Phase effects at second-harmonic generation in metamaterials

We develop the theory of second-harmonic generation in metamaterials where fundamental radiation is considered in the constant-intensity approximation taking into account the phase changes of interacting waves. We investigate the second-harmonic wave intensity in metamaterials at different parameters of the problem under consideration. We consider a self-action effect of the light wave in metamaterials in view of the phase changes of all the interacting waves and compare this effect with an analogous effect in usual homogeneous quadratic media. We show that it is possible to change the phase velocity of the pump wave by varying such parameters as the pump intensity, nonlinear medium length, and phase mismatch between the interacting waves. The metamaterials under consideration provide a possibility to change the phase of the fundamental radiation of order of magnitude higher than those in the usual homogeneous quadratic media.     

Phase effects at second harmonic generation of powerful laser radiation in noncentrosymmetrical media

There has been developed the theory of second harmonic generation of the intensive laser fields in the existence of both quadratic and cubic polarization in medium in the constant-intensity approximation accounting for the reverse effect of the excited wave on the exciting one and simultaneously allowing us to take into account phase mismatch and the damping of all the interacting waves. It is shown that the changes of pump intensity through self-phase and cross-phase modulation processes effect optimum phase relationship between interacting waves, the change of the spatial beating period. The conditions of compensating undesirable phase shifts between interacting waves have been determined, the analytical expressions for calculation of optimum values of phase mismatch, length of noncentrosymmetrical medium and the spatial beating period are offered. It is shown that in the absence of linear phase mismatch with an increase of basic radiation intensity the spatial beating period is being reduced. The numerous analysis has been made of frequency doubling process efficiency for KDP and LiNbO₃ crystals.     

On the possibility of soliton-like double-frequency propagation of femtosecond pulses in an optical fiber under conditions of second harmonic generation

A soliton-like mode of double-frequency propagation of femtosecond pulses during second harmonic generation (SHG) in optical fibers is predicted on the basis of computer simulation. The essence of this mode is that, under certain conditions, the central part of the pulses of both the fundamental and the second harmonic waves propagate without a change in the intensity of either wave. This mode can be realized by either of two schemes of the SHG process. In the first scheme, the second harmonic enters a nonlinear medium with some definite input amplitude and definite phase shift with respect to the fundamental wave. In the other scheme, the second harmonic has a zero input amplitude and a phase shift is introduced into the interacting waves in particular cross sections of the medium.     

The theory of nonlinear dispersion interferometers in the constant intensity approximation

The operation of a dispersion interferometer with intracavity location of a medium under study is analyzed in the constant intensity approximation taking into account the reciprocal influence of a harmonic on the phase of the exciting wave. This approximation allows the effects of phase mismatch and losses in a medium on the course of a nonlinear process to be taken into account simultaneously. Intensity minima of the harmonic (as opposed to the constant field approximation) in the constant intensity approximation are shown to depend on dispersion of the refractive index of the medium under study, which makes it possible to determine dispersion of the refractive index of the substance under study directly and accurately     

Phase effects at second harmonic generation in the layer media

An analysis is made of quasi-phase-matched interaction at second harmonic generation in a regular domain structure with accounts for losses and change of phases of all the interacting waves. The constant-intensity approximation of basic radiation is applied for this purpose, not to regular domain structure as a whole, but to each separately taken domain. It allows to carry out more strict analysis of quasi-synchronous interaction during the frequency conversion to the polydomain consisting of n layers, forming “grating” periods of modulation of the nonlinear susceptibility. With this, the values of complex amplitudes of basic radiation and second harmonic wave at the outlet of each domain are entrance values of the corresponding complex amplitudes to the following domain. The analytical expression is given for the case of n domains and the factors limiting the efficiency of the process of frequency conversion are analyzed. In the constant-intensity approximation, in contrast to the constant field approximation, the coherent length of domain depends on pump intensity. With increasing pump intensity the optimum length decreases. In a regular domain structure at frequency conversion from a layer to a layer, intensity of the basic radiation changes. Also the optimum length of domains at which conversion efficiency is maximal therefore changes. Thus, it is possible to obtain the high values of conversion frequency at the outlet of a regular domain structure by choice of optimum parameters of a task (length of domains, phase mismatch, pump intensity), as well as using the layers-domains of high quality.     

