

部分相干电磁光束的光谱交叉偏振度

基于光谱交叉偏振度新理论,研究了部分相干光束在传输过程中光谱交叉偏振度的变化情况.采用相干偏振统一理论和广义惠更斯-菲涅耳原理,推导部分相干电磁高斯-谢尔模型光束在自由空间传输时任意空间两点的交叉谱密度矩阵的解析式.研究表明,光谱交叉偏振度的值不再仅仅局限在0～1之间,而是可为任意的非负值.传输场中的光谱交叉偏振度与光源相关参量,初始偏振度和传输距离紧密相关.当光束经过足够长的传输距离后,轴上光谱交叉偏振度不再发生变化,而是趋向一个稳定值.保持光谱交叉偏振度不变的条件与一般偏振度相同.     

部分相干光对周期性局域空心光束的影响

用旋转毛玻璃和光阑把激光变成部分相干光, 再经过双轴棱锥系统把一束平行光变成两束同频率但不同径向波矢分量的无衍射贝塞尔光, 相干叠加产生了部分相干的周期性局域空心光束. 通过干涉理论与实验结果相互佐证, 得出局域空心光束的周期为2.5 mm. 进一步探究入射光场相干度对产生局域空心光束的影响, 发现随着相干度的降低局域空心光束中心暗斑与周围光强的衬比度会降低, 但不影响局域空心光束的周期以及中心暗斑尺寸.     

Spectral properties of stochastic electromagnetic twist anisotropic Gaussian-Schell model beam truncated by a slit aperture propagating in turbulent atmosphere

With the help of the tensor method, the cross-spectral density matrix for the stochastic electromagnetic twist anisotropic Gaussian-Schell model (ETAGSM) beam truncated by a slit aperture propagating in turbulent atmosphere are derived. The spectral properties of this kind of beam are investigated in detail. It is shown by numerical results and analysis that the affection of the slit aperture on the spectral properties of the stochastic ETAGSM beam is obvious in the near field; while in the far field, the atmospheric turbulence plays an important role; the source beam's coherence can weaken the affection of the slit aperture and the atmospheric turbulence on the spectral properties of the stochastic ETAGSM beam truncated by a slit aperture propagating in turbulent atmosphere, while the twist properties of the source beam can strong the affection of the slit aperture on the spectral properties in the near field. Also, the spectral degree of polarization and normalized spectral density distributions and corresponding contour graphs of the stochastic ETAGSM beam truncated by a slit aperture propagating in turbulent atmosphere and free space at different propagation distances are investigated in detail.     

Cross-spectral density matrix of a random electromagnetic beam propagating through an apertured axially nonsymmetrical optical system

Using the fact that a hard-edged rectangular aperture function can be approximated by a two-dimensional multi-Gaussian series, analytic formulas for the elements of the cross-spectral density matrix of a random electromagnetic beam truncated by a rectangular aperture and passing through an axially nonsymmetrical optical system is derived. The analysis is illustrated by numerical examples relating to changes in the spectral degree of polarization of electromagnetic Gaussian Schell-model beams propagating through free space, focal system and dual-focus system. In particular, the effect of the size of the hard aperture on the spectral degree of polarization of the beam along its optical axis is discussed.     

Statistical properties of correlated radial stochastic electromagnetic array beams on propagation

A kind of array beam named the correlated radial stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by use of tensor method. The analytical expression for the cross-spectral density matrix of this array beam propagating through the turbulent atmosphere and in free space is obtained after performing vector integration. Some typical numerical calculations are illustrated for the changes in the spectral density, spectral degree of polarization, and spectral degree of coherence of the beam on propagation. We find that the atmospheric turbulence can destroy the correlated effect among the beamlets.     

