Showing papers on "Four-wave mixing published in 1988"
TL;DR: In this article, the authors studied the physical processes that lead to population pulsations in nearly degenerate four-wave mixing, and showed that the gain and the index grating contribute to NDFWM.
Abstract: The theory of nondegenerate four-wave mixing (NDFWM) in semiconductor lasers and amplifiers is presented with particular emphasis on the physical processes that lead to population pulsations. In the case of nearly degenerate four-wave mixing, modulation of the carrier density at the beat frequency Ω of the pump and probe waves creates a dynamic population grating whose effectiveness is governed by the spontaneous carrier lifetime τs. Such a grating affects both the gain and the refractive index of the probe wave. In particular, the probe gain exhibits features analogous to those observed in a detuned atomic system arising from the optical Stark effect. Both the gain grating and the index grating contribute to NDFWM, with the dominant contribution coming from the index grating. For detunings such that Ωτs ≫ 1, population pulsations correspond to modulation of the intraband population arising from spectral hole burning. Our results show that NDFWM is then limited by the phase-mismatch effects governed by the transit time τ rather than by the intraband population-relaxation time T1. Significant NDFWM is expected to occur for detunings up to about 300 GHz for typical transit-time values of 3 psec in semiconductor lasers.
475 citations
TL;DR: Computed Gaussian-beam results agree well with analytic plane-wave calculations that straddle Raman-Nath and Bragg regimes for counterpropagating waves in Kerr media for both focusing and defocusing nonlinearities.
Abstract: Continuous-wave and oscillatory transverse instabilities are predicted for counterpropagating waves in Kerr media for both focusing and defocusing nonlinearities. Neither a cavity nor a finite response time is required. Computed Gaussian-beam results agree well with analytic plane-wave calculations that straddle Raman-Nath and Bragg regimes.
128 citations
TL;DR: In this article, the authors report the observation of an instability when two counter-propagating pump beams interact with sodium atoms, which they describe as a coherent emission around the pump beams axis.
122 citations
TL;DR: In this article, the third-order nonlinear optical susceptibility, χ(3), has been investigated at wavelengths of 602 and 580 nm for a 10:1 stretch-oriented uniaxial film of poly(p-phenylene vinylene) using femtosecond degenerate four wave mixing.
83 citations
TL;DR: In this paper, the conditions of observation of a mirrorless four-wave mixing oscillation in atomic vapors are described, where a nonlinear medium interacts with two pump beams propagating in opposite directions.
83 citations
TL;DR: In this paper, a model for mutually pumped phase conjugation was proposed and demonstrated for two mutually incoherent laser beams pump each other, producing a pair of phase-conjugate beams through a cross-readout process.
Abstract: A model is proposed and demonstrated for mutually pumped phase conjugation when two mutually incoherent laser beams pump each other, producing a pair of phase-conjugate beams through a cross-readout process. The model considers the buildup of two independent counterpropagating oscillations in a ring resonator containing two-beam-cbupling gain media. The experimental demonstration of the model using two photorefractive BaTiO3 crystals in a ring cavity gave simultaneous phase-conjugate images with good fidelity and no image cross talk. As expected, the counterpropagating oscillations were slightly detuned in frequency (∼1 Hz) from the corresponding pumping beams with frequency shifts related to the ring-cavity length. Frequency shifts were also observed in the phase-conjugate beams, with their magnitudes dictated by energy conservation for nondegenerate four-wave mixing.
61 citations
TL;DR: In this paper, the authors describe frequency-domain spectroscopy studies of glasses doped with CdS1−xSex using low-power cw tunable dye lasers and show a narrow resonance (4.4 kHz at room temperature) in the backward nearly degenerate four-wave mixing spectrum.
Abstract: We describe frequency-domain spectroscopy studies of glasses doped with CdS1−xSex using low-power cw tunable dye lasers. The results show a narrow resonance (4.4 kHz at room temperature) in the backward nearly degenerate four-wave mixing spectrum, which we believe is determined by the phonon-mediated inverse lifetime of a deep level trap involved in the nonlinear response.
53 citations
TL;DR: In this paper, backward coherent emission (DFWM) from 2D excitons comparable in efficiency to that in forward direction was observed, which is extremely advantageous and useful in exploring optically thin semiconductor layers.
Abstract: Time‐resolved degenerate four‐wave mixing (DFWM) on two‐dimensional (2D) excitons in GaAs single quantum wells is studied. We observe backward coherent emission (DFWM signal) from the 2D excitons comparable in efficiency to that in forward direction. This reflection or backward DFWM configuration is extremely advantageous and useful in exploring optically thin semiconductor layers.
