Diffusion of excited state molecules in FIR- and CO2-lasers

Both standing waves in laser oscillators and spatially inhomogenous cross sections of laser beam and pumprate cause a non-uniform distribution of excited state molecules in longitudinal and transversal direction, respectively. This spatial hole burning however is smoothed by diffusion of the excited molecules. The effect of diffusion is investigated theoretically for an optically pumped far infrared laser as well as the corresponding CO₂ pump laser. It is found, that the remaining spatial hole burning in the direction of wave propagation is negligible within CO₂ lasers but not within FIR lasers. Concerning the transversal direction it can be shown that in the FIR laser diffusion takes no effect, whereas the transversal distribution of the excited molecules in the CO₂ laser is significantly influenced by diffusion.FIR ring lasers avoid longitudinal spatial hole burning, which leads to the common assumption that they use the active medium more efficient than conventional standing wave lasers, hence delivering higher output powers. This expected advantage is levelled out to a great extent by diffusion.     

Light Wave Interactions in Active Nonlinear Crystals with Quadratic Nonlinearity

Recent results in the field of three-frequency wave interaction in homogeneous and inhomogeneous (periodically poled) active nonlinear crystals with quadratic nonlinearity are reviewed. The quasi-phase-matched processes of self-frequency doubling, self-frequency halving, and frequency mixing of the pump and laser radiations are studied. The consecutive quasi-phase-matched processes of the third-harmonic generation and parametric amplification with low-frequency pumping in periodically poled active nonlinear crystals are also investigated. The analysis is carried out for the case of a periodically poled Nd:Mg:LiNbO₃ crystal. Perspectives of using periodically poled active nonlinear crystals in laser devices with self-frequency conversion are discussed.     

Assignment of FIR Laser Lines of Hydrazine

With 228 known FIR laser emissions, hydrazine is the most prolific laser active molecules after methanol. But, due to the complexity of its rovibrational spectrum, only a few assignments of hydrizine FIR laser transitions are found in literature. Here we analyze 44 FIR laser lines of hydrazine excited by 20 different CO₂ pumps. The pump transitions are compared to available assignments of IR amino-wagging transitions. We propose values for the J and K quantum numbers involved in 41 FIR laser transitions, for 22 of them we give also the symmetry species.     

High efficiency long pulse FIR Raman conversion in ammonia

Generally the quantum efficiency of FIR Raman generation in molecular gases is below the theoretical value. This disagreement is particularly evident in Raman scattering from pulsed sources with short pulse length, when the vibrational saturation limits the power conversion. Other nonlinear processes can overcome this saturation, but they require a very intense pump power for too short a time to use the FIR radiation in high sensitive experiments with heterodyne detection. This is the case, for instance, of RFWM. In this work we describe the experimental conditions to achieve a high efficiency 90 micron Raman conversion in ammonia, with both short and long pulses.     

Multiple focused-waves production by parametric mixing in a layer with hysteretic quadratic nonlinearity

Nonlinear scattering of a weak probe wave by a strong pump wave in a layer with nonlinearity hysteresis is analysed. It is demonstrated that a spherical probe wave from a point source after nonlinear process of difference frequency excitation is scattered in several foci. Different foci correspond to different frequencies of the transformed wave spectrum. In the case of a plane pump wave and under the condition that nonlinear scattering proceeds without acoustic mode conversion wave front reversal is possible. To achieve wave front reversal in a layer with hysteretic quadratic nonlinearity the pump wave should have a frequency equal to the frequency of the probe wave or to any of its subharmonics.     

光子晶体光纤非线性光谱特性的理论与实验研究

光子晶体光纤具有特殊的导光机制和结构可调性,可以产生奇异的色散特性及高非线性,为非线性光纤光学领域的研究提供了新的条件。受多种非线性光学效应的共同作用,在不同泵浦光脉冲参数条件下,不同结构参数及传输特性的光子晶体光纤能产生丰富的非线性光谱。利用分步傅里叶方法求解非线性薛定谔方程,模拟飞秒激光脉冲在光子晶体光纤中的传输过程,获得输出光谱与入射光脉冲参数(泵浦光峰值功率P、泵浦光波长λ、光脉冲形状、光脉冲宽度T_FWHM)、光纤结构参数(孔间距Λ、空气填充比d/Λ、光纤长度z)、传输特性(色散、非线性系数)的关系,分析拉曼孤子、色散波、自相位调制等非线性效应产生的光谱特性。利用光子晶体光纤包层节区进行非线性光学实验研究,获得了孤子波和色散波的宽带光谱输出。理论分析与实验测量的光谱中都包括了波长0.5 μm附近可见光波段的蓝移色散波、0.82 μm波段的剩余泵浦光、1.1 μm波段的孤子波、2 μm附近的红移宽带色散波。理论分析与实验测量结果一致,阐明光子晶体光纤中非线性光谱产生的物理原理,实现了对宽带光谱的可控输出,为高非线性光子晶体光纤的结构设计、制备及非线性光谱的应用研究奠定基础。     