Phase modulation of Bloch surface waves with the use of a diffraction microrelief at the boundary of a one-dimensional photonic crystal

Phase modulation methods for surface electromagnetic waves propagating at the interface between a homogeneous medium and a one-dimensional photonic crystal have been analyzed numerically and theoretically. Modulation is performed by changing the geometrical parameters of the microrelief on the surface of the photonic crystal. The phase modulation methods under consideration can be used to create optical elements for surface waves, in particular, lenses, prisms, and diffraction gratings. A Bragg grating has been calculated as an example. According to the simulation results, the average coefficient of reflection of a surface wave in the band gap is 0.95.     

Heat dissipative solitons in optical fibers

We propose a one-dimensional model governing the propagation of heat waves in an optical fiber (the “fiber fuse”). The model has solutions in the form of high temperature localized waves moving towards the input end of the fiber, fueled by the laser power. These waves can be ignited by local heating at any point along the fiber. The effect of such a wave is irreversible damage to the fiber core. The phenomenon was observed earlier by Hand and Russell, when locally heating a fiber through which CW light of modest intensity was propagating. This induced self-destruction of the optical fiber core.     

Light Scattering from Polaritons in GaP Crystals

The theory of polariton scattering on stimulated Raman scattering and of coherent anti-Stokes scattering of light in dispersing and dissipative media has been developed in the approximation of a constant intensity which takes into account the reverse influence of excited waves on exciting ones and makes it possible to simultaneously consider the phase difference and decay of all interacting waves. It has been established that, unlike a constant-field approximation, the complex amplitude of the Stokes wave depends on the intensity of the polariton one and vice versa. A comparison of the behavior of the polariton-wave intensity for a GaP crystal in both approximations has been carried out.     

New nonlinear intensity Kerr effect in the polar geometry

The problem of the electromagnetic wave reflection on the second optical harmonic from a semi-infinite optically isotropic magnetic medium is considered for the uniform magnetization direction corresponding to the polar Kerr effect. In the first approximation in magnetization, the method of Green’s tensor functions is used to derive expressions for the complex amplitudes of the wave fields for the incidence of s-and p-polarized waves (as well as of their superposition) on the medium. It is shown that, in the latter case, the nonlinear polar Kerr effect is of the intensity type. The dependences of the intensity effect on the angle of incidence of the inducing wave and on the angle of its polarization, which were obtained in numerical experiments, are presented. A comparative analysis of the linear and nonlinear intensity Kerr effects is carried out.     

Phase effects during parametric conversion in layer structures

Coupled-wave equations that describe the parametric amplification and generation of a sum frequency in a three-layer structure are studied theoretically in the constant-intensity approximation taking into account the inverse effect of the excited wave on the phase of the pumping wave. For this purpose, the approximation of constant intensity of the fundamental radiation is applied not to the layer structure as a whole but to each separately taken layer. In this case, the complex amplitudes of the interacting waves at the output of each layer are the input values of the corresponding complex amplitudes for the next layer. Analytical expressions obtained in the constant-intensity approximation for the efficiency of conversion to the sum frequency were analyzed numerically for different parameters of the problem. The efficiency of parametric amplification at a high frequency was found to depend on the intensity of the signal wave at a low frequency.     

Efficiency of sum frequency generation by regular domain structures

We theoretically examine generation of sum-frequency radiation in a regular domain structure, taking into account phase changes for all the interacting waves in a dissipative medium. We show that in contrast to the constant-field approximation, in the constant-intensity approximation there is an optimal value for the longitudinal dimension (length) of the domains at which maximum conversion of the signal wave energy to the sum-frequency wave energy occurs. As the pump intensity increases, the optimal domain length decreases. As the losses of the interacting waves increase, both the conversion efficiency and the optimal domain dimensions decrease.     

相位匹配法在毛细管波导中产生高次谐波的分析

在理论上研究了超短强激光脉冲与毛细管中惰性气体相互作用产生高次谐波的最佳相位匹配条件,在计算中发现了特定级次 相位匹配中截止驱动光强的存在。分析表明要想使高次谐波获得相位匹配,需要超短脉宽的驱动脉冲以及电离能大的气体工作介质。讨论了毛细管波导中的强场高次谐波选择性并指出了改善谐波选择性的措施。     

Localized light waves: Paraxial and exact solutions of the wave equation (a review)

Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.     

