Four-wave Mixing Interaction Research Articles

Modeling of Semiconductor Optical Amplifiers

We present a tight-binding analysis of the polarization dependence of GaAs δ-strained semiconductors optical amplifiers. We explain how thin strained GaAs layers embedded in a lattice-matched InGaAsP/InGaAs quantum well can be used to achieve polarization insensitive optical amplification. We describe also the interaction between pulse propagation and gain compression within a pump-probe excitation in polarization insensitive MQW-SOA. Another important non-linear effect studied is Four Wave Mixing (FWM) on the pulse propagation in the active region of SOAs. Our model successfully predicts operation of optical data sampling using FWM interaction between a signal bit stream and an optical clock.

Quantum optical effects in semiconductor microcavities

Investigations of quantum effects in semiconductor quantum-well microcavities interacting with laser light in the strong-coupling regime are presented. Modifications of quantum fluctuations of the outgoing light are expected due to the non-linearity originating from coherent exciton–exciton scattering. In the strong-coupling regime, this scattering translates into a four-wave mixing interaction between the mixed exciton–photon states, the polaritons. Squeezing and giant amplification of the polariton field and of the outgoing light field fluctuations are predicted. However, polariton–phonon scattering is shown to yield excess noise in the output field, which may destroy the non-classical effects. Experiments demonstrate evidence for giant amplification due to coherent four-wave mixing of polaritons. Noise reduction below the thermal noise level was also observed. To cite this article: E. Giacobino et al., C. R. Physique 3 (2002) 41–52

Multiple four-wave mixing–induced modulational instability in highly birefringent fibers

Theoretical and experimental results are presented that illustrate efficient generation of new optical frequencies by means of induced modulational instability in birefringent fibers for an initially highly phase-mismatched process. Modulational instability is assisted by multiple four-wave mixing interactions. This technique relaxes the strict spectral limitations imposed by the phase-matching conditions on the signal used for frequency conversion by means of modulational instability.

Format conversion of optical data using four-wave mixing in semiconductor optical amplifiers

We present an analysis of the effect of four-wave mixing (FWM) on the pulse propagation in the active region of semiconductor optical amplifiers (SOAs). Our model, based on a rate equation approach, successfully predicts operation of optical data sampling using FWM interaction between a signal bitstream and an optical clock. Such a process can be used for format conversion of optical pulses from nonreturn-to-zero to return-to-zero bitstreams.

Resonant degenerate four-wave mixing spectroscopy of transitions with degenerate energy levels: Saturation and polarization effects

The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.

Temporal characteristics of polarization-decoupled, anti-Stokes-type Brillouin-enhanced four-wave mixing

The characteristics of time-dependent Brillouin-enhanced four-wave mixing (BEFWM) interaction were investigated. The temporal and spatial profiles of four optical waves and an acoustic wave in the BEFWM interaction of polarization-decoupled, anti-Stokes type were calculated using a relatively simple simulation method. In the simulation with step-function optical waves, two distinctive interaction regimes were observed: steady-state regime and reconversion regime which are distinguished by their characteristic temporal behaviors. The simulation with pump waves similar to the BEFWM experiment of polarization-decoupled, anti-Stokes scattering type showed that the temporal shape of the output signal well matched with the observed result.

Influence of beam polarization on the performance of a mutually pumped phase conjugator

The influence of polarization variation of a pump beam on the performance of a bridge mutually pumped phase conjugator has been investigated. The reflectivity, transmission, and response time were measured for different polarizations and different intensity rations of input beams. From these measured results, the variation behaviors of parameters of four-wave mixing interactions in the crystal are revealed.

