Nonlinear Mixing Process Research Articles

Instabilities and self-oscillations in atomic four-wave mixing

The development of integrated, waveguide-based atom optical devices requires a thorough understanding of nonlinear matter-wave mixing processes in confined geometries. This paper analyzes the stability of counterpropagating two-component Bose-Einstein condensates in such a geometry. The steady-state field equations of this system are solved analytically, predicting a multivalued relation between the input and output field intensities. The spatiotemporal linear stability of these solutions is investigated numerically, leading to the prediction of a self-oscillation threshold that can be expressed in terms of a matter-wave analog of the Fresnel number in optics.

Millimeter-wave generation and digital modulation in an InGaAs-InP heterojunction phototransistor: model and experimental characterization of dynamics and noise

This paper describes the use of an InGaAs-InP photoheterojunction bipolar transistor (photo-HBT) for millimeter-wave generation and digital modulation. Optical mixing of two coherent signals generates the carrier, and a digital drive signal to the base is used for the modulation. We describe an advanced large signal model of the photo-HBT that takes into account distributed effects at high frequencies and all noise sources, including optical amplifier noise and noise correlations due to the high operation frequency and the nonlinear mixing processes. The model enables one to predict carrier-to-noise ratio dependence on frequency, optical power, and the transistor operating point. Frequency- and time-domain responses of the modulated millimeter- wave carrier and bit error rates are also calculated. Experiments at 10 and 45 GHz with modulation rates ranging between 50 Mb/s and 2.5 Gb/s were performed, and a superb fit to the calculated responses is found.

Femtosecond-rate space-to-time conversion

A real-time spatial–temporal processor based on cascaded nonlinearities converts space-domain images to time-domain waveforms by the interaction of spectrally decomposed ultrashort pulses and spatially Fourier-transformed images carried by quasi-monochromatic light waves. We use four-wave mixing, achieved by cascaded second-order nonlinearities with type II noncollinear phase matching, for femtosecond-rate processing. We present a detailed analysis of the nonlinear mixing process with waves containing wide temporal and angular bandwidths. The wide bandwidths give rise to phase-mismatch terms in each process of the cascade. We define a complex spatial–temporal filter to characterize the effects of the phase-mismatch terms, modeling the deviations from the ideal system response. New experimental results that support our findings are presented.

Rayleigh–Taylor instability: Comparison of hybrid and nonideal magnetohydrodynamic simulations

The evolution of the Rayleigh–Taylor instability in a low β, two-dimensional plasma is studied using a hybrid code and a nonideal magnetohydrodynamic (MHD) code. The Rayleigh–Taylor instability was chosen as a test case because it is an important mixing process at boundary layers, and because it exhibits different behaviors in the conventional and nonideal limits. The nonideal MHD effects considered are the Hall term and finite Larmor radius (FLR) corrections. Three cases are considered in detail: conventional MHD, weak nonideal effects, and strong nonideal effects. In the conventional MHD regime the usual “bubble and spike” behavior of the Rayleigh–Taylor instability is observed. In the weak nonideal MHD regime long wavelength modes, reminiscent of the Kelvin–Helmholtz instability, dominate nonlinearly but very short wavelength filaments develop at the boundary interface. In the strong nonideal MHD regime, small-scale structures dominate and the boundary layer relaxes via a diffusion-like process rather than a large-scale nonlinear mixing process. In general, the hybrid and fluid simulations are in good agreement. The differences, both physical and numerical, are discussed.

Nonlinear vertical mixing processes in the ocean: modeling and parameterization

Nonlinear vertical mixing processes are critical in the transport of heat and momentum throughout the ocean and are especially important in the surface mixed layer and in deep convection. This paper reviews recent numerical modeling studies that are being used to help develop more effective parameterizations of nonlinear vertical mixing processes. In particular, we describe two oceanic process studies using a large-eddy simulation (LES) turbulence model and review the performance of an improved vertical mixing parameterization in an ocean general circulation model. The first process study examines the role of wind and heat-flux forcing of turbulence in the tropical western Pacific ocean surface mixed layer. Results from the LES show that mixing is dominated by three key processes: Langmuir circulation near the surface, organized circulations that extend through the mixed-layer depth, and shear instability at the mixed-layer base. The second LES study centers on the onset and strength of deep oceanic convection. Results from this study show that the growth of convective plumes is dependent on the integral properties of heat and salinity forcing. The paper concludes with a test of an improved parameterization of deep convection for ocean general circulation models.

