Multiphase patterns in self-phase-locked optical parametric oscillators

Multiphase patterns are found in a mean-field model of a singly-resonant optical parametric oscillator that converts a pump field at frequency 3ω into signal and idler fields at frequencies 2ω and ω. A complex Ginzburg-Landau equation without diffusion and with a quadratic phase-sensitive nonlinear term is derived under single-longitudinal and paraxial propagation approximations. Owing to the phase-matched multistep parametric process ω + ω = 2ω, phase locking of the resonated signal field is possible with three distinct phase states. Three-armed rotating spirals, target patterns and light filamentation are found by a numerical analysis of the mean-field equation. Received 19 April 2001 and Received in final form 21 June 2001     

Sensitive Response of the Quantum Entropies to Jaynes-Cummings Model in Presence of a Second Harmonic Generation

The behavior of a modified Jaynes-Cummings Hamiltonian model (two-level atom in interaction with an electromagnetic field) in the presence of degenerate parametric amplification is introduced. We have examined two different cases, one when the field frequency ω is not equal to the splitting photon frequency ε for which the off-resonance case is considered. In the second case we have taken each frequencies to be equal (ω = ε) and considered the system to be at exact resonance. The wave function for both cases is obtained and the result used to calculate the density matrix from which we manage to discuss the field entropy as well as the phase entropy. It is shown that the system is sensitive to any change in the splitting photon frequency ε.     

Quantum properties of optical images in coupled nondegenerate parametric processes

Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.     

On the possibility of the nondegenerate parametric amplification of optical waves at low-frequency pumping

It is shown that parametric amplification at low-frequency pumping can be implemented in coupled nonlinear optical interactions in aperiodic nonlinear photonic crystals created by the method of the superposition of the modulation of the second-order susceptibility. In this process, the intensities of waves with frequencies higher than the pump frequency increase monotonically with the interaction length as in the case of the traditional process of parametric amplification at high-frequency pumping. The dependence of the gain factor on the coupling constants of interacting waves is obtained. The process under consideration makes it possible to ensure the tuning of the generated frequency in the ultraviolet range upon pumping in the visible range. Analysis of the process is performed on the example of aperiodic nonlinear photonic crystals of lithium niobate. Original Russian Text ? A.S. Chirkin, I.V. Shutov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 11, pp. 803–807.     

The formation of a light field with suppressed photon fluctuations by nonlinear optical methods

A quantum theory is developed to describe optical parametric amplification under low-frequency pumping, which is observed in nonlinear photonic crystals in sequential interactions of light waves with multiple frequencies. Spatial variations of the mean number of photons and the Fano factor at signal and additional frequencies are analyzed. It is shown that a field with a sub-Poisson statistics of photons can be formed at a signal frequency which is 1.5 times higher than the frequency of pumping.     

New method for detection of exciton Bose condensation using stimulated two-photon emission

An investigation is reported of stimulated two-photon emission by Bose-condensed excitons accompanied by a coherent two-exciton recombination, i.e., by simultaneous recombination of two excitons with opposite momenta leaving unchanged the occupation numbers of exciton states with momenta p≠0. Raman light scattering (RLS) accompanied by a similar two-exciton recombination (or production of two excitons) is also analyzed. The processes under consideration can occur only if a system contains Bose condensate, so their detection can be used as a new method to reveal Bose condensation of excitons. The recoil momentum, which corresponds to a change in the momentum of the electromagnetic field in the processes, is transferred to phonons or impurities. If the recoil momentum is transmitted to optical phonons with frequency ω ₀ ^s , whose occupation numbers are negligible, and the incident light frequency satisfies ω<2Ω, where Ω_=Ω−ω ₀ ^s is the difference frequency and Ω is the light frequency corresponding to the recombination of an exciton with zero momentum, stimulated two-photon emission and RLS with coherent two-exciton recombination give rise to a line at 2Ω_ −ω and an anti-Stokes component at ω+2Ω_, respectively. For ω2Ω_ the RLS spectrum contains Stokes and anti-Stokes components at frequencies ω±2Ω_, whereas stimulated two-photon emission is impossible. Formulas for the cross sections at finite temperatures are obtained for the processes under consideration. Our estimates indicate that a spectral line at 2Ω_−ω, corresponding to the stimulated two-photon emission accompanied by coherent optical phonon-assisted two-exciton recombination can be experimentally detected in Cu₂O. Zh. éksp. Teor. Fiz. 115, 1353–1376 (April 1999)     

