Phase matched vectorial three-wave mixing in isotropic Kerr media

A theoretical analysis of vectorial three-wave mixing in isotropic Kerr media is presented. The analysis based on the coupled-wave equations describes the amplification of a weak wave by coupling with a strong pump wave phase matched by optically induced change of average refractive index. The phase matching condition for interacting waves with different polarizations is calculated, allowing a large amplification of a weak wave by three-wave mixing in thick Kerr media. The main conclusions of our theoretical analysis are supported by the results of experiments in CS₂ liquid medium.     

Photorefractive four-wave mixing in a high-contrast regime

The effect of high contrast in photorefractive four-wave mixing is studied using a recently proposed empirical formula for the grating amplitude. An analytical solution to the coupled-wave equation is obtained and its properties are discussed in the case of a double-phase-conjugate mirror and semilinear phase-conjugate mirror.     

Photorefractive two-wave mixing in the presence of an incoherent beam

We present the numerical results of the photorefractive two-wave mixing in the presence of an incoherent beam by considering the influence of the ratios of the intensities and the light-excitation cross sections of the incoherent beam to the coherent beams on the space-charge field and the effective coupling coefficient. The results show that the incoherent beam can control the intensity of the coherent beams effectively. The experimental results agree with the theory well. One application is demonstrated to obtain the positive and negative coherent replicas of an incoherent image. The coherent images have a resolution of 80.6 line pairs/mm. Received: 2 March 1999 / Revised version: 26 July 1999 / Published online: 20 October 1999     

Biexcitonic effects in the time integrated four-wave mixing with picosecond pulses

We propose a simple method to estimate the biexcitonic contribution to the excitonic non-linearity. The method is based on the time integrated four-wave mixing (TI FWM) with picosecond pulses. The TI FWM signal, which is measured as a function of the delay between pump and test pulses, shows shift towards positive and negative time delay when the laser is tuned at the exciton and biexciton resonance, respectively. We show theoretically that the magnitude of the shift allows us to estimate the biexcitonic contribution to the third-order non-linearity at the fundamental band edge.     

Effect of partial coherence on four-wave mixing in photorefractive materials via reflection grating approximation

We investigate the effect of beam coherence on four-wave mixing via reflection gratings in photorefractive media. For the case of phase conjugation, the results of our theoretical analysis indicate that partial coherence always leads to a drop of signal gain and phase conjugate reflectivity in non-depleted cases. In general, the mutual coherence of the signal beam and the pump beam can be enhanced due to the process of wave mixing. The mutual coherence of the phase conjugate beam and one of the pump beams depends on the beam intensity ratio as well as the optical path difference. This is distinctly different from the four-wave mixing case with a transmission grating. Received: 15 October 1999 / Revised version: 26 June 2000 / Published online: 7 February 2001     

Degenerate four-wave mixing experiments in Methyl green dye-doped gelatin film

Degenerate four-wave mixing (DFWM) was performed in Methyl green dye-doped gelatin films using continuous-wave laser radiation () generated by a He-Ne laser of total power 35 mW. Various parameters which influence the phase-conjugate (PC) signal during the DFWM process were studied. The PC signal contributions from induced holographic transmission and reflection gratings were measured. We observed a maximum PC beam reflectivity of 0.13% in these dye-doped gelatin films.     

Temporal behavior of dark spatial solitons in closed-circuit photovoltaic media

We show that the time-dependent nonlinear wave equation in closed-circuit photovoltaic media can exhibit quasi-steady-state and steady-state spatial solitons. We demonstrate that the formation time of open-circuit quasi-steady-state and open-circuit steady-state dark solitons decreases with an increase in the intensity ratio of the soliton, which is the ratio between the soliton peak intensity and the dark irradiance. We find that for the time-dependent nonlinear wave equation that exhibits only an open-circuit steady-state dark soliton, changing the electric current density J₀ does not generate quasi-steady-state dark solitons and affects the formation time of steady-state dark solitons and that for the time-dependent nonlinear wave equation that exhibits an open-circuit quasi-steady-state dark soliton, changing J₀ gives rise to three different time evolution regimes of the full width half maximum of the soliton’s intensity. The first regime shows that the formation time of steady-state dark solitons increases with J₀ whereas the formation time of quasi-steady-state dark solitons is independent of J₀. The second regime shows that the formation time of steady-state dark solitons decreases with an increases in J₀ and the formation time of quasi-steady-state dark solitons increases with J₀. The third regime shows that changing J₀ enables only steady-state dark solitons in the time-dependent nonlinear wave equation, of which the formation time increases with J₀.     