Linear processes in unsteady stably stratified turbulence

Unsteady turbulence in uniformly stratified unsheared flow is analysed using rapid distortion theory (RDT). For inviscid flow with no molecular diffusion the theory shows how the initial conditions, such as the initial turbulent kinetic energy KE0 and potential energy PE0, determine the partition of energy between the potential energy associated with density fluctuation and the kinetic energy associated with each of the velocity components during the subsequent development of the turbulence. One parameter is an exception to this sensitivity to initial conditions, namely the limit at large time of the ratio of potential energy to vertical kinetic energy. In the linear theory, this ratio depends neither on the Reynolds number Re, nor the Prandtl number Pr nor the Froude number Fr. This is consistent with turbulence measurements in the atmosphere, wind tunnel and water tank experiments, and with large-eddy simulations, where similar values of the ratio are found. The RDT results are extended to show the effects of viscosity and diffusion where Re is not very large, explaining the sensitivity of the spectra and the fluxes to the value of the Prandtl number Pr. When Pr is larger than 1, the high-wavenumber components of the three-dimensional spectra induce a vertical flux of temperature (density) that is positive (negative), and therefore ‘countergradient.’ On the other hand, when the thermal diffusivity is stronger and Pr is less than 1, lower-wavenumber components become countergradient sooner since the high-wavenumber components are prevented from becoming countergradient. When all the wavenumber components are integrated to derive the total vertical density flux, it becomes countergradient more quickly and more strongly in high-Pr than in low-Pr turbulence. All these theoretically derived differences between high-Pr and low-Pr turbulence are consistent with the experimental measurements in water tank and wind tunnel experiments and numerical simulations. It is shown that the initial kinetic and potential energy spectrum forms E(k) and S(k) near k = 0 determine the long-time limit values of the variances and the covariances, including their decay rate with time. In the special case of Pr = 1, the oscillation time period of the three-dimensional spectrum function is independent of the wavenumber and is the same as that of an inviscid fluid with the effect of viscosity/diffusion being limited to the damping of all the wavenumber components in-phase with each other. Furthermore, the non-dimensional ratios of the covariances, including the normalized vertical density flux and the anisotropy tensor, agree with the inviscid results if S(k) is proportional to E(k), or if either S(k) or E(k) is identically zero. However, even when Pr = 1, in the ‘one-dimensional spectrum’ in the x-direction, there is a transitory countergradient flux for high wavenumbers; only in this case is there a qualitative difference with the three-dimensioanl spectrum. This paper shows that the characteristic differences in the behaviour of stably stratified turbulence reported in previous DNS experiments at moderate Reynolds numbers can largely be explained by linear oscillations and simple molecular or eddy diffusion rather than by any new kinds of nonlinear mixing processes.

Frontal Wave Stability during Moist Deformation Frontogenesis. Part II: The Suppression of Nonlinear Wave Development

In this paper, the role of horizontal deformation and the associated frontogenetic ageostrophic circulation in suppressing the development of nonlinear waves is assessed. Unless linear barotropic frontal waves can become nonlinear, the associated horizontal transports of momentum will not be sufficient to halt frontogenesis or to create nonlinear mixing processes such as vortex roll-up. The analysis of Dritschel et al. suggests that such nonlinear phenomena will not occur if the wave slope remains small. For the linear model described in Part I, a simple relationship between optimal wave slope amplification over a specified time period and the amplification of an initially isolated edge wave is found. Using this relationship, the mechanisms by which strain affects the dependence of optimal wave slope amplification on wavelength and the time of entry of disturbances to the front are investigated. It is found that waves entering the frontal zone when it is intense can experience greater steepening than those appearing earlier in the development of the front. The most rapidly growing waves enter the front with a wavelength about three times the width of the front. As the front collapses, the ratio of wavelength to frontal width rapidly increases. For strain rates greater than 0.6 × 10−5 s−1, the model predicts that wave slope amplification greater than a factor of e is impossible. The variation of optimal growth with wavenumber and the time of entry of disturbances to the front is explained using diagnostics based on a mathematical model of Bretherton's qualitative description of wave growth in terms of the interaction of counterpropagating edge waves. These diagnostics yield a simple formula for the frontogenesis rate required to completely eliminate wave steepening. For the front considered in Part I, the formula predicts that no amplification is possible for strain rates greater than one-quarter of the Coriolis parameter. Diagnostics of this sort may aid attempts to predict, from the large-scale forcing, the minimum attainable cross-frontal scale of a front.

