Stimulated Raman Scattering of Squeezed Light with Pump Depletion

Abstract

Using the approximation of small fluctuations around a stationary point, photon statistics and squeezing of vacuum fluctuations are derived in stimulated Raman scattering including the coupling of photon-photon and photon-phonon modes. The depletion of pump light is described and it is shown that a regime of inversion of the process is related to an increase in quantum fluctuations, which are finally reduced again, more in the anti-Stokes mode than in the Stokes mode. If the anti-Stokes coupling is stronger than the Stokes coupling, then an oscillating behaviour of the statistical characteristics occurs and substantial squeezing can be found in photon-phonon modes.     

The Measurement of Relaxation Rates by Degenerate Four-wave Mixing with Ultrashort Light Pulses

Abstract

A method for estimating the relaxation time of nonlinear media, or the ratio of the relaxation time and the laser pulse duration in the presence of moderate or strong phase modulation, is proposed. The validity of our relaxation time measurements is verified using computer simulations of the model and comparing them with the experimental data for CS₂, nitrobenzene and an 8CB liquid crystal.     

Quantum Statistics of Stimulated Raman and Hyper-Raman Scattering of Squeezed Light with Pump Depletion

Abstract

Using the approximation of small fluctuations around a stationary solution, photon statistics and quadrature variances are derived in stimulated Raman and hyper-Raman scattering including the coupling of pumping, Stokes, anti-Stokes and phonon modes. The depletion of pump light is included. Compared to Raman scattering, additional regimes to generate anti-bunched, sub-Poisson and squeezed light were found caused by self-interaction of the pump mode. It was possible to include effects of nonlinear dynamics, initial squeezing of radiation and phonon system, external noise and losses.     

Phase Conjugation in Degenerate Four-wave Mixing with Finite Apertures

The phase-conjugate field fidelity in backward-going four-wave mixing, based on the diffraction model solvable analytically, is investigated. The method assumes interaction of the non-depleted infinite plane pump waves with the spatially limited probe and signal waves inside the nonlinear medium. Solutions are obtained applying the Fourier transformation and the Green function technique under various boundary conditions for coupled wave equations. The probe and its phase-conjugate waves are defined by using a complex phase formulation including both the phase variation and amplitude modulation. It is shown that the analysed approach can involve assumptions leading to the ideal or distorted phase conjugation.     

Time Dependence of Degenerate Four-wave Mixing with Broad Bandwidth Pulsed Lasers

Abstract

A time dependent theory of resonant degenerate four-wave mixing (DFWM) with broad bandwidth lasers is outlined and used to calculate the temporal evolution of DFWM signals generated by pulsed lasers. Experimental measurements of saturation-induced pulse-shortening and reshaping effects are reported for DFWM in atomic Na vapour and found to be in quantitative agreement with theoretical predictions.     

Angular Spectrum of Phase-conjugate Field Generated in Four-wave Mixing

Abstract

The phase-conjugate mirror realized by means of degenerate four-wave mixing in a Kerr-like medium is investigated using the angular spectrum representation of interacting fields. The analysed model is based on the nonlinear mixing of two infinite plane pump waves with the spatially limited probe and signal waves. Relations among harmonic components of the probe and signal fields are derived assuming non-depleted pumping and neglecting the evanescent waves. The influence of the injected signal field on the frequency spectrum of the generated phase-conjugate field is also examined.     

Non-classical Light in Nonlinear Symmetric and Asymmetric Couplers

Abstract

We derive the quantum-statistical properties of light beams in nonlinear symmetric and asymmetric couplers composed of linear waveguides and a nonlinear waveguide operating by the second-harmonic generation. This device can exhibit non-classical behaviour in single and compound modes and produce squeezed and/or sub-Poissonian light. Power solutions are obtained up to the twelfth order adopting a symbolic computer method. In addition, new higher-order results for the asymmetric coupler are presented.     

Polarization Characteristics of Phase Conjugation at Four-wave Mixing in Uniaxial Crystals

The phenomenon is considered of degenerate phase conjugation at four-wave mixing in uniaxial crystals. Polarization characteristics are calculated. The cases of complete and incomplete phase conjugation are analysed.     

Effects of Absorption on Multivalued Solutions in Photorefractive Four-wave Mixing with Complex Coupling Constant

Abstract

The steady-state coupled wave equations describing anisotropic photorefractive four-wave mixing with absorption in cubic crystals are solved for the general case where the coupling constant is complex. The effects of absorption on the behaviour of the multivalued solutions that occur under these conditions are examined, and the consequences for the dynamical behaviour are discussed.     

Optical Measurement Accuracy in the Case of Non-classical Light

Abstract

The influence of optical elements on the statistical properties of the input radiation is analysed by quantum-theoretical means for a representative optical arrangement consisting of beam splitters as well as for various types of grating spectrometers. In particular non-classical light states are studied. Optimum conditions for the maintenance of the signal-to-noise ratio of sub-Poissonian input radiation are derived.     