The nonlinear optical susceptibility and electro-optic tensor of ferroelectrics: first-principle study

The nonlinear optical properties of some ABO₃ materials (BaTiO₃, KNbO₃, LiTaO₃ and LiNbO₃) are studied by density functional theory (DFT) in the local density approximation (LDA) expressions based on first-principle calculations. Our goals are to give the details of the calculations for linear and nonlinear optical properties, including the linear electro-optic (EO) tensor for some ABO₃ structures with oxygen octahedral structures using first-principles methods. These results can then be used in the study of the physics of ferroelectrics, specifically, we present calculations of the second harmonic generation response coefficient X _ijk ⁽²⁾ (−2ω, ω, ω) over a large frequency range for ABO₃ crystals. The electronic linear EO susceptibility X _ijk ⁽²⁾ (−ω, ω,0) is also evaluated below the band gap. These results are based on a series of the LDA calculations using DFT. Results for X _ijk ⁽²⁾ (−ω, ω,0) are in agreement with experiments below the band gap. The results are compared with the theoretical calculations and the available experimental data.     

Simultaneous parametric generation and up-conversion of entangled optical images

A quantum theory of parametric amplification and frequency conversion of an optical image in coupled nonlinear optical processes that include one parametric amplification process at high-frequency pumping and two up-conversion processes in the same pump field is developed. The field momentum operator that takes into account the diffraction and group velocities of the waves is used to derive the quantum equations related to the spatial dynamics of the images during the interaction. An optical scheme for the amplification and conversion of a close image is considered. The mean photon number density and signal-to-noise ratio are calculated in the fixed-pump-field approximation for images at various frequencies. It has been established that the signal-to-noise ratio decreases with increasing interaction length in the amplified image and increases in the images at the generated frequencies, tending to asymptotic values for all interacting waves. The variance of the difference of the numbers of photons is calculated for various pairs of frequencies. The quantum entanglement of the optical images formed in a high-frequency pump field is shown to be converted to higher frequencies during the generation of sum frequencies. Thus, two pairs of entangled optical images are produced in the process considered.     

Influence of a magnetic field on the mutual rectification of alternating currents induced by electromagnetic waves in graphene

The direct component of the electric current induced in graphene placed in a constant magnetic field has been found in the case where two electromagnetic waves with two mutually perpendicular planes of polarization are normally incident on the surface of the sample. It has been demonstrated that the direct component of the current along the direction of the electric field vector of the wave with the frequency ω₁ arises only when the ratio between the frequencies of the incident waves is ω₁/ω₂ = 2 or 1/2. In the latter case, the direct current component appears only in the presence of a magnetic field.     

Theory of the electroacoustic echo in single crystals of order-disorder ferroelectrics

The mechanism governing the shaping of the echo response in a monodomain order-disorder ferroelectric crystal to excitation by two pulses of a microwave electric field at the frequencies ω and 2ω [(ω, 2ω) echo] and at the frequency ω [(ω, ω) echo] is described in the framework of the pseudospin formalism (S=1/2). The parameters of the echo response are calculated, and the results obtained are in good qualitative agreement with experiment. Fiz. Tverd. Tela (St. Petersburg) 39, 697–703 (April 1997)     

Parametric amplification at low-frequency pumping and generation of four-mode entangled states

