Degenerate Four-wave Interaction Research Articles

Time-division multiplexing of Mbit/s data-packets within Gbit/s data sequences through nonlinear temporal focusing

In this work, we report on an all-optical, real-time, nonlinear temporal compression technique based on a counter-propagating degenerate four-wave mixing interaction in birefringent optical fibres. As a proof-of-concept, we demonstrate the extreme temporal focusing and interleaving of a 10-Mbit/s data packet into a 10-Gbit/s data sequence, with record temporal compression factors ranging from 3 to 4 orders of magnitude and including non-trivial on-demand time-reversal capabilities. Our approach is scalable to different photonic platforms and offers great promise for ultrafast arbitrary optical waveform generation and related applications, while enabling the compression of THz-bandwidth optical signals from low-cost, low-bandwidth optical waveform generators.

Evolution of statistically inhomogeneous degenerate water wave quartets.

A discretized equation for the evolution of random surface wave fields on deep water is derived from Zakharov's equation, allowing for a general treatment of the stability and long-time behaviour of broad-banded sea states. It is investigated for the simple case of degenerate four-wave interaction, and the instability of statistically homogeneous states to small inhomogeneous disturbances is demonstrated. Furthermore, the long-time evolution is studied for several cases and shown to lead to a complex spatio-temporal energy distribution. The possible impact of this evolution on the statistics of freak wave occurrence is explored.This article is part of the theme issue 'Nonlinear water waves'.

Study of four-wave mixing in the femtosecond laser pulse propagation near the resonance rubidium doublet

In this paper, we investigated the coherent degenerate and nondegenerate four-wave interaction in the propagation of a femtosecond laser pulse in atomic rubidium vapor. In the case of degenerate four-wave interaction, the mechanism for optical switching in an optically dense resonant medium is considered. The third-order nonlinear interaction of the laser beams intersecting in the cell at a small angle leads to a nonlinear response in the form of a fourth beam, which occurs as a result of the interaction between the two pump beams and the third signal laser beam.

Dynamic wavefront-conjugating mirror based on CdF2 crystals with bistable in centers

The wavefront reversal upon degenerate four-wave interaction in a CdF2 crystal with bistable In centers is experimentally investigated using a pulsed ruby laser as a pump source. The reflectance and operating speed of the wavefront-conjugating mirror are measured and the quality of the reflected wave, as well as of the compensation of model phase distortions, is estimated. An operating speed of about 15 ns is obtained for such a mirror with a reflectance of up to 2% at room temperature. Compensation of model large-scale distortions yields a gain in the beam divergence of 20 and a quality of compensation of 1.05.

Orientational Photorefractive Effect in Undoped and CdSe Nanorods-Doped Nematic Liquid Crystal—Bulk and Interface Contributions

In the work, we revisited the orientational photorefractive effect generated in nematic liquid crystal (NLC) in a degenerate four-wave mixing interaction configuration. A detailed calculation of the bulk laser-induced space-charge fields and analytical expressions for the reorientation angles and the required dc threshold fields are obtained and compared with experimental measurements. While the bulk theory could describe the general features of the self-diffraction and threshold fields, there are significant deviations from experimental observation, particularly in an observed lowering of the threshold voltage by the optical intensity. This effect is due to an optically induced surface-charge modulation. A theoretical analysis including both the bulk and the surface-charge-modulation effects allows us to obtain better agreement with experimental observations of the threshold voltages on the optical intensity and sample thicknesses, and to estimate the relative contributions from the bulk and surface effects. Recently observed enhanced photorefractive effects of CdSe nanorods-doped NLCs are also reported to corroborate these analyses and to provide guidelines to optimize the photorefractive effect for dynamic holographic application.

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.

Noise radiation power of phase-conjugate mirrors based on a degenerate four-wave mixing

An experimental investigation was made of the influence of the state of optically polished surfaces of various materials on the scattering coefficient which governs the power of the intrinsic noise of phase-conjugate mirrors based on a degenerate four-wave interaction. The angular dependence of this coefficient was also investigated. The noise power of a phase-conjugate mirror made of InAs, operating at the optimal pump wave intensities 1— 2 MW cm-2, may be reduced to ~2 × 10-7 W per one spatial mode of the radiation to be phase-conjugated. This was achieved by increasing the angle between the axes of the signal and the pump beams up to ~1 rad without a significant reduction of the reflection efficiency, which can be ~500%.