Frequency comb generation by four-wave mixing and the role of fiber dispersion

A fiber-optic frequency comb generator utilizes four-wave mixing (FWM) to expand a modulated continuous wave (CW) lightwave into a comb of discrete, equispaced frequencies. The sign and magnitude of the fiber dispersion are shown to control comb expansion by affecting the interference among different four-wave mixing interactions at particular comb frequencies. Positive dispersion initiates comb expansion while zero and negative dispersions suppress expansion. Dispersion mapping engineers fiber links for maximum comb bandwidths. By managing dispersion in a 35 km link of dispersion-shifted fiber, a frequency comb spanning 1.1 THz is experimentally demonstrated. Promising applications include pulse train synthesis affording low-chirp, arbitrarily profiled, short pulses.

Four-wave mixing spatial soliton interaction dynamics

Three-color spatial optical solitons created by third-order nonlinear mixing of light at a central frequency with two sidebands through both cross-phase modulation and four-wave mixing are presented. Stability and interaction dynamics of these solitons are investigated.

Experimental assessment of a photorefractive bandpass joint transform correlator

An experimental implementation of a joint transform correlator based on a nondegenerate four-wave mixing interaction in the photorefractive material bismuth silicon oxide is described. An investigation is made of the pattern recognition performance of the correlator by assessing its ability to maintain a correlation response despite orientation changes of a model road vehicle while simultaneously discriminating against a similar vehicle. The full-bandwidth performance, essentially implementing an inverse filtering operation, was found to give good discrimination but to be highly sensitive to changes of the vehicle orientation from that of the reference function. A bandpass filtering strategy, based on the difference of Gaussian wavelet filter, was implemented in the correlator by exploiting the Gaussian amplitude profile of the TEM00 mode of the helium neon readout laser. An extensive experimental evaluation of the performance of the modified filtering scheme is presented, demonstrating considerably enhanced intraclass distortion tolerance while maintaining good interclass discrimination ability.

Loop resonators with self-pumped phase-conjugate mirrors in solid-state saturable amplifiers

Loop resonators with self-pumped phase conjugate mirrors (SPPCM’s) based on a four-wave mixing (FWM) interaction in solid-state saturable amplifiers are investigated in the short-pulse regime. A model using a transient treatment of FWM with the appropriate boundary conditions imposed by the loop geometry allows us to analyze the threshold condition for oscillation, the temporal dynamics, including self-Q switching, and the energy characteristics of such loop resonators. The influence of the gains of the saturable amplifiers and the influence of the transmission factors around the loop are also analyzed. A loop resonator with a SPPCM in a Nd:YAG amplifier is experimentally investigated at λ=1.064 µm in the nanosecond regime. A maximum reflectivity of 42 and a maximum extraction of 47 mJ, corresponding to a 20% extraction efficiency, are measured. Experimental and theoretical results are in good agreement.

Incoherent light amplification and phase conjugation of four beams with a photorefractive crystal

A mutually pumped phase conjugator is realized using a bridge configuration with a novel crystal of copper-doped potassium sodium strontium barium niobate. Phase conjugation reflectivity reaches 218%. The buildup times of phase conjugation outputs are measured, and a curve fit of the times is made. A self-curving coupling channel is observed. We use the theory developed by Lyubomudrov and Shkunov to model the coupling channels. The curved beam trajectory depending on the incident position and the incident angle is also calculated. With the results we show that one, two, three, and more four-wave mixing interaction regions exist in photorefractive bridge mutually pumped phase conjugators. Additionally, the simultaneous phase conjugation outputs of four incident beams are also demonstrated experimentally with the crystal.

Origin of Self-Pumped Phase Conjugate Waves in KNSBN Crystals

A multistage four-wave mixing interaction region model resulting in self-pumped phase conjugation output of the incident beam is suggested to explain the experimental observations. The competition between forward and backward two-wave mixing is demonstrated and used to explain the formation of the mechanism. The backscattering beams from random noise beams may be amplified by contradirectional two-wave mixing selectively and act as pumped beams from our experimental observations under a laser entering the negative c face of copper-doped potassium sodium strontium barium niobate crystal. The phase conjugation reflectivity of as high as 33% is measured.