We show that parametric amplification at low-frequency pumping can be implemented in aperiodic nonlinear photonic crystals. In this process, the intensities of the waves with frequencies higher than the pumping frequency increase with increase in the interaction length as in the case of the standard process of parametric amplification at high-frequency pumping. The process under consideration includes a nondegenerate parametric down-conversion followed by two parametric up-conversions in the same pumping wave. As a result, generation at four new frequencies arises. Quantum analysis of the process demonstrates the presence of entanglement in the states of four modes. Talk presented at the oral issue of J. Russ. Laser Res. dedicated to the memory of Professor Vladimir A. Isakov, Professor Alexander S. Shumovsky, and Professor Andrei V. Vinogradov held in Moscow February 21–22, 2008.     

High-frequency asymptotic behavior of T-odd optical effects

It is shown that the contribution of low-frequency excitations with characteristic energy ℏω _l to T-odd (nonreciprocal) optical effects, including spatial dispersion effects, at optical frequencies ω≫ω _l can be calculated in the zeroth-order approximation with respect to the parameter ω _l/ω. This greatly simplifies their analysis. Some of these effects are found to be frequency independent in the spectral regions where the refractive index n(ω)≈ const. It is shown that frequency-independent Faraday rotation can be observed in media with zero magnetization, including in media with zero microscopic magnetic moment density. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 7, 510–513 (10 April 1999)     

Return current instability and its effects on beam-plasma system

The return current induced in a plasma by a relativisitc electron beam generates a new electron-ion two-stream instability (return current instability). Although the effect of these currents on the beam-plasma e-e instability is negligible, there exists a range of wave numbers which is unstable only to return current (RC) instability and not to e-e instability. The electromagnetic waves propagating along the direction of the external magnetic field, in which the plasma is immersed, are stabilized by these currents but the e.m. waves with frequencies,ω ²≪Ω _e ² ≪ω _pe ² (Ω _e andω _pe being cyclotron and plasma frequency for the electrons of the plasma respectively) propagating transverse to the magnetic field get destabilized. Heuristic estimates of plasma heating, due to RC instability and due to decay of ion-acoustic turbulence generated by the return current, are made. The fastest time scale on which the return current delivers energy to the plasma due to the scattering of ion-sound waves by the electrons can be ∼ω _pi ⁻¹ (ω _pi being the plasma frequency for the ions).     

“Quasi-Planck” spectra of capillary turbulence on the surface of liquid hydrogen

We report the first observation of “quasi-Planck” spectra of capillary turbulence on the surface of liquid hydrogen in the dissipation domain. Capillary waves have been driven by low-frequency random force. We have observed that the frequency spectrum of surface elevation changes its dependence from power-like 〈|η_ω²|〉 ∼ ω^−2,8 at middle-frequency domain to “quasi-Planck” distribution ∼e ^ω/ω _d at higher frequencies. The frequency ω _d is proportional to the boundary frequency between inertial interval and dissipation domain and it is scaled up with the increase of driving force.     

Photoelectric instability in oxide glass

The spatially periodic modulation of optical anisotropy (MOA) induced in oxide glass by mutually coherent light beams with different frequencies (ω and 2ω) is unstable under illumination with monochromatic light with frequency ω. Disturbances with small amplitudes intensify and disturbances with large amplitudes relax. Irrespective of its initial degree, the MOA reaches the same steady-state level, which depends on the illumination intensity. Intensification of MOA is accompanied by the appearance of second-harmonic radiation whose intensity grows in time to a steady-state level. The instability of the anisotropy is due to degenerate three-wave mixing and to feedback arising as a result of the coherent photogalvanic effect. A hypothesis that takes into account the observed giant growth (by three orders of magnitude) of light absorption in the MOA region is proposed to explain the stabilization of the instability and the formation of stationary periodic refractive-index gratings. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 12, 771–776 (25 December 1997)     

