Dynamics of a phase conjugate resonator: Transient build-up and decay rates

The standard four wave mixing model in a sluggish photorefractive medium is used to calculate the transient response of a phase conjugate resonator. General trends are unveiled and discussed in view of the possible use of the system in image processing. Experimental results are shown to confirm qualitatively the predicted behaviour.     

The identification of nonlinear molecular systems by spectroscopic methods

The Wiener functional expansion method for the analysis of nonlinear systems is applied to identify and analyze both nonlinear and linear molecular systems by spectroscopic methods. As the sampling filter (monochromator) of any spectroscopic apparatus may be defined by a Weber-Hermite polynomial, an analysis of the refracted or scattered light by orthogonal polynomials is easily achieved. Time averaging obtains the Weber-Hermite coefficients which permit the characterization of the molecular system with respect to the polarization of the incident and scattered light. In the case of two series of measurements made with incident and emerging light polarized in different directions: the identification of the JonesM matrices for the molecular system irradiated is possible. In the case of three series of measurements made, for example, with incident and emerging light (a) circularly polarized corotating, (b) circularly polarized contrarotating, and (c) plane polarized perpendicular: the identification of the molecular system's McClain invariants related to the vibrational symmetry group for Raman inelastic light scattering is possible. The analysis presents a unified picture of elastic and inelastic light scattering and one-photon and two-photon processes. The apparatus described would detect those instances in molecular systems for which Beer's law does not apply.     

The role of the biexciton in a dynamic density matrix theory of the semiconductor band edge

We describe the dielectric response of the semiconductor band edge in a dynamic density matrix model. Our treatment is based on a set of ₃-relevant constitutive equations involving two-, four- and six-point density matrices. We demonstrate that under certain conditions all contributions to the third order susceptibility can be expressed in terms of excitonic and biexcitonic transitions. As a first application of these ₃-relevant equations we investigate the influence of the biexciton on the optical Stark effect in CuCl. We calculate shifts and lineshapes. Our results turn out to be in excellent agreement with experiments as well as with other theoretical predictions.     

Using the seventh-order numerical method to solve first-order nonlinear coupled-wave equations for degenerate two-wave and four-wave mixing

Using a new seventh-order numerical method [theO(h ⁷) method] for solving two-point boundary value problems, numerical solutions of the first-order nonlinear coupledwave equations for degenerate two-wave and four-wave mixing in a reflection geometry have been obtained. A computer program employing the Gauss-Jordan elimination technique has also been adopted to effectively solve the resultant large, sparse and unsymmetric matrix, obtained from theO(h ⁷) method and the Newton-Raphson iteration method. Numerical results from the computer calculations are presented graphically. A comparison between thisO(h ⁷) method and the shooting method, mainly from the viewpoint of computational efficiency, is also made.     

Identity of the conjugate gradient and Lanczos algorithms for matrix inversion in lattice fermion calculations

Two of the methods that are widely used in lattice gauge theory calculations requiring inversion of the fermion matrix are the Lanczos and the conjugate gradient algorithms. Those algorithms are already known to be closely related. In fact for matrix inversion, in exact arithmetic, they give identical results at each iteration and are just alternative formulations of a single algorithm. This equivalence survives rounding errors. We give the identities between the coefficients of the two formulations, enabling many of the best features of them to be combined.     

Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: application to CS2

A simple experimental technique is presented capable of separating the contribution of purely optical Kerr effects from that of thermo-optical effects in the nonlinear response of materials under high-repetition-rate laser irradiation. The technique has been realized by combining the single-beam Z-scan method with the single-beam thermal lens measurement method. We demonstrate this technique by analysing the nonlinear response at 770 nm of CS₂ which exhibits cumulative thermal effects when irradiated by very intense femtosecond laser pulses at a 76-MHz repetition rate. Received: 3 November 1998 / Revised version: 4 January 1999 / Published online: 2 June 1999     

Elimination of variables in simple laser equations

The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorenz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 (, ) and case 2 (, ), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 (, ) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant (). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities.     

