Effects of coherence on the degree of polarization in a young interference pattern

Recent predictions concerning the relationship between the degree of polarization at a typical point of a Young interference pattern and the degree of coherence of the electromagnetic field at the pinholes are tested by a simple experiment. In particular, it is shown that light that is completely unpolarized at the pinholes can become partially polarized across the fringe pattern.     

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.     

Changes in the state of polarization of apertured stochastic electromagnetic modified Bessel–Gauss beams in free-space propagation

By using the generalized Huygens–Fresnel diffraction integral, the analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse of apertured stochastic electromagnetic modified Bessel–Gauss beams (MBGBs) through a paraxial optical ABCD system are derived, and used to study the changes in the state of polarization of apertured stochastic electromagnetic MBGBs propagating in free space. The invariance of the on-axis state of polarization of unapertured stochastic electromagnetic MBGBs propagating through paraxial optical ABCD systems is illustrated analytically and numerically. For apertured stochastic electromagnetic MBGBs, the on-axis spectral degree of polarization, orientation angle and degree of ellipticity of polarization ellipse increase with increasing propagation distance, and approach asymptotic values when the propagation distance is large enough. There is a uniform distribution region of the state of polarization around the center of the beams whose range decreases with increasing truncation parameter. In addition, the state of polarization of apertured stochastic electromagnetic MBGBs upon propagation can be modulated by controlling the truncation parameter.     

Polarization properties of stochastic spatially and spectrally partially coherent electromagnetic flat-topped pulses

The propagation behavior of the spectral degree of polarization of stochastic spatially and spectrally partially coherent electromagnetic flat-topped pulses in free space is studied. Numerical calculation results are given to illustrate the dependence of spectral degree of polarization on the beam order, pulse frequency, temporal coherence length, pulse duration and spatial correlation length. It is shown that with increasing beam order M the position z of the on-axis spectral degree of polarization P = 0 decreases, and the distribution of spectral degree of polarization is different for different values of M.     

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 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.     

Polarization properties of stochastic electromagnetic beams

The behavior of the degree of polarization of a Gaussian Schell-model beam propagating in free space is investigated. Contour diagrams for the degree of polarization, and for the spectral density (‘intensity’) of the polarized and the unpolarized portions of the beam are presented.     

Stokes parameters and polarization contrasts in Young's interference experiment

We derive a spectral interference law that governs the behavior of the four Stokes parameters in Young's two-pinhole experiment with a random electromagnetic beam. In addition to the visibility of intensity fringes, we introduce three new contrast parameters that describe the interference-induced changes in the field's state of partial polarization. The polarization modulation depends on the electric field correlations at the pinholes and is closely related to the two-point Stokes parameters. The results are expected to be particularly useful in polarization interferometry and electromagnetic coherence theory. The formalism is demonstrated with specific examples.     

Changes of polarization of light beams on propagation through tissue

The values of the degree of polarization and the coherence of the light beam are of great importance in many areas. In this paper, we study the effects of tissue turbulence on the degree of polarization of a partially coherent electromagnetic beam. Based on the unified theory of coherence and polarization for random electromagnetic beams and the spectral density of the index of refraction fluctuations of tissue, we have established the detailed formula for calculating the change of the degree of polarization of the beam when propagating through tissue. Compared with the light propagation through atmosphere, the result shows that although the propagation distance in tissue imaging is very short, the degree of polarization of the beam may change greatly. An example was given which clearly shows the effect of the correction properties and the tissue turbulence on the degree of polarization of the light beam propagating within the tissue.     

Nonparaxial propagation of spatially and spectrally partially coherent electromagnetic Cosh-Gaussian pulsed beams

Based on the generalized Rayleigh–Sommerfeld diffraction integral, the analytical expression for 3×3 cross-spectral density matrix of nonparaxial spatially and spectrally partially coherent electromagnetic Cosh-Gaussian (ChG) pulsed beams propagating in free space is derived, and used to formulate the spectral density and spectral degree of polarization of electromagnetic pulsed beams at the z-plane. It is found that the parameters f and f_αα are the key parameters in determining the nonparaxiality of spatially and spectrally partially coherent electromagnetic ChG pulsed beams. And the decentered parameter, pulse duration and temporal coherence length can change the nonparaxial behavior of the electromagnetic ChG pulsed beams. The effect of decentered parameter, pulse duration and temporal coherence length on the spectral density and spectral degree of polarization of electromagnetic ChG pulsed beams is illustrated through numerical calculations. Propagation of nonparaxial spatially and spectrally partially coherent electromagnetic Gaussian Schell-model pulsed beams can be treated as a special case when the decentered parameter of electromagnetic ChG pulsed beams approaches to zero.     

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.     