Measurement of the frequency response of the electrostrictive nonlinearity in optical fibers

The electrostrictive contribution to the nonlinear refractive index is investigated by use of frequency-dependent cross-phase modulation with a weak unpolarized cw probe wave and a harmonically modulated pump copropagating in optical fibers. Self-delayed homodyne detection is used to measure the amplitude of the sidebands imposed upon the probe wave as a function of pump intensity for pump modulation frequencies from 10 MHz to 1 GHz. The ratio of the electrostrictive nonlinear coefficient to the cross-phase-modulation Kerr coefficient for unpolarized light is measured to be 1.58:1 for a standard step-index single-mode fiber and 0.41:1 for dispersion-shifted fibers, indicating a larger electrostrictive response in silica fibers than previously expected.     

On reconstructing photon statistics by on/off detectors: Toward the multi-partite case

The propagation of pulses of the pump and its second harmonic in a quadratically nonlinear medium whose linear properties are characterized by a negative refractive index at the pump frequency and by a positive refractive index at the harmonic frequency is considered theoretically. In the case of a low intensity of the interacting waves, the pump and second-harmonic pulses propagate in the opposite directions, but sufficiently powerful pulses can form a simulton—a solitary two-frequency wave propagating in a certain direction as a single whole. Solutions to a set of equations are found which describe the steady-state propagation of a solitary wave and of a nonlinear periodic (cnoidal) wave.     

Electric field effects on an optically-pumped HCOOH FIR laser and Zeeman laser theory

Electric field effects have been investigated on the output power of six far-infrared (FIR) laser lines from H¹²COOH optically-pumped by a CO₂ laser with its polarization arranged perpendicular to the Stark field. Optoacoustic signals observed on the pump lines were hardly affected by the applied electric field up to 0.6 kV/cm. By neglecting the electric field effects on the pump transitions, Zeeman laser theory has been applied to the FIR laser transitions. Numerical calculation predicts the observed FIR output power as a function of electric field. Experessions for oscillation frequency and intensity in homogeneous limit are given, which may be applicable to any FIR Stark laser so far as the pump transition is free from electric field effects.     

Nonlinear structuring of the ionosphere modified by powerful radio waves at low latitudes

The problem of the nonlinear structuring of the modified ionosphere due to the self-focusing of the pump wave on the bunches of striations is investigated. Two main conditions of self-focusing are formulated: (1) propagation of the pump wave quite along the magnetic field for effective excitation of striations, and (2) trapping of the pump wave by large-scale irregularities. It is shown that both conditions can be easily satisfied for small inclination angles α of the magnetic field to the vertical. A detailed study of the low latitude case was performed using model calculations of the pump wave propagation. It is shown that at low latitudes self-focusing conditions also can be satisfied but mostly for the special form of the large-scale irregularities and mostly in the southern part of the pump wave beam. These results may reconcile apparent differences between radiowave and rocket probing of the irregularities.     

Effects of finite probe intensity on degenerate frequency mixing in saturable amplifiers

Phase conjugation by degenerate frequency mixing (DFM) in saturable amplifiers, including the effects of pump depletion, a non-zero incident probe wave intensity and saturated gain of all waves in the nonlinear medium, is analyzed numerically. Plane wave DFM reflectivities greater than unity are predicted, even in the presence of pump depletion, for sufficiently large amplifier gains. At a given level of incident probe-wave intensity the DFM reflectivity approaches its weak probe-wave value at sufficiently large incident pump intensities, but deviates from these values at lower pump intensities. Conditions are established under which the DFM reflectivity is effectively independent of the incident probe-wave intensity even when the incident pump intensity is smaller than that of the incident probe wave. Under these conditions the system holds the potential for faithful conjugation using pump waves that are considerably weaker than the probe waves being conjugated. The results also predict that under certain conditions, the intensity of the backward-generated wave can be larger than either the incident probe wave or the incident pump wave.     

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.     

