Vector singularities of superposition of mutually incoherent orthogonally polarized beams

It is shown that, at an incoherent superposition of orthogonally polarized laser beams, a special type of singularities are formed in the cross section of a combined beam in place of the well-known singularities, such as optical vortices (for scalar fields); C points, at which the polarization is circular; and L lines, along which the polarization is linear (for coherent vector fields). These new singularities are U lines, along which the degree of polarization is zero and the state of polarization is undetermined, and P points, at which the degree of polarization is equal to unity and the state of polarization is determined by the nonzero component of the combined beam. Conditions of topological stability of U and P singularities are discussed, as well as peculiarities of the spatial distribution of the degree of polarization of the field in the vicinity of such singularities. First experimental results on the reconstruction of a vector skeleton formed by U and P singularities in combined speckle fields are presented.     

Polarization singularities in Young's two-slit experiment

Young's interference experiment is regarded as a two-slit diffraction phenomenon, the polarization singularities in Young's two-slit configuration illuminated with two linearly, orthogonally polarized Gaussian vortex beams are studied. It is shown that generally, there exist L-lines (linearly polarization) and polarization singularities including C-points (circular polarization), S₂₃ and S₃₁ singularities even though the parameters of two beams are the same. The pair creation-annihilation and motion of polarization singularities take place upon propagation, or by varying a control parameter, such as the amplitude ratio of two beams or obscure ratio of slits etc. For a special case of the illumination with two linearly, orthogonally polarized Gaussian vortex-free beams, polarization singularities, in particular, C-points may occur if a parameter of two beams is not equal.     

Nongeneric polarization singularities in combined vortex beams

Nongeneric polarization structures of singular beams formed as a coherent coaxial mixture of weighted orthogonally polarized single-charged Laguerre-Gauss modes with different radial indices are analyzed. A general solution for the superposition of elliptically orthogonally polarized partial vortex beams is obtained; the limiting special cases in which the mixed modes are linearly or circularly polarized are investigated. It is established that unusual spatially stable polarization structures such as closed C contours and L contours with a fixed azimuth of linear polarization arise in such combined beams. The results are experimentally confirmed by using a new diffraction method for testing phase singularities in optical beams.     

Vortex solitons with inhomogeneous polarization in nonlocal self-focusing nonlinear media

Both azimuthally and radially polarized vortex solitons are investigated to be able to exist in highly nonlocal nonlinear media. We get exactly analytical solutions of azimuthally polarized vortex solitons with only polarization singularities and radially polarized vortex solitons with both phase singularities and polarization singularities. Both azimuthally and radially polarized vortex solitons can exist in nonlocal self-focusing nonlinear media with proper modulation of the beam power and the degree of nonlocality. Contrary to those of radially polarized counterparts in local Kerr media, the topological charge can be any integer. When the topological charge m ≠ 0, both phase singularities and polarization singularities work. When m = 0, the polarization singularities work. Azimuthally polarized vortex solitons with polarization singularities corresponds to the linearly polarized vortex solitons with single charge. Our results show that polarization singularities work the same way as phase singularities in some sense.     

A cascade of singular field patterns in Young’s interference experiment

We analyze Young’s interference experiment for the case that two correlated, linearly polarized beams are used. It is shown that even when the incident fields are partially coherent, there are always correlation singularities (pairs of lines where the fields are completely uncorrelated) on the observation screen. These correlation singularities evolve in a non-trivial manner into dark lines (phase singularities in the paraxial approximation). The latter in turn each unfold into a triplet of polarization singularities, namely an L-line and two C-lines of opposite handedness.     

Composite spectral Stokes singularities in coherent and incoherent superpositions of partially coherent nonparaxial vortex beams

Taking the partially coherent cosh-Gaussian (ChG) vortex beam as an illustrative example, the composite spectral Stokes singularities formed by coherent and incoherent superpositions of partially coherent vortex beams beyond the paraxial approximation are studied, where the effect of superposition scheme on composite spectral Stokes singularities is stressed. It is shown that there exist s₁₂ (C-points), s₂₃ and s₃₁ composite spectral Stokes singularities, which are variable by varying a control parameter, such as the spatial correlation length, waist width, off-axis distance, or decentered parameter, as well as the propagation distance. In particular, the number, position, degree of polarization of composite spectral Stokes singularities and the critical point at which the creation–annihilation process takes place depend on the superposition scheme. A comparison with the previous work is also made.     

Polarization-dependent intensity transmittance of optical systems

The intensity transmittance α of a linear nondepolarizing optical system is investigated as a function of the state of polarization of the incident light. For totally polarized incident light the state of polarization is completely described by a single complex variable χ. In the χ-plane, the loci of incident polarizations that experience equal attenuation or amplification [α(χ)=constant] upon passing through the system constitute a family of nonintersecting coaxal circles. The zero-radius point circles of the coaxal family represent two orthogonal polarizationsχ _max andχ _min that pass through the system with maximum and minimum transmittances, respectively. Simple elegant expressions are derived for α in terms of the propertiesχ _max,χ _min;α _max andα _min of the system. When χ is expressed in terms of the azimuth and the ellipticity of the polarization ellipse a generalized version of Malus' law is obtained which is applicable to any optical system. Special cases of optical systems are discussed. The condition that a Jones matrix represents an active system is derived. Such a system may amplify polarization states inside a circular domain in the complex χ-plane and attenuate all other states. The results for totally polarized incident light are used to derive the polarization-dependent intensity transmittance of the system for unpolarized and partially polarized incident light. A new set of three parameters is introduced to describe the state of polarization of partially polarized light. The polarization-dependent intensity transmittance is completely determined by four real quantities which can be measured photo-ellipsometrically.     