51 citations
TL;DR: In this article, a theory of nonlinear optical properties of fractals is developed and a giant enhancement of optical susceptibilities is predicted for impurities bound to a fractal, which occurs if the exciting radiation frequency lies within the absorption band of the fractal.
Abstract: A theory of nonlinear optical properties of fractals is developed. Giant enhancement of optical susceptibilities is predicted for impurities bound to a fractal. This enhancement occurs if the exciting radiation frequency lies within the absorption band of the fractal. The giant optical nonlinearities are due to existence of high local electric fields in the sites of impurity locations. Such fields are due to the inhomogeneously broadened character of a fractal spectrum, i.e. partial conservation of individuality of fractal-forming particles (monomers). The field enhancement is proportional to theQ-factor of the resonance of a monomer. The effects of coherent anti-Stokes Raman scattering (CARS) and phase conjugation (PC) of light waves are enhanced to a much greater degree than generation of higher harmonics. In a general case the susceptibility of a higher-order is enhanced in the maximum way if the process includes “substraction” of photons (at least one of the strong field frequencies enters the susceptibility with the minus sign). Alternatively, enhancement for the highest-order harmonic generation (when all the photons are “accumulated”) is minimal. The predicted phenomena bear information on spectral properties of both impurity molecules and a fractal. In particular, in the CARS spectra a narrow (with the natural width) resonant structure, which is proper to an isolated monomer of a fractal, is predicted to be observed.
48 citations
TL;DR: In this paper, nearly degenerate four-wave mixing (NDFWM) of two copropagating light waves inside a traveling wave amplifier (1.3μm) at input light powers of less than 10μW was investigated.
Abstract: The letter reports on nearly degenerate four-wave mixing (NDFWM) of two copropagating light waves inside a travelling wave amplifier (1.3μm) at input light powers of less than 10μW. It describes the first experimental determination of the range of frequency spacing of the two light waves for efficient NDFWM and of the dependence on the state of polarisation.
46 citations
TL;DR: In this paper, a detailed measurement of the self-pumped phase-conjugate emission that arises from internal reflections within crystals of BaTiO3 has been made, possibly enhanced by stimulated photorefractive scattering around loops of light internally generated within the crystal and four-wave mixing at coupling regions of a ring cavity set up between diagonal corners of the crystal.
Abstract: Detailed measurements of the self-pumped phase-conjugate emission that arises from internal reflections within crystals of BaTiO3 have been made. Four-wave mixing, possibly enhanced by stimulated photorefractive scattering around loops of light internally generated within the crystal, and four-wave mixing at coupling regions of a ring cavity set up between diagonal corners of the crystal are two mechanisms believed to give rise to phase-conjugate beams. An explanation is also given for the unstable effects often observed on the phase-conjugate beam and that give rise to frequency shifts, pulsations, and oscillations. The power of the beam incident upon the crystal determines the threshold characteristics for self-pumped phase-conjugate emission.
TL;DR: In this article, a 20 kHz ac square-wave electric field was used to enhance the beam-coupling gain and the degenerate four-wave mixing reflectivity of photorefractive GaAs at 1.06 μm.
Abstract: We have used a 20-kHz ac square-wave electric field to enhance the beam-coupling gain and the degenerate four-wave mixing reflectivity of photorefractive GaAs at 1.06 μm. The largest measured four-wave mixing reflectivity in the steady state was 15% at a grating period of 9 μm and an applied voltage of 3.2 kV across 0.4 cm. Theoretical results predict substantially higher reflectivity values for a field of 8 kV/cm; the origin of this discrepancy is thought to be space-charge effects that prevent us from obtaining the full field inside the crystal. We have also measured a transient reflectivity of 510% during the switch on of the backward pump beam. Finally, we have determined the accuracy of wave-front reversal through measurements of piston-error correction and conjugation fidelity.
TL;DR: In this article, it was shown that an interference effect involving parametric four-wave mixing can almost totally suppress predicted examples of stimulated hyper-Raman emission in the direction of a laser pump beam, creating unidirectional backward stimulated hyper Ramming scattering.
TL;DR: Coherent vacuum-ultraviolet pulses with energy of 1.1 mJ, 2.2-nsec pulse length, and measured bandwidth ≤0.1 cm−1 have been achieved at 130 nm from four-wave mixing in Hg vapor, and conversion efficiencies of 5% have been demonstrated.