Backward-wave phonon echoes from tunneling systems in chalcogenide glasses

We have studied backward-wave phonon echoes at 9.3 GHz in several chalcogenide glasses. The input power dependence of the echo power can be modeled in terms of the non-linear mixing process of two laser fields in a gas consisting of two-level systems. A difference in this dependence between the arsenic and germanium chalcogenide glasses is observed.

Measurement of fiber nonlinear Kerr coefficient by four-wave mixing

We demonstrate a Kerr coefficient measurement of dispersion-shifted fibers based on the nonlinear mixing process between two continuous pump waves and on the power measurements of the created frequencies. A numerical model simulates the experimental conditions and is exploited to determine the Kerr coefficient. Unavoidable polarization effects are precisely taken into account both experimentally and numerically by launching the pump waves on the principal polarization states. This allows us to obtain reproducible measured values and a better than 5% resolution. >

Nonlinear Quantum Beats of Excitons in CdSe

By observing quantum beats in the self-diffracted signal from a nonlinear mixing process in a crystal, and by spectrally resolving this signal, information is obtained about solid state parameters, such as energy splittings and energy shifts. This technique is used to study bound excitons in CdSe with a strong, resonant third-order susceptibility. Furthermore, in the region of free exciton propagation, effects on the third-order nonlinear polarization are observed and explained by quantum beats between propagating polaritons

Frequency doubling of 1.053 μm radiation in KTP

Abstract Thermal-optical modeling of a 1.053 μ m → 0.526 μ m potassium titanyl phosphate (KTP) frequency doubler was performed in support of the Los Alamos National Laboratory free-electron laser (FEL) program. Radiation at the doubled frequency is used to excite electron emission from the FEL photoinjector. The fully coupled thermal-optical behavior of the frequency doubler is described by curves of conversion efficiency and plots of the KTP steady-state temperature profile. It is found that thermally induced phase mismatches reduce the conversion efficiency, but can be partially compensated with intentional mismatches introduced by means of a small rotation of the crystal away form the nominal phase matching direction. The computed thermal gradients are used to assess the risk of crystal damage. A general calculational procedure for modeling thermal-optical interactions in the nonlinear three-wave mixing process is presented.

Spatial frequency mixing in electrooptic crystals: Application to nondestructive read-out of optically erasable volume holograms

Recently the main mechanism responsible for spatial frequency mixing in electrooptic crystals has been identified using elementary gratings. Now we apply the nonlinear mixing process to generate frequency difference holograms of real objects. We theoretically derive the properties of these holograms and experimentally demonstrate their application to the problem of nondestructive read-out of optically erasable volume holograms.

Variability of planetary-scale waves at mid-latitudes in the course of strat-warmings during DYANA

This work investigates the variability of planetary-scale waves from motion field observations in the middle atmosphere carried out at the Budrio radar station near Bologna (45°N; 12°E) in the 1989–1990 winter during DYANA (DYnamics Adapted Network for the Atmosphere). Meso-thermospheric zonal winds associated with long-period waves give evidence of significant energy input from below mainly in the course of the two strat-warmings recorded at the end of January and in mid February 1990. Amplification of 10-day waves in the upper mesosphere and lower thermosphere just a few days before the temperature peak at the 10hPa stratospheric level, and the effects induced by these waves on tidal and mean fields, are here taken into account to clarify the influence and the evolution of strat-warmings in the middle atmosphere. Nonlinear mixing processes between planetary and tidal oscillations are indicated to be responsible for the short-term variability pointed out in the amplitude variations of tides.