Propagation of astigmatic stochastic electromagnetic beams in oceanic turbulence

In this paper, we investigate the characteristics of astigmatic stochastic electromagnetic beams through oceanic turbulence. Taking the electromagnetic Gaussian Schell-model (GSM) beam as an example, the analytic expressions for the spectral density and the spectral degree of polarization of the beam propagating the oceanic turbulence are derived. It is indicated that the spectral density along the z-axis of the GSM beam in the oceanic turbulence is severely influenced by the source correlation properties, as well as by the sea-related parameters. We show that the characteristics of the spectral density along the x-axis, y-axis and z-axis of astigmatic electromagnetic GSM beams passing through the oceanic turbulence are qualitatively different. Furthermore, we find that as the astigmatic coefficient becomes larger, the maximum value of the spectral density along the z-axis increases rapidly and the width of the spectral density becomes shorter rapidly. Finally, the results have shown that different strengths of astigmatism have different effects on the spectral degree of polarization.     

Propagation properties of a partially polarized electromagnetic twist anisotropic Gaussian Schell-model beam in turbulent atmosphere

Based on the extended Huygens-Fresnel integral formula, analytical formulae for the elements of cross-spectral density matrix of partially polarized electromagnetic twist anisotropic Gaussian Schell-model (TAGSM) beam propagating in turbulent atmosphere can been derived by a tensor method. Our main attention was focus on the effect of the atmospheric turbulence, twist parameters and partial coherence on the spectral degree of polarization, the spectral degree of coherence and the spectral density. Numerical calculation results and analysis are given.     

Modulation in the statistical properties of stochastic electromagnetic beams through an electromagnetic induced transparency atomic vapor

We report analytical expressions for the elements of the 2 × 2 cross-spectral density matrix of a stochastic electromagnetic beam passing through an electromagnetic induced transparency (EIT) atomic vapor. By use of the derived formulas the changes in the spectral density, the spectral degree of coherence, and the spectral degree of polarization of such a beam on propagation can be studied in detail. Numerical examples show that the statistical properties of the stochastic electromagnetic beam can be modulated by the Rabi frequency of the control light when the beam propagates through the EIT atomic vapor.     

Experimental generation of a partially coherent flat-topped beam

An efficient optical system is proposed to generate a partially coherent flat-topped (FT) beam theoretically. Furthermore, we report the experimental generation of a partially coherent FT beam based on the proposed optical system. The intensity distribution and the modulus of the square of the spectral degree of coherence of the generated partially coherent FT beam are measured. The experimental results are consistent with the theoretical results.     

Spectral properties of apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model beam propagating in turbulent atmosphere

Based on the extended Huygens-Fresnel principle, analytical formulas are derived for the cross-spectral density matrix of an apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model (ETAGSM) beam propagating in a turbulent atmosphere by use of a tensor method. Spectral properties of apertured ETAGSM beam are closely related with the strength of atmospheric turbulence, the aperture widths and the beam's parameters, etc. Our main attention was focused on the influence of the aperture widths, atmospheric turbulence, twist parameters and partial coherence on the spectral properties (including spectral degree of polarization, the spectral degree of coherence and the spectral density) of apertured ETAGSM beam propagating in turbulent atmosphere. Numerical calculation results and analysis are given.     

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.     

Changes in the statistical properties of stochastic anisotropic electromagnetic beams propagating through the oceanic turbulence

On the basis of the extended Huygens?CFresnel principle, an analytical propagation expression for the elements of the cross-spectral density matrix of a stochastic anisotropic electromagnetic beam through oceanic turbulence is derived. From this formula the spectral density, spectral degree of coherence, spectral degree of polarization, orientation angle and the degree of ellipticity of such a beam on propagation are determined. Some numerical calculations are illustrated relating to the anisotropic electromagnetic Gaussian Schell-model beams propagating through oceanic turbulence. The results indicate that the spectral degree of coherence of stochastic anisotropic electromagnetic beams tends to zero with increasing propagation distance through oceanic turbulence, which is in agreement with results previously reported for turbulent atmosphere. It is also found that the changes in the statistical properties of the anisotropic source on propagation are qualitatively different from those of the isotropic source.     

Propagation of radially polarized beams in the oceanic turbulence

Based on the extended Huygens–Fresnel principle and the unified theory of coherence and polarization of light, we investigate the propagation properties of a radially polarized beam through turbulent ocean. Analytic formulae for the spectral density, the spectral degree of polarization, and the beam characteristics of such a beam on propagation are discussed. It is shown that under the influence of oceanic turbulence, the radially polarized beam will change to a partially polarized one and the beam profile will approach to a Gaussian distribution.