Abstract: Coherent vacuum-ultraviolet (VUV) pulses with energy of 1.1 mJ, 2.2-nsec pulse length (2 MW cm−2 unfocused), and measured bandwidth ≤0.1 cm−1 have been achieved at 130 nm from four-wave mixing in Hg vapor. Conversion efficiencies of 5% have been demonstrated in a collimated beam geometry over 1-m interaction lengths. These high efficiencies are made possible by using two-photon-resonant sum-frequency mixing through the Hg 71S level. The experimental facility assembled to produce this efficient VUV source is described, and a comparison between experimental measurements and theory is provided.
TL;DR: In this article, a theoretical description of the interaction of optical waves due to the resonant nonlinear response of an atomic system is presented, which is explicitly applied to several examples of current interest, including single-beam saturation spectroscopy, pump-probe saturation, modulation and phase conjugation.
Abstract: We present a theoretical description of the interaction of optical waves due to the resonant nonlinear response of an atomic system. We emphasize how the resonant nature of the nonlinear coupling is modified by the shifting of the atomic energy levels as a consequence of the dynamic Stark effect and show the equivalent role played by population pulsations in determining the nature of the nonlinear coupling. A general formalism is developed to treat these effects and is explicitly applied to several examples of current interest, including single-beam saturation spectroscopy, pump–probe saturation spectroscopy, modulation spectroscopy, degenerate four-wave mixing for phase conjugation, and instabilities in the beam propagation through resonant media.
TL;DR: In this paper, a detailed theoretical analysis of degenerate four-wave mixing by a laser-induced thermal grating in a nematic liquid-crystal film is presented, and it is shown that the coupling of the pump beam to the first-order diffracted beam can give rise to substantial amplification of a probe beam.
Abstract: We present a detailed theoretical analysis of degenerate four-wave mixing by a laser-induced thermal grating in a nematic liquid-crystal film. In particular, we show that the coupling of the (strong) pump beam to the first-order diffracted beam can give rise to substantial amplification of a (weak) probe beam. Experimental verification of this effect with a CO2 laser beam is also made. A probe-beam gain of greater than 20 can easily be observed in a 120-μm film with a pump intensity of the order of a few watts per square centimeter.
TL;DR: The site selective laser spectroscopy (SSLS) method as mentioned in this paper is based on the idea that a narrow band laser can be tuned to excite selectively an absorption line of a specific component or site within a sample so the resulting fluorescence spectrum came only from the site or component excited.
Abstract: High resolution laser techniques were developed that address the problems listed above. The techniques are collectively called site selective laser spectroscopy. They relied upon the idea that a narrow band laser could be tuned to excite selectively an absorption line of a specific component or site within a sample so the resulting fluorescence spectrum came only from the site or component excited. One could simplify spectral congestion with this approach. One could also eliminate broadening that was caused by inhomogeneities in the samples because excitation within a broadened line would only excite components that had energy states resonant with the laser so the resulting fluorescence spectrum would not reflect the inhomogeneities. These methods were applied to matrix isolation, low temperature organic glasses, Shpol'skii systems, inorganic analysis using precipitates, and supersonic jet spectroscopy to measure a variety of inorganic and organic materials at ultra-trace levels. The methods all relied upon sample fluorescence and they failed if the samples were non-fluorescent. We have recently shown that there is a new family of high resolution laser spectroscopies that have the same capabilities but do not require a fluorescent sample. These spectroscopies are based upon nonlinear mixing where several tunable lasers are focused into a material and new frequencies are formed at all of the sums and differences of the original laser frequencies. This nonlinear mixing is resonantly enhanced when some of the laser combinations match resonances of components in the sample. The nonlinear mixing can be used to perform atomic spectroscopy and molecular spectroscopy. We will concentrate on molecular spectroscopy in this discussion. One can perform component selection by tuning the lasers to match resonances on one specific component in the sample. One would then expect to have that component contribute dominantly to the nonlinear mixing. One can also eliminate inhomogeneous broadening by tuming the lasers to match the resonances of specific sites within the inhomogeneously broadened line. Again, one would expect that those sites would contribute dominantly to the mixing and the nonresonant sites would be discriminated against. We have tested these ideas in several model systems using four wave mixing spectroscopy. The two model systems are pentacene doped into p-terphenyl crystals and pentacene doped into benzoic acid crystals where p-terphenyl was added in small amounts to introduce controlled amounts of inhomogeneous broadening. The experiments were done at 2 K to eliminate thermal effects. There are four schemes that one can use to establish resonances with the pentacene molecules. In all of them, one establishes resonances with the vibrational levels, the excited electronic states, and the vibrational levels of the excited electronic state (which we will call vibronic states). The four schemes differ in which states are involved in the resonance associated with the emitted light. If the emitted light involves transitions between two levels that are not initially populated, the technique is classified as a nonparametric process. If one of the levels were initially populated, the technique is a parametric process. Theories for the ideas predict that each possibility will have a different ability to provide selectivity in the measurement. The pentacene in p-terphenyl system was studied first. Pentacene has four different crystallographic sites in this crystal, some of which differ only slightly from each other. Conventional spectroscopy shows that the transitions from each
TL;DR: Fast parallel analog and digital optical computing operations are demonstrated by using an interferometric arrangement with photorefractive bismuth silicon oxide.
