Degenerate Multiwave Mixing Research Articles

Intrinsic symmetry of nonlocal nonlinear optical susceptibility tensor in degenerate multi-wave mixing

Using energy and momentum conservation laws, we obtained the intrinsic symmetry relations for the nonlocal nonlinear optical susceptibility tensor in lossless nth order nonlinear medium of arbitrary symmetry class for the case when less than n + 1 electromagnetic waves with different frequencies interact. Particular attention is devoted to the relations of the components of this tensor, which cannot be obtained as limiting case from the symmetry relations for the nonlocal nonlinear susceptibility tensor describing interaction of exactly n + 1 waves with different frequencies. The examples of these symmetry relations for degenerate second- and third-order processes often considered are given.

High-order optical nonlinearities in nanocomposite films dispersed with semiconductor quantum dots at high concentrations

We describe the nonlinear optical properties of inorganic-organic nanocomposite films in which semiconductor CdSe quantum dots as high as 6.8 vol.% are dispersed. Open/closed Z-scan measurements, degenerate multi-wave mixing and femtosecond pump-probe/transient grating measurements are conducted. It is shown that the observed fifth-order optical nonlinearity has the cascaded third-order contribution that becomes prominent at high concentrations of CdSe QDs. It is also shown that there are picosecond-scale intensity-dependent and nanosecond-scale intensity-independent decay components in absorptive and refractive nonlinearities. The former is caused by the Auger process, while the latter comes from the electron-hole recombination process.

Degenerate polarization multiwave mixing between light beams in a solution of rhodamine 6G dye

The characteristics of diffracted waves derived from four- and six-wave mixing in a solution of Rhodamine 6G dye are studied in different combinations ofthe polarization states of waves that participate in wave interaction.

High-order nonlinear optical response of a polymer nanocomposite film incorporating semiconducotor CdSe quantum dots

We report on observation of high-order optical nonlinearities in our recently developed photopolymerizable semiconductor CdSe quantum dot (QD)-polymer nanocomposite films at various volume fractions of CdSe QDs as high as 0.91 vol.% (3.6 wt.%). We performed Z-scan and degenerate multi-wave mixing (DMWM) measurements using a 532-nm picosecond laser delivering single 35 ps pulses at a repetition rate of 10 Hz. Using the uniformly cured polymer nanocomposite films, we observed the third- and fifth-order nonlinear optical effects in closed-aperture Z-scan measurements by which it was found that saturable nonlinear absorption (light-induced transparency) and large negative nonlinear refraction were induced. We also measured dependences of the effective third- and fifth-order nonlinear refraction constants on CdSe QD volume fraction. Based on the Maxwell-Garnett model, we estimated the third- and fifth-order nonlinear optical susceptibilities of CdSe QD and discussed a contribution of the third-order effect to the fifth-order one due to the cascaded (local-field) effect. Coexistence of the third- and fifth-order nonlinear refraction was also confirmed by DMWM.

Degenerate multi-wave mixing inside a 4f imaging system in presence of nonlinear absorption

We report on multiwave mixing inside a 4f coherent imaging system using an I-scan configuration and taking into account nonlinear absorption inside materials. A simple mathematical calculation is presented in order to explain the nonlinearly induced diffracted beam distribution in the image plane. The influence of nonlinear absorption is discussed and a study on the sensitivity of the technique and experimental methodology for absorbing materials is proposed. We provide also a simple quadratic relation to characterize the cubic nonlinear refraction for absorbing media.

Sensitivity of the 4f coherent imaging system used in degenerate multiwave mixing experiments

We analyze the influence of different objects on the sensitivity of using a 4f imaging system for nonlinear optical measurements. By defining the diffraction efficiency as the physical quantity to measure, it is possible to perform different measuring methods (Z-scan, eclipsing Z-scan, I-scan, degenerate four-wave mixing) by matching the field stop in the image plane with the object at the entry. One, two, three, and four waves mixing are considered in order to compare their related sensitivities. We provide simple quadratic relations for each object that allow the characterization of the cubic optical nonlinearity. A systematic comparison is done showing that one circular aperture object gives the highest sensitivity. The experimental measurements are performed in order to validate our simulation.

Degenerate multiwave mixing using Z-scan technique

This study deals with a multiwave mixing experiment using Z-scan technique. We show that it is possible to simplify the complex degenerate four-wave mixing (DFWM) experimental setup in order to characterize nonlinear materials. One object composed of three circular apertures is used as an input in a 4f coherent imaging system. When the nonlinear material is moved around the focus, we observe the variations of the forward fourth wave at the output as well as other diffracted waves. Experimental and simulated images are presented here to validate our approach. We show also that this method increases significantly the sensitivity of the measurement compared to DFWM. We provide a simple quadratic relation that allows the characterization of the cubic optical nonlinearity.

Comparative analysis of multi-wave mixing and measurements of the higher-order nonlinearities in resonant media

The features of degenerate multi-wave mixing in resonant media (dye solutions) have been studied theoretically and experimentally. It has been demonstrated that thermal nonlinearity due to the induced absorption from the excited level contributes significantly to the efficiency of four-wave mixing, but results in lower efficiency of higher-order interactions. The measurement results obtained for the energy efficiency of four-, six- and eight-wave mixing enable calculations of the third-, fifth- and seventh-order nonlinear optical susceptibilities, respectively. Experimentally, the method proposed for measurements of the higher-order nonlinearities has been realized with the use of the multi-wave mixing at second harmonic λ=532nm of monopulse YAG:Nd3+ laser radiation in a Rhodamine 6G dye solution. The ratios ∣χ(5)∣/∣χ(3)∣ and ∣χ(7)∣/∣χ(5)∣ are determined to be of the order of 10−5cm3/erg.