双孔干涉产生偏振奇点分析

在近轴近似的条件下,采用标量衍射积分的方法,对电磁场的双孔干涉进行了研究,并对千涉场中产生偏振奇点的情况进行了推广。在研究中通过双孔的光电场为线偏振状态,具有不同的偏振方向。数值计算结果表明,即使通过双孔的光电场的相位相同,只要双孔的尺寸存在一定的差异,干涉场中除了能够产生普通的的线偏振外,圆偏振奇点也会出现。     

Interpretation of the recipe for synthesizing genuine cross-spectral density matrices

A physical interpretation of the recipe for synthesizing genuine 2 × 2 cross-spectral density matrices that characterize stochastic electromagnetic sources and beams is described. In this interpretation, the synthesized field is regarded as an incoherent superposition of spatially coherent fields originating from a partially polarized, spatially incoherent virtual source. The coherence and the polarization properties of the synthesized field are also examined in view of this interpretation. As a result, we found that the spectral degree of coherence and that of polarization of the synthesized field are generally different from those of the virtual source by the effect of the superposition. We also found, however, that there are some situations in which the spectral degree of polarization of the synthesized field remains unchanged even though the superposition takes place.     

Polarization and coherence properties of a beam formed by superposition of a pair of stochastic electromagnetic beams

General expressions are derived for the spectral degree of polarization and for the spectral degree of coherence of a beam generated by the superposition of two stochastic electromagnetic beams. A method to calculate the mutual cross-spectral density matrix of the superposed beam is discussed, as well as experiments to determine it.     

Propagation of random electromagnetic beams through axially nonsymmetrical optical systems

When random electromagnetic beams passing through axially nonsymmetrical ABCD optical systems, the analytical formula for the transformation of the elements of 2 × 2 cross-spectral density matrix is obtained with the help of vector integration. We derive analytical expressions of the spectral degree of polarization, the spectral degree of coherence, and the spectral density in any output plane z > 0. Some numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams propagating through such optical systems.     

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.     

偏振分辨激光诱导击穿光谱的铝铁合金信背比改善效果研究

偏振分辨激光诱导击穿光谱(PRLIBS)以其低成本压制背景的特点在LIBS降低检测限上有着重要意义,但是理论上的争议和信背比改善效果不稳定限制了其应用前景。为深入分析等离子体产生偏振特性的原理和PRLIBS信背比的改善效果,采用1 064 nm纳秒脉冲激光器和光纤光谱仪对铝铁合金样品进行了偏振分辨LIBS的信背比改善效果及偏振原理的探索性实验。通过对辐射能量的估算,大胆地推测轫致辐射在背景辐射中的占比是由大变小的,并据此解释了背景辐射强度在时间上的变化。通过改变能量密度、检偏角度、探测角、延时时间、积分时间等因素,采集光谱强度和波长数据、计算偏振度和信背比,观察到铝铁合金的等离子体光谱中背景谱和分立谱均有偏振且存在偏振度和偏振方向的差异,发现偏振LIBS改善信背比的效果与实验参数包括能量密度、延时时间、检偏角度以及波长有关。PRLIBS信背比关于能量密度的变化与一般LIBS类似,在能量较大时会趋于饱和。检偏角度会影响信背比大小,与光谱的偏振方向和偏振度有关,推导了信背比改善效果关于偏振度、检偏角度、偏振方向夹角的公式。在波长上连续谱偏振度趋势较为稳定而分立谱偏振度随光谱强度增大而减小。随延时时间增加,偏振度变化不明显,原因是相比于积分时间延时的改变量很小,而信背比的变化趋势与无偏振LIBS一致。总结了国内外对PRLIBS机理具有代表性的解释并进行了讨论,排除了激光光场、菲涅尔反射、各向异性电子速度分布等因素对等离子体偏振特性的决定性作用。研究结论是在ns-LIBS实验中,复合辐射在可见光和紫外光范围内占背景辐射的大部分,其偏振特性主要源于等离子体复合阶段产生的各向异性复合过程,原子谱偏振特性可能源于该过程中受激原子的磁性支能级间数量的不平衡,而背景谱与原子谱的偏振度及偏振方向的差异主要取决于偏振特性产生机理的不同。研究发现, PRLIBS并不总能提升元素的信背比,尤其对弱光谱信号改善效果有限,要获得较好的压制背景的效果,可以对PRLIBS的能量密度、检偏角度、延时与积分时间等条件加以控制,在能量密度20 J·cm-2积分时间30μs检偏角度20°下FeⅠ407.12 nm处的信背比由4.86提升至12.97。偏振度与探测角相关性较小,原因可能是导体的菲涅尔反射效应很弱。研究结果对PRLIBS的原理研究和应用提供了有效的理论基础。     

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.     

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.     

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.