Soliton switching in inhomogeneous nonlocal media

We address a simple way to achieve routing of optical spatial solitons via soliton interactions in the inhomogeneous nonlocal media. We reveal that the variation of the nonlocality disturbs the solitons pairs and splits them into two individual solitons which have the same escape angle but opposite deflection directions. In particular, the escape angle monotonically increases with the increase of the nonlocality variation rate. We demonstrate that the soliton pairs could form self-consistent waveguides that are able to controllably guide a weak signal by any output positions.     

Broadband four-wave optical parametric amplification in bulk isotropic media in the ultraviolet

We report on four-wave optical parametric amplification of the ultrashort ultraviolet light pulses in bulk fused silica and CaF₂. Exact phase-matching in these isotropic media is achieved by means of non-collinear interaction with cylindrical beam focusing. Four-wave optical parametric amplifier efficiently operates in the UV spectral range with 1-ps laser pulses, delivering amplified signal energy exceeding 50 μJ using millijoule pump pulses in the visible (527 nm). Results of scanning of the parametric gain profile suggest that broad amplification bandwidth as wide as ∼20 nm (at FWHM) under these experimental settings is achieved, which might support amplification of sub-10-fs ultraviolet pulses with central wavelength around 330 nm. It is also shown experimentally and verified theoretically that the parametric gain profile exposes a distinct inhomogeneity and its bandwidth notably broadens due to effects of self- and cross-phase modulation imposed by the intense pump beam.     

Photorefractive four-wave mixing with partially coherent light beams

Received: 11 April 1997/Revised version: 22 May 1997     

An analysis of the three-valence model of photorefraction

In this paper we present an analysis of the three-valence model of photorefraction. The basic equations of the model are studied and solved to find zero- and first-order solutions in the steady state, including expressions for the space-charge field and the effective trap density. The intensity dependence of the solutions for the population densities and space-charge field are analysed and discussed for varying proportions of the different valence states in the material, and the influence of some important material parameters considered. The possible applications of these results to the experimental characterisation of three-valence-state materials are discussed and some comparisons are made between the three-valence and the two-independent-centre models of photorefraction. Received: 17 November 1998 / Revised version: 8 January 1999 / Published online: 31 March 1999     

High sensitive measurements of absorption coefficient and optical nonlinearities

Accurate knowledge of absorption coefficient of a sample is a prerequisite for measuring the third-order optical nonlinearity of materials, which can be a serious limitation for unknown samples. We introduce a method, which measures both the absorption coefficient and the third-order optical nonlinearity of materials with high sensitivity in a single experimental arrangement. We use a dual-beam pump-probe experiment and conventional single-beam z-scan under different conditions to achieve this goal with communication relevant wavelength. We also demonstrate a counterintuitive coupling of the non-interacting probe-beam with the pump-beam in pump-probe z-scan experiment.     

Photorefractive hologram writing with high modulation depth in photovoltaic media under different boundary conditions

Photorefractive recording response to sinusoidal intensity pattern in photovoltaic media under different boundary conditions, namely, open-circuit, crystal-resistor-circuit, short-circuit and crystal-voltage supply-circuit, are investigated by solving steady-state Kukhtarev equations numerically. In high modulation depth m limit and when photovoltaic field becomes sufficiently large, we find that both the magnitude and imaginary part of fundamental space-charge field E₁ as a function of m may transit from superlinear increment to sublinear increment for short-circuit condition. The role of photovoltaic field in holographic storage and two-wave mixing is also discussed in comparison with an earlier experimental literature [G. Cook et al., Opt. Commun. 192 (2001) 393]. We further generalize Gu et al.’s remark on photovoltaic field and dc space-charge field, which is for small m only [C. Gu et al., J. Appl. Phys. 69 (1991) 1167], to whole range of m in the limit donor density much larger than ionized donor density that the effect of photovoltaic field cannot be cancelled or considered as an externally applied field for an arbitrary non-zero m.     

Degenerate four-wave mixing diagnostics on OH and NH radicals in flames

Degenerate four wave mixing (DFWM) is applied as a diagnostic to study OH and NH radicals in flames. DFWM is a coherent technique which offers the advantages of a highly collimated signal beam permitting efficient rejection of interfering radiation and requiring minimal optical access. Rotational temperatures have been determined from the DFWM spectra and are in close agreement with the temperatures measured using coherent anti-Stokes Raman scattering of nitrogen.Work performed at the Combustion Research Facility, Sandia National Laboratories, supported by the U.S. Department of Energy, Energy Conversion and Utilization Technologies Program and Office of Basic Energy Sciences, Division of Chemical Sciences     

Solutions for the propagation of light in nonlinear optical media with spatially inhomogeneous nonlinearities

In this paper, we present solutions for the nonlinear Schrödinger (NLS) equation with spatially inhomogeneous nonlinearities describing propagation of light in nonlinear media, under two sets of transverse modulation forms of inhomogeneous nonlinearity. The bright soliton solution and Gaussian solution have been obtained for one set of inhomogeneous nonlinearity modulation. For the other, bright soliton solution, black soliton solution and the train solution have been presented. Stability of the solutions has been determined by exact soliton solutions under certain conditions.     