INTERMODE FOUR-WAVE INTERACTION OF LIGHT WAVES IN PLANAR WAVEGUIDES

The intermode frequency degenerate four-wave interaction of light waves in planar waveguides is considered in the present paper. The rigorous solution of the nonlinear set of equations for complex amplitudes of the interacting waves is obtained and numerical analysis of the obtained solution is carried out. The possibility of realization of optical logic gates NOT and AND on the basis of the considered process is also shown. The described interaction is experimentally studied in a LiNbO 3: Ti:Fe planar waveguide.

Polarization restoration by phase conjugation in photorefractive crystals

Theoretical and experimental investigations are reported of polarization phase conjugation in a photorefractive LiNbO3 crystal. It is shown that the photogalvanic mechanism of hologram formation by orthogonally polarized beams can ensure complete restoration of the polarization as a result of a degenerate four-wave interaction.

Stability of stationary nonlinear states of optical waves in a system of two coupled double phase-conjugating mirrors based on photorefractive crystals

An investigation is reported of the stability of stationary nonlinear states of the fields of optical waves in a system comprising two coupled regions of a degenerate four-wave interaction pumped by two mutually incoherent optical beams. The importance of allowing for the finite values of scattered-wave seeds in the excitation of the scattering in such a system is demonstrated.

Phase conjugation under conditions of degenerate four-wave interaction involving simulated Raman scattering in a resonator

A system for phase conjugation of Stokes radiation by a four-wave interaction involving intracavity stimulated Raman scattering (STRS) in a Raman-active medium with a nonresonant nonlinearity. This method can be used in construction of high-power sources of highly directional Stokes radiation on the basis of round-trip STRS amplifiers coupled to a phase-conjugating element. It is shown that an STRS converter utilizing organic liquids and subjected to laser pumping of less than 100 MW/cm2 intensity inside a resonator can ensure a highly efficient phase conjugation with a peak reflection coefficient in excess of unity. Depending on the ratio of the Raman and nonresonant susceptibilities of a medium, there is an optimal value of the coefficient representing the degree of conversion of laser pump radiation into STRS radiation, which ensures the maximum phase conjugation efficiency.

Small-scale density inhomogeneities in the case of parametric interaction of radiation with gaseous media

A one-exposure holographic method was used in a study of small-scale inhomogeneities of the density in gaseous media. A study was made of the dynamics of a thermal grating formed in gaseous SF6 by a degenerate four-wave interaction of CO2 laser pulses. The main mechanism destroying such a density grating was found to be a shift of gas particles under the influence of pressure gradients. The thermal grating deformation distorted the wavefront of the diffracted beam.

Spectral dependences of reflection in a degenerate four-wave interaction of infrared laser radiation in resonant SF6, CF3Br, and CD4gases

Spectral dependences of reflection in a degenerate four-wave interaction of CO2 laser radiation in resonant SF6, CF3Br, and CD4 gases were investigated with a spectral resolution of 5 × 10 −2 cm − 1. A structure associated with one- and two-photon vibrational transitions in the gases was observed in the spectra. High reflection coefficients (of some tens of percent) were achieved by optimizing the phase conjugation conditions whilst maintaining the resonant character of the reflection.

Efficiency of ring systems for phase self-conjugation of radiation by four-wave interaction in media with thermal nonlinearity

A theoretical analysis is made of the efficiency of typical ring systems of phase-conjugating mirrors utilizing a degenerate four-wave interaction in media with a thermal nonlinearity. The analysis is made for steady-state conditions taking into account wave saturation effects in an amplifier situated in a positive feedback circuit. It is shown that the reflection coefficient in these systems is extremely sensitive to the level of the phase-conjugate signal (as the ratio of the signal intensity to the saturation intensity of the amplifier active medium is increased, the reflection coefficient of the ring phase-conjugating mirror decreases sharply). It is also found that at a high level of the nonlinearity and for an appreciable gain per pass, these systems exhibit multistability (i.e., several different steady states exist).

