Dynamics of the parameters of pulses in uniaxial crystals

A set of equations describing the dynamics of the parameters of an electromagnetic pulse is derived using the Ritz-Whitham variational principle. An ordinary pulse component is a quasi-monochromatic pulse, and its extraordinary component is a videopulse. The transverse dynamics of pulses having the super-Gaussian shape is considered for propagation along an optical crystal axis.     

Nonlinear regimes of ultrashort pulse propagation in an array of anisotropic tunneling states

Dynamics of an ultrashort electromagnetic pulse in a system with an array of anisotropic tunneling states spanned by the pulse spectrum are analyzed. A system of nonlinear wave equations is derived for the ordinary and extraordinary components of the pulse propagating at an arbitrary angle to the anisotropy axis. Different regimes of ultrashort pulse propagation parallel and perpendicular to the anisotropy axis are examined. Ultrashort-pulse propagation regimes analogous to self-induced transparency and extraordinary transparency are identified. The properties of rational soliton-like pulses having no quasi-monochromatic analogs are analyzed. A longitudinal electric field component is generated in each regime, whereas off-resonance quasi-monochromatic pulses propagating under similar conditions (parallel and perpendicular to the anisotropy axis) have no longitudinal components. Stability of the solutions obtained and the effect of diffraction on ultrashort pulse dynamics are analyzed. The values of pulse parameters for which defocusing dominates over self-focusing are calculated.     

On the effect of transverse perturbations on the propagation of soliton-like two-component pulses in a uniaxial crystal

The combined approach including the method of analytic continuation of dispersion parameters to the complex plane and an averaged variational principle of the Ritz-Whitham type is used for studying the propagation of a soliton-like two-component pulse in a uniaxial crystal in the direction perpendicular to its optic axis. The ordinary component of the soliton is a pulse with an arbitrary number of light oscillations (down to one period), and the extraordinary component is a video pulse. Such a pulse is shown to be stable against small transverse perturbations, including small-scale ones.     

On nonlinear propagation of extremely short pulses in optically uniaxial media

Nonlinear wave equations describing the propagation of optical pulses of duration up to a period of electromagnetic oscillations in transparent media with uniaxial optical anisotropy are derived on the basis of a quantum-mechanical model of material response. The electron and electron-vibrational nonlinearities, electron and ion dispersion, and diffraction are taken into account. It is shown that the inclusion of the electron response alone leads to a system of two constitutive equations for the ordinary and extraordinary polarization components. When a pulse propagates across the optical axis, this system is reduced to an inhomogeneous model of the Henon-Heiles type and, hence, generalizes the Lorentz classical electron model. In order to take into account stimulated Raman scattering (SRS) processes, an anisotropic analog of the Bloembergen-Shen quantum-mechanical model taking into account the population dynamics of SRS sublevels is obtained. The generation of an extraordinary wave video pulse with the help of the high-frequency ordinary component in the Zakharov-Benney resonance mode is investigated. Some analytic soliton-like solutions in the form of propagating bound states of ordinary and extraordinary video pulses corresponding to different birefringence modes are considered and their stability to self-focusing is analyzed.     

Propagation of vector solitons in a quasi-resonant medium with stark deformation of quantum states

The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces ?? transitions, while the extraordinary component induces the ?? transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.     

单轴晶体的光程差和Lyot型滤光器的视场

 建立了以光线入射方向和晶体光轴方向为基准的入射坐标系，利用波法线反曲面方程和电磁场在晶体折射界面处切向分量连续性的边界条件，得到了晶体中波法线方向、射线方向、波法线折射率和射线折射率的表达式。从非常光的射线方向和射线折射率出发，得到了在任意的晶体光轴方向和入射角条件下，光通过单轴晶体后寻常光、非常光的光程差表达式。对Lyot型滤光单元的透射率和视场进行了计算分析后发现，滤光单元的透射率随光线入射角的变化呈现一定的周期性，视场随光轴倾角的增大而减小。得出了透射率和视场随光轴倾角(光轴与晶体表面的夹角)和光线入射角(光线在晶体表面的入射角)的变化规律。讨论了通过改变晶体倾角实现滤光器调谐和补偿晶体厚度加工误差等技术问题。     

Frequency tuning of an ordinary-extraordinary pulse in a uniaxial crystal

The spectral dynamics of a two-component pulse propagating at an arbitrary angle to the optical axis of a uniaxial crystal is analytically studied. Frequencies for which spectral densities of components are maximal are found from asymptotic solutions. Contributions of quadratic and cubic nonlinearities into the signal spectrum dynamics are analyzed.     