Beam divergence effects on nonlinear frequency mixing

The effects of the beam divergence of the input pump laser beams on the nonlinear frequency mixing process in a dielectric medium is discussed. The divergent laser beams have finite angular spreads so that all of the interactions between the two input beams can never satisfy the phase-matching condition exactly. A numerical model is developed to investigate the effects of input beam divergence on conversion efficiency. The angular spread of each of the input beams is represented by a set of plane waves having a distribution of propagation directions. Each of the plane-wave components from one input beam is allowed to interact with all the plane-wave components of the second input beam. This model is applicable to processes such as sum frequency generation, difference frequency generation, and optical parametric amplification. Second-harmonic generations as a special case of sum frequency generation is used as an example in the numerical studies. Results indicate that the conversion efficiency is dependent on the amount of beam divergence, the input intensity, and the length of the nonlinear medium. These parameters must be optimized with respect to one another to maximize the conversion. The optimization is especially critical in high-power systems where high conversion efficiency is sought.

Two-photon gain and lasing in strongly driven two-level atoms.

Driven two-level atoms are shown to exhibit strong, resonantly enhanced, two-photon gain. This gain, unlike that observed in nonlinear mixing processes, is not constrained by a phase-matching condition involving the pump beam. Physically, the gain can be associated with inverted two-photon transitions between dressed states or multiphoton stimulated Raman scattering, and it may be useful in the realization of a two-photon laser. Comparison with the well-known single-photon gain found in the same system is made.

Subharmonic Raman effect in nonlinear mixing

Following the recent experiments of Trebino and Rahn [Opt. Lett. 12, 912 (1987)], I show on general grounds the existence of the fractional Raman resonances in a variety of nonlinear mixing processes in atomic vapors, molecules, and solids. I present theoretical models, both classical and quantum, for such resonances.

Ionic contributions to the Raman tensor of insulators.

Earlier authors have pointed out that at infrared frequencies, ionic contributions to the nonlinear optical susceptibilities of crystals can become important. Of particular interest is their frequency variation, which may exhibit resonances when the frequency of one or more optical beams coincides with that of an optical phonon. We present a simple theory of the nonlinear optical response of insulators in the infrared region which incorporates both the electronic and ionic contributions to the Raman tensor. The method is easily extended to the discussion of other nonlinear mixing or harmonic-generation processes in the infrared region. Primary application is to crystals of the zinc-blende structure, and the processes examined explicitly are the generation of optical phonons by resonances with the difference frequency of two infrared waves mixed in the crystal, and the ionic Raman effect.

Resonant four-wave frequency mixing in the cw regime in sodium vapor

An experimental investigation was made of resonant nonlinear four-wave frequency mixing processes involving cw laser radiation in sodium vapor. It was found that, in spite of an increase in absorption, the use of resonant atomic nonlinearities can substantially improve the frequency conversion efficiency in the cw regime. The results of the measurements were compared with the theoretical conclusions. Ultraviolet radiation was generated at the sum frequency (λs = 268 nm) with the proportionality factor C=Ws/W1W2W3≈2W−2

Nonlinear mixing in the ionosphere

When the ionosphere is illuminated with two strong HF signals, nonlinear mixing processes can take place near the region of reflection. The first direct experimental evidence of such processes occurring in ionospheric plasma are presented in this paper. The experiments were performed at Arecibo, where the HF ionospheric modifier was split to operate as two pure isolated and independent pumps over the frequency range of 3‐8 MHz and the frequency difference between the two pumps was varied between a fraction of a Hz and several kHz. The purity of the trans‐ mitted signals was always ensured. Strong nonlinear effects were observed when the frequency difference was several Hz. Specifically, the HF signal from the ionosphere contained sidebands which were separated by multiples of the difference (Δf) between the two pumping frequencies. The first sidebands were typically 20‐40 db below the pump signal. The strengths of the first sidebands increased, when the difference (Δf) between the two pumping frequencies decreased. Below about 5‐10 Hz, the power in the first sidebands varied almost in Δf−n fashion, with n between 1 and 2. The power in the sidebands was also a strong nonlinear function of the incident pump field strength, showing the presence of a threshold. It is suggested that studies of such nonlinear mixing processes would be valuable both for diagnostic and practical usage of ionospheric plasma.

Multivariable Direct Adaptive Control of Thermal Mixing Processes

Multivariable direct adaptive control is tested on a nonlinear thermal mixing process and is compared with state space based nonadaptive controllers. The linear quadratic optimal control approach is used to design two nonadaptive controllers: one without integral action (ordinary LQ) and the other with integral action (LQI). The operating point is changed over a wide region in the experiment. The adaptive controller is verified to perform most consistently under the tested conditions.