Degenerate four-wave interaction based on photodissociation of chemically active media

An analysis is made of a nonlinear interaction of laser radiation with a chemically active medium in which a branched-chain reaction takes place. This reaction enhances greatly the contrast of phase gratings formed as a result of photodecomposition. The example of a gaseous mixture of hydrogen disulfide with oxygen is used in a theoretical investigation of a degenerate four-wave interaction in the course of photodissociation of CS2 molecules and subsequent reactions of the dissociation products. The dynamics of reflection is calculated for different CS2 concentrations and radiation intensities, and it is shown that a high efficiency can be achieved in such systems.

Theory of an opposed four-wave interaction in arbitrary-intensity fields applied to media with resonant and thermal nonlinearity mechanisms

A system of equations is derived to describe a transient opposed degenerate four-wave interaction (FWI) in fields of arbitrary intensity in gaseous media exhibiting resonant and thermal nonlinearity mechanisms. A system of closed equations describing an opposed degenerate FWI in fields of arbitrary intensity is obtained for the steady-state case. It is found that, unlike linearly absorbing media, the optimal reflection coefficients of a signal wave in nonlinearly absorbing media are only achieved at reference wave intensities comparable with the saturation intensity of the resonant medium. Numerical calculations illustrate a fall in the reflection coefficient as the amplitude of the signal wave is increased.

Degenerate four-wave mixing of multifrequency radiation in resonant media due to cascade transitions in diatomic molecules

The example of two-frequency radiation is used in an analysis of a resonant antiparallel degenerate four-wave interaction of multifrequency radiation involving cascade transitions in diatomic molecules. The approximation of homogeneous broadening of spectral lines is used in the derivation of equations describing transient interaction of waves in fields of arbitrary intensity allowing for the diffusion of particles in a gas. Numerical calculations illustrate some characteristics of the two-frequency four-wave interaction in resonant media.

Phase conjugation of pulsed CO2laser radiation by four-wave mixing in CCl4

An experimental investigation was made of phase conjugation under conditions of degenerate four-wave interaction of CO2 laser radiation in carbon tetrachloride as a function of various parameters of the signal radiation and of the experimental geometry. It was found that the conjugation accuracy for a single-mode signal beam with a divergence of 2 mrad was 87%, but when a phase plate introducing a divergence of 70 mrad was used, the accuracy was 77%. The reflection efficiency and the phase conjugation quality depended strongly on the ratio of the energy density of the signal wave to the energy density of the pump wave. An investigation was made of the dependence of the reflection coefficient on the angular mismatch between the counterpropagating pump waves and on the matching of the optical paths of the interacting waves.

Phase conjugation of an optical wave in the case of a degenerate four-wave interaction in an amplifying medium of a chemical HF laser

The approximation of a constant intensity of reference waves is used in the case of low values of the reflection coefficients (less than unity) to investigate numerically the efficiency of optical phase conjugation of a wave from a pulsed chemical HF laser based on a chain reaction. It is shown that the reflection coefficient for the three strongest emission bands P1–0, P2–1, and P3–2 of a pulsed chemical HF laser can be 0.1.

Theory of a transient opposed four-wave interaction in resonant media subjected to fields of arbitrary intensity

A theory is developed of an opposed degenerate four-wave interaction in resonant two-level media subjected to fields of arbitrary intensity. An allowance is made for the transient nature of the response of a relaxing medium. An infinite chain of equations is used to describe the interaction in such fields, the cases of steady-state and transient interactions are discussed separately, and the results of numerical calculations illustrating the theory are given. It is shown that in the steady-state case the equations derived in the present study reduce directly to the familiar equations of a small-signal theory. A qualitative analysis of the equations for the transient degenerate four-wave interaction shows clearly that in strong fields this interaction may be more effective than the steady-state interaction.