Self-pumped phase conjugation with mechanism transformation in potassium sodium strontium barium niobate

Both multistage and a great number of four-wave mixing interaction region models arising from contradirectional two-wave mixing to generate phase conjugation beam are suggested for the first time to our knowledge with a beam entering negative c face of the crystal. The mechanism transformation with geometric parameters is also observed and discussed. The backscattering beams from random noise beams may be expected to be amplified by contradirectional two-wave mixing under the beam entering negative c face of copper-doped potassium sodium strontium barium niobate. The maximum of reflectivity attains 33%.

Photorefractive Self-Bending and High-Performance KNSBN:Cu Crystal Self-Pumped Phase-Conjugator

The mechanism for the high-performance KNSBN:Cu crystal self-pumped phase-conjugator is first put forward in this letter as no-loop photorefractive self-bending succesive four-wave mixing interaction. And the photorefractive backscattering amplification was found to play a very important role in it.

Nondegenerate four-wave mixing in a cavity: instabilities and quantum noise reduction

Abstract We consider the four-wave mixing interaction of three longitudinal cavity modes in a unidirectional ring cavity containing a system of two-level atoms. The set of equations which governs the dynamics of the system coincides with that of multimode optical bistability, and describes the behaviour of the system over all its parameter space. We identify an appropriate limit in which the model reduces exactly to a parametric interaction among the three modes. In this limit the model is fully quantum mechanical and it includes all the physical processes that are relevant in the limit (four-wave mixing, phase modulation, cross phase modulation). The stationary solutions of the parametric model are calculated analytically and display a complex scenario, which includes also the possibility of undamped oscillations of the modal amplitudes. Using the parametric model we calculate analytically also the spectrum of the fluctuations of the intensity difference between the signal fields, above the threshold of generation of the signals. It turns out that this coincides with the expression of the spectrum that is well known in the case of the nondegenerate parametric oscillator.

Double phase-conjugation in sodium

We present the results of an experiment showing double phase-conjugation in an atomic vapor. Two pump beams incident on a sodium cell placed in a ring cavity induce the generation of two counterrotating oscillating beams. The four-wave mixing interaction of each pump beam with the counterpropagating beams in sodium generates a beam which is phase-conjugate of the pump beam. Reflectivities of the order of 2×10 −4 have been observed.

Closed-form solution for parametric second Stokes generation in Raman amplifiers

The efficiency of a first Stokes Raman amplifier can be seriously reduced by the generation of a second Stokes beam. The dominating process for this generation is often a Raman four-wave mixing interaction which couples the pump and second Stokes beams. A one-dimensional model for this effect has a closed-form solution, simply described in terms of an equivalent input, under conditions where high first Stokes conversion efficiency is possible. Excellent agreement with numerical integration results has been obtained. Use of the model for maximizing conversion efficiency of pump beams with large temporal or spatial intensity nonuniformity is described, with an example worked out for a triangular pulse shape.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Thermally induced phase conjugation by transient real-time holography: a review

The underlying principles and key experimental demonstrations of thermally mediated phase conjugation through transient real-time holography processes in absorbing liquid media are reviewed. The basic elements of the formalism developed to study thermal-grating evolution dynamics and diffraction efficiency are presented, emphasizing the method’s traceability to analytic techniques originally formulated to study stimulated thermal Rayleigh scattering processes. The significance of the thermo-optic interaction in generating some of the highest known phase-conjugate reflectivities in four-wave mixing interactions is highlighted, with emphasis on the temporal parametrics underlying the nonlinear process in absorbing liquid media. Thermal gratings in liquid crystals are also briefly reviewed.

Four-wave transverse-longitudinal mixing in a plasma

A four-wave mixing interaction is described in which one of the fields is that of a plasmon. Consideration of the plasmon dispersion relationship shows that this non-linear process should be automatically phase-matched. Full spectral and spatial resolution of the product photons will enable the plasmon dispersion relationship to be observed directly by an optical method.