Extension of the van Cittert-Zernike theorem for completely polarized incoherent electromagnetic beam propagating through non-Kolmogorov turbulence

Based on the 2 × 2 cross-spectral density matrix, the van Cittert-Zernike extended theorem is developed for the completely polarized incoherent beams propagation through the paraxial non-Kolmogorov turbulence. On the consequence of the extended theorem and the definition of general spectral degree of cross-polarization of a beam, we found that the spectral degree of cross-polarization of the resultant field is independent of the refractive index structure constant of atmospheric turbulence. We investigated the influences of the propagation distance and the distance of two detection points on the degree of coherence and the spectral degree of cross-polarization.     

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.     

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.     

Effect of cross-polarization of electromagnetic source on the degree of polarization of generated beam

In this paper we study the degree of cross-polarization of a beam-like field whose cross-spectral density matrix is symmetric with respect to the permutation of its spatial arguments. Formulas were derived expressing the degree of cross-polarization in terms of the generalized Stokes parameters. With the help of an uniformly polarized quasi-homogeneous model source, the effect of degree of cross-polarization of a source on the degree of polarization of the radiated beam was demonstrated, that, two sources with same spectral degrees of coherence and polarization but with different degrees of cross-polarization can generate beams that have different spectral degrees of polarization in the far field.     

Propagation of the degree of cross-polarization of stochastic electromagnetic pulsed beams in free space

The concept of the degree of cross-polarization is extended from stochastic electromagnetic stationary beams to stochastic electromagnetic pulsed beams, and the propagation properties of the degree of cross-polarization of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams is studied. The influence of pulse duration and temporal coherence length on the degree of cross-polarization P is emphasized. It is shown that P exhibits an oscillatory behavior in free-space propagation. An increase in the pulse duration or a decrease in the temporal coherence length can weaken the oscillation of P. The validity of the results is interpreted physically.     

Slanting propagation of stochastic electromagnetic twist anisotropic Gaussian–Schell model beams in turbulent atmosphere

Based on the extended Huygens–Fresnel diffraction integral and the unified theory of coherence and polarization, the slanting propagation properties of stochastic electromagnetic twist anisotropic Gaussian–Schell model (ETAGSM) beams in turbulent atmosphere have been investigated. Both numerical calculation and physical interpretation are obtained. The influence of the atmospheric turbulence and the source parameters on the polarization distribution, intensity distribution and coherence distribution has been studied in great detail. The investigation reveals that slanting propagation can weaken the influence of atmospheric turbulence on the spectral properties of stochastic ETAGSM beams more obviously. It is also shown that we can modulate the spectral degree of polarization in the output plane especially in the far field by simply controlling the coherence, the spot width or the twisty properties of the source beams. The distribution of the spectral degree of polarization and cross-polarization of the beams in the output plane is also given out.     

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.     

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.     

Properties of the degree of cross-polarization in the space-time domain

A definition of the degree of cross-polarization in the space-time domain is introduced which is based on considerations of the correlations of intensity fluctuations of an electromagnetic beam at two points. Some general properties of this quantity are discussed. For the special cases of fully coherent and fully polarized light it is shown that the degree of cross-polarization exhibits a relationship between the states of polarization at the two points.     

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.     

Diffraction and Spectral Characteristics of Chiral Layer

Diffraction problems for the E- and H-polarized plane waves incident on a chiral magneto-dielectric layer are solved. The spectral characteristics (complex natural frequencies and oscillations) of the layer are investigated. A comparative analysis of diffraction and spectral characteristics is made. The phenomenon of the quasi-complete wideband cross-polarization transformation of plane waves by a chiral layer is found. The conditions for complete cross-polarization transformation of a plane wave normally incident on a chiral layer are determined.     

Stokes parameters and degree of polarization of nonparaxial stochastic electromagnetic beams

On the basis of angular spectrum representation and the stationary-phase method, far-field expressions for generalized Stokes parameters of nonparaxial stochastic electromagnetic beams are derived, which permits us to study the changes in the ordinary Stokes parameters upon propagation, and the changes in the spectral degree of polarization of partially polarized nonparaxial stochastic electromagnetic beams. It is shown that the spectral degree of polarization changes across the section on beam propagation.     

Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues

The general analytical expression of the stochastic electromagnetic vortex beams through turbulent biological tissues is derived based on the fractal model. The statistical properties, including the spectral density, the spectral degree of coherence and the spectral degree of polarization are investigated in detail. It can be found that the normalized spectral density of the stochastic electromagnetic vortex beams with higher topological charge is less influenced by turbulence than that with lower topological charge. In addition, the change of the degree of polarization versus propagation distance of the anisotropic vortex beams in biological tissues differs from that of the isotropic vortex beams. The findings might be useful in the investigation of the structures of biological tissues and operation of communication and sensing systems involving biological tissues turbulence channels.     

Cross-spectral density matrix of the far field generated by a blackbody source

An expression is derived for the cross-spectral density matrix, valid in the paraxial region of the far field, generated by a planar blackbody source. With the help of it we determine the spectral degrees of polarization and of cross-polarization of the far field.     

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.     

Multiple-quantum cross-polarization and two-dimensional MQMAS NMR of quadrupolar nuclei

Cross-polarization from (1)H to the multiple-quantum coherences of a quadrupolar nucleus is used in combination with the two-dimensional multiple-quantum magic angle spinning (MQMAS) NMR experiment in order to extract high-resolution CPMAS NMR spectra. The technique is demonstrated on (23)Na (S = 3/2), (17)O, (27)Al (both S = 5/2), and (45)Sc (S = 7/2) nuclei, showing the applicability of multiple-quantum cross-polarization to systems with differing spin quantum number, gyromagnetic ratio, and relative nuclide abundance. The utility of this two-dimensional MAS NMR experiment for spectral editing and site-specific measurement of cross-polarization intensities is demonstrated. The possibility of direct cross-polarization to higher order multiple-quantum coherences is also considered and three-, five-, and seven-quantum cross-polarized (45)Sc MAS NMR spectra are presented.     

Cross-polarization properties of two Gaussian Schell-model beams through non-Kolmogorov turbulence

General expressions are derived for the spectral degree of cross-polarization (SDCP) of a beam generated by the superposition of two Gaussian Schell-model (GSM) beams, which illuminated with the same Gaussian Schell-mode source propagating in non-Kolmogorov turbulent atmosphere by adopting beam cross-spectral density matrix and Young's interference theory. In particular, through numerical examples based on our analytical formal the SDCP of two GSM beams is analyzed. Detailed analysis demonstrate that the SDCP is closely to the spacing of two beams on source plane as well as the strength of the atmospheric turbulent, but the fractal constant α has no affect on the SDCP.     

Changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic J0-correlated Schell-model pulsed beams propagating in free space

Taking the stochastic electromagnetic J ₀-correlated Schell-model pulsed (JSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the analytical expressions for the cross-spectral density matrix, spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic JSMP beams propagating in free space are derived, and used to study the changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic JSMP beams. It is shown that the on-axis spectrum is blue-shifted in free-space propagation and is dependent on the pulse temporal coherence length and spatial correlation parameter. The distribution of the on-axis spectral degree of polarization depends on the frequency and spatial correlation parameter. The spectral degree of coherence increases with increasing pulse temporal coherence length. The results derived are interpreted physically.     

大气湍流对部分相干电磁平顶光束传输的影响

基于相干性和偏振性统一理论,采用Rytov相位结构函数平方近似推导出了部分相干电磁平顶光束在湍流大气中传输的偏振度、相干度和光谱强度公式,并研究了湍流对其传输特性的影响.研究表明,偏振度和相干度与源光谱的带宽无关.大气湍流使得不同阶数的部分相干电磁平顶光束的偏振度经长程传输后均趋于其初始值.大气湍流使得部分相干电磁平顶光束与电磁高斯一谢尔模型光束相干度的差别减小,并导致相干度的振荡和相位奇异现象消失.大气湍流使得相干性较好的部分相干电磁平顸光束的光谱跃变现象消失.