部分偏振部分相干光光栅衍射场的偏振特性和角相关研究

为了研究部分偏振部分相干光光栅衍射场的衍射特性.利用部分偏振部分相干光的光束相干-偏振(BCP)矩阵,推导出了部分偏振部分相干光通过任意偏振光栅后,衍射场的偏振度及场中衍射级次角相关的一般解析表达式.以部分偏振的高斯-谢尔模型光束(PGSM)为例,数值分析了偏振光栅TE和TM波的复振幅透过率、入射光束的光学参量对衍射场偏振度和场中各衍射级次的角相关的影响.计算结果表明,部分相干光透过偏振光栅后的其衍射光场是一非均匀、周期变化的部分偏振相干光场;场中对称级次的角相干值对应相等,且随衍射级次序数的增大而缓慢递减至零.     

Large inverse relaxation of photoinduced birefringence in an azobenzene-containing ionic self-assembly complex

Photoinduced anisotropy and polarization holographic recording were investigated in an azobenzene-containing ionic self-assembly complex. The complex film was found to possess large photoinduced dichroism (D～0.36) and photoinduced birefringence (Δn～10^?2). A noteworthy observation was that the photoinduced birefringence did not show any decay, but strongly increased after switching off the pump light at room temperature. The diffracted signals of the polarization holographic gratings, written by two orthogonally linear and circular polarized beams respectively, exhibited similar inverse relaxation behavior as the photoinduced birefringence after switching off the writing lights. A discussion about the mechanism accounting for the abnormal relaxation process of photoinduced birefringence is presented.     

Stokes parameters of optical singularities of random electromagnetic beams

In this paper,the relation between the spectral degree of coherence and degree of polarization of random electromagnetic beams is derived by the Stokes parameters.And the concept of polarization singularity is extended from spatially fully coherent beams to partially coherent electromagnetic beams.Theoretical analysis shows that correlation vortices are linearly polarized singularities.The results are illustrated by numerical examples.     

Effect of polarization on the evolution of electromagnetic hollow Gaussian Schell-model beam

Based on the theory of coherence, an analytical propagation formula for partially polarized and partially coherent hollow Gaussian Schell-model beams (HGSMBs) passing through a paraxial optical system is derived. Furthermore, we show that the degree of polarization of source may affect the evolution of HGSMBs and a tunable dark region may exist. For two special cases of fully coherent and partially coherent δ_xx = δ_yy, normalized intensity distributions are independent of the polarization of source.     

A novel orthogonally linearly polarized Nd:YVO4 laser

We presented a novel orthogonally linearly polarized Nd:YVO₄ laser. Two pieces of a-cut grown-together composite YVO₄/Nd:YVO₄ crystals were placed in the resonant cavity with the c-axis of the two crystals orthogonally. The polarization and power performance of the orthogonally polarized laser were investigated. A 26.2-W orthogonally linearly polarized laser was obtained. The power ratio between the two orthogonally polarized lasers was varied with the pump power caused by the polarized mode coupling. The longitudinal modes competition and the corresponding variable optical beats were also observed from the orthogonally polarized laser. We also adjusted the crystals with their c-axis parallele to each other, and a 40.7-W linearly polarized TEM₀₀ laser was obtained, and the beam quality factors were M²_x=1.37 and M²_y=1.25.     

Degree of polarization for quantum light field propagating through non-Kolmogorov turbulence

Nonclassical polarization properties of a quantum field propagating through non-Kolmogorov turbulence are studied in a turbulent atmosphere paraxial channel. The analytic equation for the quantum degree of polarization of linearly polarized light is obtained. It is shown by numerical simulation that the polarization fluctuations of the quantum field are a function of the turbulent strength, the photon number, the propagation distance, the fractal constant α and the coherence length ρ₀.     

The impact of light polarization on imaging visibility of Nth-order intensity correlation with thermal light

The relationship between the imaging visibility of arbitrary Nth-order intensity correlation with thermal light and light’s degree of polarization is investigated. It is shown that for the same order correlation, the value of visibility with partially polarized light is greater than that with natural light but smaller than that with completely polarized light, and the visibility in all three cases is remarkably enhanced as N increases.     