Peculiarities of self-action in second harmonic generation of laser radiation in nonlinear crystals

By using the generalized method of strong interaction of nonlinear waves and computer simulation, an analysis of the influence of self-action effects on second harmonic generation of an intense diverging picosecond pulse is performed. Using the approximation of strong wave interaction, an analytic solution is obtained for frequency conversion of the laser radiation taking into account the pump intensity depletion, the influence of the angular dispersion effect (ADE), and the higher nonlinearities. It is shown that the self-action effects, the ADE, and the linear phase mismatch can compensate for each other, increasing the efficiency of second harmonic generation. Optimum conditions for second harmonic generation in converging and diverging laser beams were found. An asymmetry of the angular dependence of the second harmonic intensity was experimentally observed and theoretically explained. The asymmetry is caused by the reverse energy conversion of the second harmonic into the pump by the influence of the ADE and Kerr nonlinearities.     

Interaction of ion-acoustic solitons with Langmuir turbulence

The interaction of ion-acoustic solitons with Langmuir waves has been considered. Investigation was performed in the approximation of a slow change in soliton parameters compared with the time of evolution of wave spectrum. This permitted a two-stage solution of the problem. First the Langmuir wave spectrum changes in the given field of a soliton were found. Then the action of high-frequency waves on the soliton was taken into account.     

Modulation instability in systems of coupled waves with nonlinearity dispersion

Conditions for the appearance of modulation instability of an optical wave packet formed by one or two unidirectional strongly interacting waves are studied taking into account the influence of the temporal dispersion of a nonlinear response of the medium on this process. The regions of values of the frequency, input radiation intensity, and dispersion parameters in which the wave perturbations are increased are found. It is shown that the initial conditions for excitation of optical fibers of this type significantly affect the dynamics of the modulation instability.     

The inverse excitation-induced abnormal spiral wave

The effects of a local constant forcing on spiral waves in two-dimensional excitable media described by Bär model are investigated. A constant external forcing is imposed on the core of spiral wave, leading to parameter variability of a medium. It is found that the forcing can significantly alter the shape and rotation period of spiral wave when the values of related parameters are properly chosen. The change of wave structure is attributed to the transition from normal excitation to inverse excitation in the forced medium. An abnormal spiral wave with a very thick spiral arm has been observed. The physical mechanism underlying these phenomena is theoretically analyzed.     

Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams

This article deals with the wave propagation analysis of single/double layered functionally graded (FG) size-dependent nanobeams in elastic medium and subjected to a longitudinal magnetic field employing nonlocal elasticity theory. Material properties of nanobeam change gradually according to the sigmoid function. Applying an analytical solution, the acoustical and optical dispersion relations are explored for various wave number, nonlocality parameter, material composition, elastic foundation constants, and magnetic field intensity. It is found that frequency and phase velocity of waves propagating in S-FGM nanobeam are significantly affected by these parameters. Also, presence of cut-off and escape frequencies in wave propagation analysis of embedded S-FGM nanobeams is investigated.     

Parametric reflection phenomenon in quadratic uniaxial crystals with birefringence

Effects of parametric refraction and reflection of optical beams in uniaxial crystals have been considered with allowance for birefringence. The equation of the signal wave trajectory, taking into account the medium anisotropy, has been obtained and analyzed. Pecularities of these effects for different types of three-frequency interaction of ordinary and extraordinary waves are shown. In the presence of birefringence, the effective mismatch sign can change and consequently the cascade nonlinearity can become focusing; in this case, the effect of reflection disappears.     

Dynamics of the amplitude and phase of a signal in the process of quasi-phase-matched parametric interaction

The parametric amplification of a light wave in nonlinear optical crystals under a high-frequency pump and a periodic spatial modulation of the coefficient of nonlinear coupling of the waves is considered. The value of the period of modulation of the nonlinear coefficient that corresponds to the maximum gain is found. The behavior of the phase and intensity of the amplified wave is studied using the matrix approach. For the case of the optimum phase relation between the interacting waves, the expression for the intensity of the amplified wave is obtained, which, in the limit, gives the result for a homogeneous nonlinear crystal.