Abstract: Fast parallel analog and digital optical computing operations are demonstrated by using an interferometric arrangement with photorefractive bismuth silicon oxide. Image subtraction, coherent weighted-image addition, exclusive OR/NOT, and OR optical gates are achieved by controlling the relative phase shifts of two phase-conjugate waves generated by degenerate four-wave mixing.
TL;DR: In this article, the authors studied the line-narrowing capability of fully resonant four-wave mixing for inhomogeneously broadened transitions in both parametric and nonparametric nonlinear spectroscopies.
Abstract: Pentacene doped benzoic acid crystals are used to study the line‐narrowing capability of fully resonant four wave mixing for inhomogeneously broadened transitions. Both parametric and nonparametric nonlinear spectroscopies are used to scan the vibronic resonances of excited electronic states while maintaining resonance with a vibrational mode of the ground state and the vibrationless level of the excited state. The observed vibronic transitions correspond to modes that are coupled to the ground state mode. The spectra contain both lines that are narrowed and lines that have the full inhomogeneous width. Narrowing of the vibronic transitions is observed when site selection is performed on the vibrationless electronic transition in both parametric and nonparametric methods. Narrowing of the vibrational resonance is not observed under the same conditions showing that the vibrational and electronic inhomogeneous broadenings are not correlated. The shifts of the line positions and the changes in linewidths and...
TL;DR: In this article, the response of a photorefractive phase conjugator to time-varying signals is examined, and the effects of various parameters on the fidelity and stability of the conjugation process are determined.
Abstract: The response of a photorefractive phase conjugator to time-varying signals is examined. Maxwell’s equations are coupled to the material equations followed by linearization using a strong undepleted pump approximation and simplification by the slowly varying envelope approximation. The resulting set of equations is solved by frequency-domain techniques. The solution is expressed in terms of a transfer function that relates the complex frequencies of the probe and the conjugate field. Limiting forms of the transfer function are derived, and a comparison with a Kerr material is made. The effects of various parameters on the fidelity and stability of the conjugation process are determined. Numerical results are presented showing the distortion of time-varying signals owing to the nonideal conjugation process.
TL;DR: In this article, a detailed model of two-photon-resonant four-wave mixing that includes the consideration of efficiency-limiting processes is presented, and the model provides a generally applicable systematic approach for maximizing conversion efficiencies for both exact and near-twophoton resonance.
Abstract: A detailed model of two-photon-resonant four-wave mixing that includes the consideration of efficiency-limiting processes is presented. The model provides a generally applicable systematic approach for maximizing conversion efficiencies for both exact and near two-photon resonance. For exact two-photon resonance, an interference effect limits efficiency to a value determined by ratios of nonlinear susceptibilities and input intensities. For near two-photon resonance, nonlinear refractive indices limit efficiencies unless input intensities are properly balanced. For the specific case of 130.2-nm generation in Hg, we examine a number of potential additional efficiency-limiting processes, including amplified spontaneous emission, stimulated Raman and hyper-Raman gain, parametric gain, linear absorption, and population transfer. We include isotopic effects and Gaussian-profile beams. From our analysis, we conclude that efficiencies of approximately 10% should be feasible by using collimated light beams in an energy-scalable system.
TL;DR: The predictions of a quantum-mechanical theory of forward four-wave mixing in a homogeneously broadened system of two-level atoms are presented and it is shown that Rabi sideband generation in the forward direction can be understood as parametric amplification of weak radiation emitted spontaneously at the Rabisidebands.