Topological invariants and the dynamics of an axial vector torsion field

A generalized theory of gravitation is discussed which is based on a Riemann-Cartan space-time,U ₄, with an axial vector torsion field. Besides Einstein's equations determining the metric of theU ₄, a system of nonlinear field equations is established coupling an axial vector source current to the axial vector torsion field. The properties of the solutions of these equations are discussed assuming a London-type condition relating the axial current and torsion field. To characterize the solutions use is made of the Euler and Pontrjagin forms and the associated quadratic curvature invariants for theU ₄ space-time. It is found that there exists for a Riemann-Cartan space-time a relation between the zeros of the axial vector torsion field and the singularities of the Pontrjagin invariant, which is analogous to the well-known Hopf relation between the zeros of vector fields and the Euler characteristic.     

Radiative and non-radiative relaxation of excitons in strain-compensated quantum dots

We have investigated the population dynamics of excitons in strain-compensated InAs quantum dots (QDs) using a pump–probe technique under resonant excitation. Precise control of polarization directions of incident pulses enabled us to selectively estimate population lifetimes for two orthogonally polarized exciton ground states according to polarization selection rules. Measured decay times of the probe transmissions were highly dependent on the polarization directions of the exciton states. We found that the ratio of the decay times for the orthogonally polarized states is in quantitative agreement with the ratio of square of the transition dipole moments. This indicates that radiative recombination processes have a dominant effect on the population dynamics and that non-radiative and spin relaxations are negligible in our QDs. As a result, we can estimate the radiative lifetimes to be 1.0±0.1 and 1.7±0.2 ns for orthogonally polarized exciton ground states.     

The Hanle effect with partial frequency redistribution. Construction of a frequency-dependent polarization matrix and numerical solution by a PALI method

The polarized approximate lambda iteration (PALI) technique developed for the weak field Hanle effect relies on the decomposition of the Stokes parameters I, Q and U into six cylindrically symmetrical components. It has been applied to complete and partial frequency redistribution with redistribution matrices in which frequency redistribution is decoupled from scattering polarization. For partial frequency redistribution, the decoupling is obtained by an adequate decomposition of the frequency space into several domains. By angle-averaging frequency-dependent terms in the exact weak field Hanle redistribution matrix for a normal Zeeman triplet, we construct a redistribution matrix with coupling between frequency redistribution and polarization and no domain decomposition. The coupling is contained in generalized frequency redistribution functions that depend on the magnetic field. The redistribution matrix is expanded in the Landi Degl’Innocenti spherical tensors for polarimetry and the Stokes parameters are decomposed into cylindrically symmetrical components. A PALI method is set up for the calculation of these components. The Stokes parameters are calculated for different simple atmospheric models. The positive Q direction corresponds to the linear polarization perpendicular to the solar limb. It is shown that the frequency space decomposition may induce large errors on Stokes U in the transition region between line core and line wings but can safely be used for Stokes I and Q, the errors staying less than 1% at all the frequencies.     

Two-photon bremsstrahlung processes in atoms: Polarization effects and analytic results for the Coulomb potential

The partial wave analysis of two-photon free-free (bremsstrahlung) electron transition cross sections during scattering by a static potential U(r), as well as by an atom with a nonzero angular momentum, is carried out. The dipole interaction with radiation is taken into account in the second order of perturbation theory for the general case of elliptic polarization of photons. The polarization and angular dependences of the two-photon potential scattering amplitude is presented as a combination of the scalar product of electron momenta and photon polarization vectors and five atomic parameters containing Legendre polynomials of the scattering angle as well as radial matrix elements depending on the initial (E) and final (E′) electron energies. The results are applicable both for spontaneous double bremsstrahlung at nonrelativistic energies and for induced absorption and emission in the field of a light wave. Specific polarization effects (circular and elliptic dichroism) are analyzed for two-photon bremsstrahlung processes associated with the interference of the Hermite and anti-Hermite parts of the amplitude and depending on the sign of photon helicity. The limiting cases of high and low photon frequencies are investigated analytically, and the asymptotic forms of radial matrix elements and amplitudes for the general form of the U(r) potential are determined. Closed analytic expressions are derived for the radial matrix elements of the Coulomb potential in the form of integrals of hypergeometric function, and singularities are singled out in explicit form for E′ → E. The methods of approximate calculation of the radial matrix elements are discussed, and the results of their exact numerical calculation, as well as angular distributions and the cross sections of induced one-and two-photon emission and absorption, are given for the case of the Coulomb potential. The numerical results show that dichroism effects are quite accessible for experimental observations.     

Scattering polarization in the presence of magnetic and electric fields

The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect, and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle-Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts, and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field, or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the Q/I profiles and rotation of the plane of polarization in the U/I profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady-state and time-varying electric fields that surround radiating atoms in solar atmospheric layers.     

部分相干刃型位错光束的谱Stokes奇点

利用交叉谱密度函数的传输公式,推导出部分相干刃型位错光束在自由空间中传输的解析表达式.结合谱Stokes参数,详细讨论了其Stokes场的奇点变化规律.结果表明,部分相干刃型位错光束在自由空间传输过程中存在谱s12,s23和s31奇点.改变刃型位错的离轴量、斜率、空间相关长度等光束参数以及随着传输距离的变化,会有谱Stokes奇点的移动、产生和湮没,也会有V点的产生和C点旋性的反转.