Propagation of an arbitrary incident light in a uniaxially planar slab

Similarly to the Jones calculus, a propagation formulation of an arbitrary incident light in a uniaxially planar slab with any orientation of the optic axis is derived, where both the multi-reflections and multi-refractions and the phase difference between the ordinary and extraordinary waves arising at the interface are considered. Unlike the case of propagation in the stratified isotropic media, the elements of the reflection and transmission matrices not only include the reflection and transmission coefficients, but also comprise phase differences caused by the mutual couples between ordinary (O) and extraordinary (E) waves. At this point, the propagation of an arbitrary light in a stratified uniaxially anisotropic media may be viewed as the multi-reflections and multi-refractions of a compound wave composed of one O wave and one E wave.     

Soliton regimes of ultrashort pulse propagation through an array of asymmetric quantum objects

Nonlinear regimes of two-component ultrashort pulse propagation through an array of anisotropic quantum systems are analyzed theoretically under conditions when the slowly varying envelope approximation is inapplicable. It is shown that if the spectral width of the pulse is much larger than the quantum transition frequency, then the dynamics of its ordinary component can be described by a modified sine-Gordon equation that belongs to the class of integrable models but has never been used in physical applications. It is shown that the extraordinary pulse component responsible for the dynamic Stark shift of the transition frequency is coupled to its ordinary component by an algebraic relation. The soliton solutions to the derived equation are classified. Depending on the pulse duration, the solutions have the form of 2π pulses (kinks and antikinks) or steady traveling 0π pulses having no counterparts in isotropic models (neutral kinks). Interactions between the medium and solitons of different types and soliton collisions are analyzed.     

Resonant transparency effects in an anisotropic medium with a permanent dipole moment

The propagation of a two-component laser pulse in an optically uniaxial medium is investigated under the conditions of the Zakharov-Benney resonance (viz., resonance of long and short waves). The short-wave ordinary component of the pulse, which is in resonance with the atomic subsystem, effectively generates a video pulse of the extraordinary wave (long-wave component). The latter dynamically detunes the ordinary pulse from the resonance and causes its phase modulation due to nonzero diagonal matrix elements of the dipole moment. An approximate operator approach is proposed for solving constitutive equations for the density matrix, which is equivalent to the asymptotic WKB method and makes it possible to reduce the analysis to solving a system of nonlinear wave equations for both components of the pulse. The possibility an extraordinary wave video pulse being generated with the help of a quasimonochromatic ordinary pulse with a longer wave-length. It is shown that, when the ordinary component dominates, the self-induced transparency mode is realized; in the opposite limit, the effect known as extraordinary transparency takes place. Solitary pulses corresponding to the latter case experience a decrease in the velocity of propagation, which is similar to that observed for self-induced transparency and practically do not change the population of quantum levels. Physical situations reducing the initial system of constituent and wave equations to familiar integrable models are analyzed.     

Quasi-microscopic theory of propagation of extremely short pulses in media with induced anisotropy

The nonlinear polarization response of a medium with induced anisotropy to the action of a high-intensity pulse containing an arbitrary number (down to one) optical oscillations is studied using quantum-mechanical concepts. Based on the proposed model, a set of nonlinear wave equations is obtained for the ordinary and extraordinary components of the pulse. The previously known equations for quasi-monochromatic pulses are shown to follow from this set as a special case.     

Effects of soliton dynamics of acoustic pulses in a paramagnetic crystal

Nonlinear dynamics of longitudinal-transverse acoustic pulses in the deformed cubic crystal containing a paramagnetic impurity with effective spin S = 1 is theoretically investigated. Soliton solutions of systems of equations describing the propagation of extremely short and ultrashort pulses at an arbitrary angle to the direction of external deformation parallel to the crystal symmetry axis are obtained. Classification of longitudinal-transverse soliton types and resonant acoustic transparency regimes is given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 31–36, August, 2007.     

Characteristics of paraxial propagation of a super Lorentz-Gauss SLG₀₁ mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss(SLG) 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

Calculations of spontaneous emission rates of a single-impurity molecule in uniaxial host crystals

In a uniaxial host crystal the spontaneous emission rate of the dipole transition of the zero-phonon line of a single-impurity molecule depends on the angle between the transition dipole moment and the optical axis of a crystal and as well as on the ordinary and extraordinary refractive indices. The relative spontaneous emission rate (the spontaneous emission rate divided by the spontaneous emission rate in the case when the transition dipole moment is parallel to the optical axis) is determined through a simple formula by one coefficient. Here this coefficient is calculated as a function of the extraordinary refractive index for 40 values of the ordinary refractive index on the interval from 1.25 to 3.20. For comparison, the effects caused by the nearness to the plane interface between cinnabar crystal (HgS) and air, as an example, are calculated.     