Simulation of pumping beams self focusing and defocusing in NH3 Raman laser

High power IR pumping beams self focusing and defocusing in NH₃ Raman laser is investigated by numerical methods on the basis of the solution of nonlinear quasioptical equations. The analysis of self focusing have been done for a wide range of parameters of radiation and of active medium. Spatial evolution of the beam configuration have been investigated for different regimes of nonlinear diffraction. Developed model enables to allow exactly for the spectroscopic features of active molecules and may be applied to the analysis of the properties of powerful optically pumped FIR lasers.     

Two-dimensional diffraction on a cylinder induced by a laser beam in a nonlinear gradient medium

A wave theory was developed and a numerical simulation performed of the diffractive flow of a signal wave around a negative inhomogeneity induced by a cylindrical pump beam in nonlinear medium while keeping both waves in the potential well. It was shown that a broad pump beam reflects a narrow signal beam. A nonlinear waveguide (a dark soliton) is described as well. These phenomena can be observed in Bose-Einstein condensate (BEC) and in a gradient waveguide.     

Oscillating two-stream instability of laser wakefield-driven plasma wave

The laser wakefield-driven plasma wave in a low-density plasma is seen to be susceptible to the oscillating two-stream instability (OTSI). The plasma wave couples to two short wavelength plasma wave sidebands. The pump plasma wave and sidebands exert a ponderomotive force on the electrons driving a low-frequency quasimode. The electron density perturbation associated with this mode couples with the pump-driven electron oscillatory velocity to produce nonlinear currents driving the sidebands. At large pump amplitude, the instability grows faster than the ion plasma frequency and ions do not play a significant role. The growth rate of the quasimode, at large pump amplitude scales faster than linear. The growth rate is maximum for an optimum wave number of the quasimode and also increases with pump amplitude. Nonlocal effects, however reduce the growth rate by about half.     

Transformation of a nonlinear plasma wave into electromagnetic radiation in a periodic magnetic field

We study transformation of a nonlinear plasma wave into electromagnetic radiation in the periodic static magnetic field of an undulator. Such a wave can be excited by a short laser pulse or a relativistic electron bunch. The features of relativistic upper-hybrid plasma oscillations are analyzed. In the approximation of constant pump, resonance conditions of excitation of an electromagnetic wave and the characteristic transformation length are found. The nonlinear stage of transformation with allowance for pump depletion is considered. The studied phenomenon can be used for development of a high-power terahertz-radiatoin source. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 496–507, June 2007.     

光学微腔中倍频光场演化和光谱特性

在考虑光学微腔中二阶和三阶非线性效应的情况下,引入了可同时描述腔内基频和倍频光场的演化过程的Lugiato-Lefeve方程,分析了SiN微腔中二次谐波的产生,并讨论了各参数对腔内基频和倍频光场的影响.理论分析结果表明,失谐参量为0时,稳定后的基频光场为平顶脉冲的形式,而倍频光场呈正弦分布;失谐参量增加,将导致腔内基频和倍频光功率在演化过程中出现振荡,且最终稳定的光功率变弱,稳定后的光场分布为周期性变化;失谐参量的值过大,会使得微腔光场处于混沌状态.抽运光强较弱时,腔内可形成稳定的光场分布;抽运光强较强时,会导致腔内色散以及非线性效应过强,最终稳定的光场仍然呈周期性变化,且抽运光功率越强,光功率的演化曲线振荡越强.此外,选取特定的微腔尺寸,微腔可工作于"图灵环"状态.理论分析结果对研究光学微腔中二次谐波的产生有重要意义.     

Nonlinear all-photonic-crystal Fabry-Perot resonator with angle-independent bistability

We propose a nonlinear all-photonic-crystal (PhC) Fabry-Perot cavity tuned to the subdiffractive regime of the interior PhC, and we study angular-resolved nonlinear propagation of monochromatic plane wave excitations. With rigorous numerical simulations, we show that, for sufficiently large negative pump detunings and a focusing nonlinearity, the transmitted field has a bistable dependence on the pump field. Moreover, we reveal that, in contrast to a homogeneous resonator for different inclinations, the hysteresis curve is virtually unchanged for a fairly wide angular range. This may pave the way for obtaining novel kinds of nonlinear localized solutions in driven nonlinear resonators.     

Parametric interaction and compression of optical pulses in field of high-power pump wave

It is shown that, in the undepleted pump approximation, the nonlinear problem of the three-wave parametric interaction under the conditions of phase mismatch can be reduced to a problem of linear interaction of the signal and idle waves with a strong low-frequency pump wave. The whole wave packet formed by the two waves breaks down to partial pulses whose dynamics is controlled by effective dispersion parameters. This can be accompanied by the compression of either one of the pulses that comprises the wave packet or the whole wave packet.