Abstract: The predictions of a quantum-mechanical theory of forward four-wave mixing in a homogeneously broadened system of two-level atoms are presented. In the limit of a very short interaction region, the predictions of this theory reproduce those of well-known theories for the spontaneous-emission spectrum of an atom in the presence of an intense laser field. More generally, the theory predicts how the emission spectrum is modified due to propagation effects for a medium of arbitrary length. For long propagation path lengths, the emitted radiation can be quite intense and has a spectrum that is strongly peaked at the Rabi sidebands of the incident laser frequency. The theory shows that Rabi sideband generation in the forward direction can be understood as parametric amplification of weak radiation emitted spontaneously at the Rabi sidebands. The quantum noise that initiates the four-wave-mixing process has contributions both from fluctuations in the incident vacuum radiation field and from fluctuations in the polarization of the atomic dipoles. Both contributions are important for the case of a radiatively broadened medium, although the material fluctuations make the dominant contribution for the case of a medium in which the broadening is largely collisional. Under certain conditions large amounts of squeezing in the radiated field are predicted.
TL;DR: In this paper, a spatially dependent dynamic carrier concentration model was proposed for a broad-area laser diode, which includes the effects of carrier diffusion, and the results provided a direct determination of the ambipolar diffusion constant in the device D = 9.5 cm2/s.
Abstract: By injecting two external optical beams into a broad‐area laser diode, four‐wave mixing is generated via gain nonlinearities in the device. The nonlinear signals are observed by spectrally analyzing the transverse far‐field profile of the emission from the device. By varying the injection angle and oscillation wavelength of one of the injected beams, the spatial and frequency dependence of this nonlinear process is measured. The results support a spatially dependent dynamic carrier concentration model which includes the effects of carrier diffusion. These measurements provide a direct determination of the ambipolar diffusion constant in the device D=9.5 cm2/s.
TL;DR: In this article, the coupled wave equations for four-wave mixing in a cubic, non-optically-active photorefractive crystal are solved for the case of orthogonally polarized pumping beams.
TL;DR: In this paper, two distinct forms of conical emission are observed when a strong near-resonant laser pulse propagates through sodium vapor, one originates in a resonantly enhanced parametric four-wave mixing process, and the other is produced by the radiative decay of the coherently prepared population of the excited state at a frequency close to that of the unperturbed atomic resonance.
Abstract: Two distinct forms of conical emission are observed when a strong near-resonant laser pulse propagates through sodium vapor. One of the cones originates in a resonantly enhanced parametric four-wave mixing process. A spatially and spectrally distinct cone is produced by the radiative decay of the coherently prepared population of the excited state at a frequency close to that of the unperturbed atomic resonance.
TL;DR: Qualitatively different polarization behavior is observed for pump intensities near or above the two-photon saturation intensity, as predicted by third-order theories.
Abstract: We have studied the polarization properties of phase conjugation by degenerate four-wave mixing resonantly enhanced by the sodium 3S1/2 → 6S1/2 two-photon-allowed transition. As predicted by third-order theories, this interaction leads to simultaneous conjugation of the optical wave front and state of polarization (vector phase conjugation) when the pump intensities are sufficiently weak. However, qualitatively different polarization behavior is observed for pump intensities near or above the two-photon saturation intensity.
TL;DR: In this paper, the anisotropic four-wave mixing in the scheme recently proposed by S.I. Stepanov and M.P. Petrov is studied, where the same phase hologram (index grating) has opposite contrasts for orthogonally polarized, counterpropagating waves.
Abstract: The anisotropic four-wave mixing in the scheme recently proposed by S.I. Stepanov and M.P. Petrov (Opt. Commun. vol.53, p.64-8, 1985) is studied. The main feature of this interaction arrangement is that the same phase hologram (index grating) has opposite contrasts for orthogonally polarized, counterpropagating waves. The coupled nonlinear equations, in the case of transmission and reflection gratings, for the pi /2 photorefractive phase shift are exactly solved, and their properties are discussed in detail. The numerical evidence of the effects of bistability and self-oscillation is included. >
TL;DR: A novel method for the exact solution of four-wave mixing in photorefractive media is presented, which allows us to treat exactly the effects of nonequal angles of incidence, different refractive-index modulation of interacting waves, and external incoherent illumination of the photoreFractive crystal.
Abstract: A novel method for the exact solution of four-wave mixing in photorefractive media is presented. This method allows us to treat exactly the effects of nonequal angles of incidence, different refractive-index modulation of interacting waves, and external incoherent illumination of the photorefractive crystal.