双泵浦SOA四波混频效应全光波长变换的研究

本文报道了半导体光放大器 (SOA)在偏振方向相互垂直的双泵浦光作用下 ,利用其四波混频 (FWM )效应实现的全光波长变换实验 ,其变换效率和信噪比在很宽的调谐范围内较高并且基本稳定。     

Prediction-Correction Scheme for Decoupled Forward Backward Stochastic Differential Equations with Jumps

By introducing a new Gaussian process and a new compensated Poisson random measure, we propose an explicit prediction-correction scheme for solving decoupled forward backward stochastic differential equations with jumps (FBSDEJs). For this scheme, we first theoretically obtain a general error estimate result, which implies that the scheme is stable. Then using this result, we rigorously prove that the accuracy of the explicit scheme can be of second order. Finally, we carry out some numerical experiments to verify our theoretical results.     

Polarization Effects of Degenerate Four-wave Mixing in Photorefractive Bi12GeO20 Crystals

Abstract

Owing to the anisotropy and optical activity of photorefractive crystals of the sillenite type (Bi₁₂GeO₂₀ and Bi₁₂SiO₂₀), degenerate four-wave mixing strongly depends on the polarization characteristics of the interacting waves. In this paper, theoretical calculations and experimental measurements are presented which characterize this dependency. A qualitatively good coincidence between experiment and theory is achieved.     

Laser Pulses Shortening at Transient Backward SRS and Forward Scattering Suppression

Abstract

Mathematical simulation of the transient SRS process is performed taking into account backward scattering and Stokes-anti-Stokes parametric coupling of the forward waves. It is shown that the parametric coupling has a slight influence on the suppression of forward scattering. A main contribution to the SRS asymmetry is made by pumping exhaustion by the backward Stokes waves. The dynamics of scattering radiation formation is studied and the conditions for obtaining high-contrast pulses at SRS compression are formulated.     

High-order Finite-element Method to Solve the Nonlinear Coupled-wave Equations for Degenerate Two-wave and Four-wave Mixing

Abstract

We use the one-dimensional finite-element method (FEM) to solve the nonlinear coupled-wave equations for degenerate two-wave mixing (DTWM) and four-wave mixing (DFWM) in a reflection geometry. High-order (quadratic) elements have been used. A comparison is made between the results obtained using the high-order FEM, and those using the first-order FEM, which have been reported previously. High accuracy is achieved using the high-order FEM which employs substantially fewer elements.     

Asymmetry of the Forward and Backward Raman Gain Coefficient at 1.54 mum in Methane

The threshold pump energies at 1.06 mum and Raman gain coefficients of stimulated Raman scattering (SRS) at 1.54 mum have been measured in both single-pass and half-resonator configurations at various methane pressures. In the single-pass configuration, the Raman gain coefficients of the backward and forward SRS are 0.32 and 0.23 cm/GW at 95 atm, respectively. The backward Raman gain coefficient is higher than the forward Raman gain coefficient. This gain reduction is caused by the depletion of local pump intensity, the phase-matching conditions, and the transient effect of the high amplification rate in the forward SRS process. In the half-resonator configuration, the Raman gain coefficient was 0.46 cm/GW at 75 atm of methane.     

An Approximation Method for the Backward Scattering of Light by a Soft Spherical Obstacle

Abstract

The optical analogue of a formula by Reading and Bassichis for the backscattering of a high-energy scalar wave by a square-well potential has been examined. In optical scattering, this corresponds to the problem of the back-scattering of light by a homogeneous spherical particle. Numerical checks with the Mie theory are presented for various values of the refractive index and size parameter. The formula is found to reproduce some scattering features extremely well for intermediate-size soft particles.     

Effect of Strong Pump Depletion on Two-beam Coupling in Photorefractive BaTiO3 at 442 nm

Abstract

Photorefractive BaTiO₃ crystal illuminated at 442 nm gives a large initial scattering level, which leads to strong pump depletion into beam fanning. Studies on the time development of beam fanning show a temporal shift of the fanned beam maximum towards the c-axis direction. The effect on the signal beam amplification of the strong pump depletion into beam fanning has been investigated, revealing different temporal development of the amplified signal for various cross-angles. Our observations on beam fanning in the presence and in the absence of a signal reveal that there is appreciable coupling between the fanned beam and the signal.     

基于高剪切泵油墨混合的三维流场数值模拟

研究了油墨在剪切泵内的混合过程,并应用FLUENT软件及RNGκ-ε湍流模型对该过程进行三维流场数值模拟,揭示了定转子齿间的压力场、速度场、湍流应力场以及空穴现象,分析了油墨中的溶剂和颜料在混合过程中,受到剪切力、摩擦力、撞击力、湍流应力和空穴效应等机械力及液力剪切的综合作用。结果表明采用剪切技术对油墨进行剪切均质,能够使油墨达到微观上的混合,从而提高油墨混合分散后的稳定性。