Optical Boolean logic based on degenerate multi-wave mixing in bR film

When two coherent beams interfere in bacteriorhodopsin (bR) film with a very small crossing angle, degenerate multi-wave mixing appears. In this paper, the properties of degenerate multi-wave mixing in bR film were studied. By use of degenerate multi-wave mixing in bR film, we realized optical Boolean logic operations.

Femtosecond, Frequency-Agile, Phase-Sensitive-Detected, Multi-Wave-Mixing Nonlinear Optical Spectroscopy Applied to π-Electron Photonic Materials

Degenerate four-wave mixing (DFWM) spectroscopy is modified to exploit femtosecond pulses, phase-sensitive-detection, frequency (wavelength) agility, two-color (nearly degenerate multiwave mixing) radiation, and improved signal-to-noise capabilities that can be realized through a combination of new solid state lasers, nonlinear optical components, and novel design concepts. The resulting time-resolved nonlinear optical techniques permit “instantaneous” optical nonlinearities, such as two-photon absorption cross sections, to be accurately measured over the spectral range from 450 to 2500 nm (and with significantly greater effort from 225 to 5000 nm). The power of the new techniques is illustrated by their application to the definition of Hg two-photon resonances of C60 and C70 as well as to the characterization of optical nonlinearities in two linear chromophores of putative utility for sensor protection and electrooptic modulation. Explicitly, these measurements provide accurate determination of both tran...

Three-dimensional degenerate multiwave mixing and optical storage effects in C 60 Langmuir-Blodgett films

We present here the generation of forward phase conjugate waves (FPCWs) by means of degenerate multiwave mixing with three-dimensional geometry in C 60 arachidic acid (C 60−AA) complex Langmuir-Blodgett films. The FPCWs are induced by third- and higher-order (5th-order) nonlinear effects of the films. The 3rd-order susceptibility χ (3) was measured to be 1.8 ×10 −8 esu for the film at 532 nm wavelength. In the meantime, optical storage effects in C 60−AA complex LB films were observed. The origin of the effects is considered mainly due to the light-induced transformation between the aggregate and monomer structure of C 60 molecules.

Nearly degenerate multiwave mixing in quasi-equilibrium semiconductors

A theoretical analysis is presented of nearly degenerate multiwave mixing in quasi-equilibrium semiconductors, including many-body effects. Multiwave mixing coefficients are expressed in terms of the single-wave susceptibility and its derivative with respect to carrier density. The theory is illustrated with parameters appropriate for bulk GaAs including the many-body effects of bandgap renormalization and Coulomb enhancement.

Saturated optical non-linearity of bacteriorhodopsin Langmuir-Blodgett films derived from degenerate multiwave mixing

Optical phase conjugate and higher order diffractions in degenerate multiwave mixing in bacteriorhodopsin (BR) Langmuir-Blodgett films are reported for the first time in this paper. A model that describes the higher order diffractions by population gratings has been developed on the basis of a simplified BR photocycle (BR 570 ⇄ M 412). The saturated absorption intensity and the non-linear saturation index of refraction of the LB films have been estimated to be 0.42 W cm −2 and 5 × 10 −2 cm 2 W −1 respectively. A typical response time of the non-linearity is of the order of milliseconds.

Doppler-free spectroscopy by noncollinear degenerate multi-wave mixing

Phase matched resonant degenerate wave mixing in a Doppler broadened gas medium is shown to give rise to narrow spectral lineshapes even for non-dollinear arrangements. The effect is related to velocity selection in more than a single direction. Numerical calculations for six-wave mixing were well verified experimentally for CO 2 laser diffraction on low pressure SF 6.

Degenerate multiwave mixing and phase conjugation in silicon.

Degenerate multiwave mixing and phase conjugation in silicon.

Probe beam amplification and phase conjugation self-oscillation in a Kerr medium

In a highly-nonlinear thin Ker medium, the intersection of a strong pump beam and a much weaker probe beam produces a sizeable diffracted beam whose presence changes both the transmitted probe beam gain and the phase conjugation self-oscillation thresholds. An analytical calculation of these effects involving degenerate multiwave mixing processes is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Degenerate multiwave mixing in SF 6

High-order diffraction of CW CO 2 laser radiation was observed in SF 6 in the Doppler broadening limit. The nonlinear susceptibilities, up to χ (9), were separately monitored in Doppler free resonance lineshapes, using a near-collinear phase matched multiwave mixing configuration.

Nanosecond laser amplification via degenerate multiwave mixing in silicon

We present the results of a detailed study of degenerate multiwave mixing mediated nanosecond 1.06 μm pulse amplification in silicon, taking into account higher order diffracted beams, self-phase modulation, pump depletions, intensity-dependent absorption losses, electron-hole plasma attenuation, and other geometrical optical parameters. Excellent agreements between theory and experiment are obtained.

Spatially multiplexed phase conjugate imaging and processing in photorefractive BSO

Theoretical considerations and experimental results are presented for simultaneous degenerate multi-wave mixing in photorefractive BSO. Using the same crystal volume and common pump beams, multiple imaging has been achirved in which each image shows no cross-talk. The mutual modification of the multiplexed gratings presents no problem in terms of destructive depletion effects. Simultaneous correlation of two images with the same test image has also been achieved, verifying the independent nature of each grating within the crystal.