The application of single-pulse CARS for temperature measurements in a turbulent stagnation flame

N₂ Q-branch CARS spectra have been recorded and evaluated for temperature determination in a turbulent, premixed CH₄/air stagnation flame with a burner of 40 mm diameter and 22 kW thermal load. Temperature histograms on the flame axis at different distances from the stagnation plate have been measured. Problems of practical applicability are addressed, including those arising from the limited spatial resolution of the BOXCARS geometry, from an insufficient dynamic range of the diode array detector, and from a memory effect of the detector in the case of measurements in highly turbulent flame areas with strong intermittency. Some information is given on the computerized acquisition and on the evaluation of the large amounts of data that are necessary for extensive investigations in large combustion systems.     

The application of a raman-shifted tunable KrF excimer laser for laser-induced fluorescence combustion diagnostics

Four wavelength extensions have been investigated by stimulated Raman scattering in hydrogen or deuterium gas of the 248 nm fundamental output of a narrow-band tunable KrF excimer laser. They have been used to acquire laser-induced fluorescence spectra of NO and OH in flames at atmospheric pressure. NO is detected in relatively high rotational states within the -band electronic system at 225 nm. OH was excited at 291.5 nm in the (1–0), at 313 nm in the (1–1) and at 268.5 nm in the predissociative (3–1) band of the ²–² electronic band system, respectively. Prospects of 2D imaging for concentration and temperature measurements in flames using these wavelength extensions are discussed.     

On generation of coherent structures induced by modulational instability in linearly coupled cubic-quintic Ginzburg-Landau equations

We study the properties of the coherent structures induced by the modulational instability (MI) of the two linearly coupled complex Ginzburg-Landau equations with both cubic and quintic terms, which in nonlinear optics can model ring lasers based on dual-core fibers. We obtain new stationary solutions different from the previous result and the analytic gain formula as function of the linear coupling constant and the model parameters. The fact that the system can be modulationally unstable for the vast region of the parameters space is demonstrated. The effects of the linear coupling constant on the evolution of a continuous wave under the MI are numerically investigated in the presence of the linear loss or gain. It is found that doubly asymmetric stable solitary pulses and stable breathers can be formed from the perturbed continuous waves state by the MI. The conditions for generating the periodic stable solitary pulses and fronts by the MI are identified by varying the linear coupling constant.     

The matrix rate of return

In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous analysis of evolution of baskets parameterized by complex variables in both continuous and discrete time models.     

Bifurcation structures into chaos of delay-differential equations for a passive optical ring resonator

The delay-differential equation system describing the passive optical ring cavity is investigated. A survey of different bifurcation scenarios into chaos of the solutions on one branch and specific transitions between different branches of the multistable system are discussed. Precipitation via a heteroclinic cycle and crisis induced intermittency are found.     

Response of a BaTiO3 phase conjugate mirror to broadband and narrowband radiation

The bandwidth of a BaTiO₃ self-pumped phase conjugate mirror is measured in three different ways. 1) The crystal is exposed to infrared light with a phase change that is sinusoidal in time and the degree of phase modulation on the reflected wave is measured. As the modulation frequency is increased from 0.1 to 3 GHz, the modulation transfer function of the phase conjugate mirror decreases by a factor of 2. 2) The crystal is exposed to visible light from a laser operated both in a single longitudinal mode and in multiple longitudinal modes. When the laser bandwidth is increased from 20 MHz to 2 GHz the reflectivity of the phase conjugate mirror increases by up to a factor of 7. 3) A laser cavity is formed with the crystal as one end mirror and the lasing bandwidth is measured. Depending on the exact conditions, lasing bandwidths range from 2 to 240 GHz.     

Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.     

The application of incoherent light for the study of femtosecond-picosecond relaxation in condensed phase

A convenient technique for the ultrashort-relaxation-time measurement using temporally incoherent light instead of short pulses can be applied to the studies of relaxation processes. Theoretical studies on measuring various types of relaxation times by this method are summarized. We have applied this technique to the studies of the electronic dephasing in a polydiacetylene film, the vibrational dephasing in dimethylsulfoxide and the relaxation of optical Kerr effect in CS₂ and nitrobenzene.     