Relaxation of the optical density of glass modulated with bichromatic radiation

Exposure of oxide glass to two coherent light beams with different frequencies ω and 2 ω leads to the buildup of spatial index gratings in the glass. The kinetics of the writing and relaxation of the gratings is investigated. Illumination with one beam or a background illumination of the sample accelerates the relaxation process; this acceleration is due to the appreciable photoconductivity of the glass. The diffraction is found to reach a residual self-maintaining level when a grating is illuminated continuously with a beam at the fundamental frequency. The results are analyzed on the basis of a model that includes the coherent photogalvanic current, the accumulation of a grating of nonuniform charges under the action of this current, and the back-effect of the static field, via electrooptic effects, on the propagation of the beams. It is shown that an optical instability of the photoinduced index gratings exists in the glass. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 166–170 (10 February 1996)     

Transport and dielectric properties of thin polycrystalline CoO films

Transport and dielectric properties of polycrystalline CoO films were studied as functions of the applied field, frequency and temperature. TheI–V plots showed that the Poole-Frenkel field emission mechanism is responsible for conduction at fields>10⁵ V/cm. The ac conductivity σ(ω), the imaginary part of the dielectric constantε ₂, and tan δ plots as functions of frequency revealed three dispersion regions. The σ(ω) andε ₂ frequency dependence indicates a non-adiabatic hopping of charge carriers at low frequencies and adiabatic hopping at high frequencies. The activation energy of a dielectric oscillator is 0.15 eV. Work supported by the Office of Naval Research.     

On the possibility of the nondegenerate parametric amplification of optical waves at low-frequency pumping

It is shown that parametric amplification at low-frequency pumping can be implemented in coupled nonlinear optical interactions in aperiodic nonlinear photonic crystals created by the method of the superposition of the modulation of the second-order susceptibility. In this process, the intensities of waves with frequencies higher than the pump frequency increase monotonically with the interaction length as in the case of the traditional process of parametric amplification at high-frequency pumping. The dependence of the gain factor on the coupling constants of interacting waves is obtained. The process under consideration makes it possible to ensure the tuning of the generated frequency in the ultraviolet range upon pumping in the visible range. Analysis of the process is performed on the example of aperiodic nonlinear photonic crystals of lithium niobate.     

微弱光学图像的光参量放大特性的研究

研究了微弱光学图像在光参量图像放大中的放大特性,分析了相位匹配和晶体的空间频率带宽对图像信号增益的影响,从实验上验证了不同的相位匹配时输入图像信号在傅里叶平面上的增益分布.结果表明,当晶体的空间频率带宽大于输入图像信号的空间频率带宽且完全相位匹配时,光参量图像放大器能够对输入图像信号实现无失真、高增益的理想放大;有相位失配时,图像信号的增益峰值向高空间频率范围移动,并且在峰值附近范围变窄,随相位失配量大小的变化能够对图像信号光场中某特定空间频率实现放大,对图像信号进行滤波处理,突出图像特定频率的信息,实现图像边缘增强.     

Evanescent Plane Waves in Multilayer Structures

We have considered evanescent plane waves in structures with a layer of a substance with ε, μ < 0 and with a layer of a well-reflecting metal, ε < 0, μ ≥ 1. Waves with increased amplitude as compared with the initial wave have been found to occur, due to which evanescent waves with wave number as in the initial wave but with increased amplitude arise behind these layers. A composite material with ε, μ < 0 at optical frequencies are proposed. Surface waves on a metal layer are considered in detail. It is shown that surface waves with a sufficiently arbitrary wave number can be excited. It is also shown that, on very thin layers, surface waves with wave number exceeding ten times that of a homogeneous plane wave in vacuum can be excited. Propagation losses are calculated. For a silver layer, the wave path can be from 30 up to 100 wavelengths. Practical use in developing techniques for optical transformations of short-wave surface waves in 2D space, similar to those in 3D space, are pointed out.