Nonlinear acoustic transparency phenomena in strained paramagnetic crystals

Nonlinear dynamics of longitudinal acoustic pulses propagating in a strained paramagnetic cubic crystal at low temperature is analyzed. The direction of constant uniform strain is parallel to one of the fourth-order symmetry axes. Effective-spin 1 ions are considered as paramagnetic impurities with the strongest spin-lattice interaction. In this medium, normally degenerate magnetic sublevels are dynamically shifted by the quadrupole Stark effect, and the frequencies of the transitions induced by an acoustic pulse change accordingly. The self-consistent system of equations derived in this study without using the slowly varying envelope approximation describes pulse propagation at an arbitrary angle to the direction of the static strain. Exponentially and rationally decaying monopolar and breather-like solutions to the system are obtained. An analysis of the solutions reveals an asymmetry of the pulse polarity depending on the type of strain (extension or compression) and the pulse propagation direction. In particular, it is shown that acoustic transparency associated with monopolar strain pulses exhibits threshold behavior. The sign of the time area (zeroth harmonic) of breather-like strain pulses is such that the transition frequency averaged over an oscillation period dynamically decreases. This behavior determines the efficiency of generation of high-order harmonics of acoustic pulses in strained paramagnetic crystals.     

Characteristics of paraxial propagation of a super Lorentz—Gauss SLG01 mode in uniaxial crystal orthogonal to the optical axis

Analytical propagation expression of a super Lorentz-Gauss（SLG） 01 mode in uniaxial crystal orthogonal to the optical axis is derived.The SLG 01 mode propagating in uniaxial crystal orthogonal to the optical axis mainly depends on the ratio of the extraordinary refractive index to the ordinary refractive index.The SLG 01 mode propagating in uniaxial crystals becomes an astigmatic beam.The beam spot of the SLG 01 mode in the uniaxial crystal is elongated in the x-or y-direction,which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index.With the increase of the deviation of the ratio of the extraordinary refractive index to the ordinary refractive index from unity,the elongation of the beam spot also augments.In different observation planes,the phase distribution of an SLG 01 mode in the uniaxial crystal takes on different shapes.With the variation of the ratio of the extraordinary refractive index to the ordinary refractive index,the phase distribution is elongated in one transversal direction and is contracted in the other perpendicular direction.This research is beneficial to the practical applications of an SLG mode.     

Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis

The propagation of partially polarized and partially coherent beams in uniaxial crystals orthogonal to the optical axis is investigated. The analytical formulae for the elements of the cross-spectral density matrix of partially polarized and partially coherent beams propagating through uniaxial crystals orthogonal to the optical are derived. The numerical results show that the degree of polarization decreases with the increase of the ratio of extraordinary to ordinary refractive indices at a certain propagation distance, and the influence of uniaxial crystals on the degree of coherent is not so evident. And the beams spread more rapidly in the direction parallel to the optical axis than orthogonal to the optical axis in positive crystal with the propagation distance increasing.     

Propagation of an Airy vortex beam in uniaxial crystals

The propagation dynamics of an Airy beam superimposed with a unit topological charge optical vortex is investigated analytically and numerically in uniaxial crystals orthogonal to the optical axis. Upon propagation, the Airy vortex beam is mainly dependent on the ratio of the extraordinary refractive index to the ordinary refractive index. Due to the anisotropic effect of the crystals, the acceleration of an Airy vortex beam in the transversal direction along the optical axis is more rapidly than that in the other transversal direction, which is alike to a conventional Airy beam but with twice the vortex acceleration velocity.     

非常偏振光在单轴晶体表面的反射-透射研究

为分析非常偏振光在晶体表面的能量损耗,给出一种求解反射率和透射率的方法,即根据电磁场的边值关系以及晶体的双折射和双反射现象,求解晶体光轴在入射面内时,非常偏振光从各向同性介质入射到晶体和从晶体出射到各向同性介质两种情况的反射率和透射率的方法,并给出反射率和透射率的解析解,同时得到对于晶体光轴在入射面内的情况,光轴的取向对非常偏振光反射率的大小几乎没有影响,但对产生全反射的临界角θc影响较大的结论。实验上用LiNbO3晶体验证了非常偏振光从各向同性介质入射到晶体时的反射率公式。求解方法简单实用,所给的表达式具有一般性,可以直接使用。     

Nonparaxial propagation of Hermite-Laguerre-Gaussian beams in uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of the nonparaxial propagation of a Hermite-Laguerre-Gaussian （HLG） beam in uniaxial crystal orthogonal to the optical axis are derived. The intensity distribution of an HLG beam and its three components propagating in a uniaxial crystal orthogonal to the optical axis are demonstrated by numerical examples. Although the y and z components of an HLG beam in the incident plane are both equal to zero, they emerge upon propagation inside the uniaxial crystal. Moreover, the beam profile of the x component is relatively stable and the beam profiles of the y and z components have the same evolution law. If the ratio of the extraordinary refractive index to the ordinary refractive index is larger than unity, the beam profile of the HLG beam is elongated in the x direction and generally rotates clockwise. Otherwise, the beam profile of the HLG beam is elongated in the y direction and generally rotates anticlockwise. This research is beneficial to the optical trapping and nonlinear optics involved in the rotation of a beam profile.