Numerical methods for multiscale transport equations and application to two-phase porous media flow

We discuss numerical methods for linear and nonlinear transport equations with multiscale velocity fields. These methods are themselves multiscaled in nature in the sense that they use macro and micro grids, multiscale test functions. We demonstrate the efficiency of these methods and apply them to two-phase flow in heterogeneous porous media.     

Development of a dual-wavelength dye-laser system for the UV and its application to simultaneous multi-element detection

In this paper, the design and performance characteristics of a pulsed tunable dye laser system for the simultaneous generation of two UV wavelengths are presented. The system is composed of an oscillator and an amplifier stage, pumped by the second harmonic of a commercial Nd:YAG laser. Dual-wavelength operation is achieved with one additional tuning mirror introduced to the prism expanded grazing incidence oscillator. The two obtained wavelengths are independently tunable, their separation is only limited by the gain profile of the dye. Both wavelengths are frequency doubled by Second-Harmonic Generation (SHG) in two KDP or BBO crystals. Performance characteristics such as bandwidth, efficiency, tuning range and wavelength separation are reported. As application two such systems are used for the simultaneous detection of the four elements cadmium, nickel, manganese and lead by Laser-Excited Atomic Fluorescence Spectrometry in a graphite furnace (ETA-LEAFS).     

The application of quasi-phase-matched parametric light sources to practical infrared chemical sensing systems

Quasi-phase-matched (QPM) materials allow the generation of spectroscopically useful infrared radiation in an efficient and broadly tunable format. Here, we describe several applications of QPM-based light sources to remote and local chemical sensing. The remote systems are gas imagers that employ a fiber-pumped continuous-wave optical parametric oscillator or a microlaser-pumped, diode-seeded optical parametric amplifier as the illumination source. Technology described for local sensing includes a cavity ring down spectrometer that employs a novel optical parametric generator–amplifier to achieve ≥350 cm^-1 of contiguous tuning and a long-wave infrared light source based on QPM GaAs. In each case the use of QPM materials in conjunction with effective pump sources instills simplicity and ruggedness into the sensing systems. Received: 15 April 2002 / Revised version: 6 June 2002 / Published online: 12 September 2002 RID="*" ID="*"Corresponding author. Fax: +1-925/294-2595, E-mail: tjkulp@sandia.gov RID="**" ID="**"Present address: Corning Inc., Corning, NY 14831, USA RID="*" ID="*"Present address: Corning Inc., Corning, NY 14831, USA RID="**" ID="**"Present address: Blue Leaf Networks, Sunnyvale, CA 94086, USA RID="***" ID="***"Present address: Sandia National Laboratories, Albuquerque, NM 87185, USA     

High-flux high harmonic soft X-ray generation up to 10 kHz repetition rate

We report the operation of a Ti:sapphire oscillator-amplifier system with a high, variable repetition rate adjustable between 1 and 15 kHz. The oscillator uses cavity dumping and the multipass amplifier is based on a liquid nitrogen cooled crystal. The system produces pulses with 28 fs duration at 1.1 mJ pulse energy. When pumping the amplifier crystal with 72 W, an average output power of 11 W is obtained at a repetition rate of 10 kHz, resulting in a quantum efficiency of 25%. The output pulses are used to generate high harmonic radiation in argon, neon, and helium, which are detected up to a photon energy of 110 eV, limited by the sensitivity of the toroidal grating employed.     

Ultrafast beam-deflection method and its application for measuring the transient refractive index of materials

We represent an ultrafast beam-deflection method as a simple and powerful tool for the time-resolved measurement of induced changes of the refractive index in the order of n=10^–5. The method is applied for measuring the changes of components of the refractive index parallel and perpendicular to the pump-pulse polarization on a femtosecond time scale. Fused silica and CS₂ are used as samples for demonstrating our method.