Experimental investigation of the effect of collisions and temperature on degenerate four-wave mixing

An experimental investigation (including a comparison with a simple theoretical model) of the effect of buffer-gas composition, pressure and temperature on resonant Degenerate Four-Wave Mixing (DFWM) has been performed. The DFWM signal from NO in a quartz cell was measured and the effect of quenching as well as elastic (phase-changing) collisions was studied by varying the total and partial pressures of N₂ and CO₂ as buffer gases. It was found that the DFWM signal first slowly increased with buffer-gas pressure (up to 10 mbar) and then rapidly decreased. It was furthermore found that the DFWM signal was considerably less sensitive to quenching collisions as compared to Laser-Induced Fluorescence (LIF) (for laser intensities approximately equal to half the DFWM saturation intensity of the transition). On the other hand, while LIF is virtually insensitive to elastic collisions, DFWM displays a larger sensitivity to elastic collisions than to quenching collisions. The DFWM saturation intensity was found to increase with buffer-gas pressure (although slower than expected). When varying the temperature of the gas composition, it was found that the DFWM signal decreased markedly with increasing temperature. This decrease is too fast to be explained solely by a change in the population of the molecular state probed by the laser.     

Identification of optical nonlinearities of dye-doped nematic and polymer-dispersed liquid crystals using Z-scan technique

This study investigates the nonlinear optical properties of azo-dye-doped nematic and polymer-dispersed liquid crystal (ADDPDLC) films with nano-sized LC droplets using the Z-scan technique, which is a simple but powerful technique for measuring the optical Kerr constants of materials. The results indicate that the optical Kerr constant (n₂) of the azo-dye-doped nematic LC (ADDLC) film is large because of the photoisomerization effect and the thermal effect. Therefore, the optical Kerr constant of this material can be modulated by varying the temperature of the sample and the direction of polarization of incident laser. The range of n₂ modulated is from −5.26 × 10⁻³ to 1.62 × 10⁻³ cm²/W. The optical Kerr constants of ADDPDLC films at various temperatures are also measured. The experimental results reveal that liquid crystals in the ADDPDLC film strengthen the nonlinearity. The n₂ of the ADDPDLC film is maximal at ∼35 °C, because of the decrease in the clearing temperature of the ADDPDLC films. The clearing temperatures of the liquid crystals (E7), and the ADDPDLC film used in this work were found to be 61 °C and 43 °C, respectively.     

Power and beam-width dependence of a BaTiO3: Ce self-pumped phase conjugator

Power and beam-width dependences of the performance of self-pumped phase conjugators using a BaTiO₃: Ce crystal have been investigated. The incident beam was permitted to enter the crystal by thea-face or the +c-face. In both cases, the phase-conjugate reflectivity was observed to vary with the power and beam width of the incident beam. In the former case, two different optical beam patterns in the crystal can be observed under different conditions. Qualitative explanations are given to some of the results observed.     

Coherent and Incoherent Interactions between Discrete-Soliton Trains in Two-Dimensional Light-Induced Photonic Lattices

The coherent and incoherent interactions between discrete-soliton trains are numerically investigated in lightinduced two-dimensional photonic lattices. The solutions of discrete-soliton trains for diamond and square lattices are obtained by Petviashvili iteration method. It is found that for both the kinds of lattices, two in-phase （out- of-phase） discrete-soliton trains attract （repel） each other, and the intermediates are always accompanied with energy transfer. While the interaction forces between two incoherent discrete-soliton trains are always attractive.     

Solitary Wave Evolution of Optical Planar Vortices in Self-Defocusing Photorefractive Media

Solitary wave evolution of optical planar vortices in isotropie self-defoeusing photorefractive media is investigated in detail. We demonstrate that the formation of a planar vortex soliton intensively depends on the diameter and maximum intensity of the input vortex Seam. The exact solutions of planar vortex solitons are obtained due to the Petviashvili iteration method. It is found that, with the increasing soliton maximum intensity, the soliton core will be gradually diminished to a minimum value.