Forward Degenerate Four-wave Mixing Research Articles

Saturated FDFWM lineshapes and intensities: theory and application to quantitative measurements in flames

The present paper deals with a three-level model of interaction with three cross-polarized and co-propagating fields having the same frequency. The two pump waves have arbitrary intensities and the third one (the probe wave) is assumed to be non-saturating. Using the radiative renormalization method, density matrix equations are solved analytically. The forward degenerate four-wave mixing (FDFWM) signal is calculated under thermodynamic conditions where collisional and Doppler broadenings are comparable. The calculation also takes into account crossed-polarization effects. The FDFWM intensity is computed as a function of power densities and pressure. FDFWM experimental spectra of the - (0 - 0) band of OH obtained in a welding torch flame are compared to theoretical profiles. For incident laser intensities in the range of a few , a good agreement is obtained between calculated and experimental profiles. Discrepancies arise under stronger conditions of saturation, showing the limits of application of our model. However, because there is little virtue in using higher laser powers, the model should be extremely useful in practical applications. In particular, we demonstrate that the signal intensity is optimal and the pressure dependence is minimized when the saturation parameter is unity.

Observation of strong field effects and rotational line coupling in DFWM processes resonant with [formula omitted] electronic system

Isolated and merged features within the NO A ← X (0,0) and the OH A ← X (0,0) bands have been observed using a crossed-polarization arrangement in forward degenerate four wave mixing (FDFWM). The spectra are interpreted both using the conventional perturbative treatment, which is appropriate in the low-field limit, and using the dressed-molecule formalism when analysing saturation behaviour. The use of the latter formalism is essential in the range of saturation parameters which has been investigated experimentally. Emphasis is placed on reproducing the signal intensity while taking into account strong field effects, rotational line coupling, and laser beam polarization. A simple model of M-level degeneracy is used to depict the various laser polarization arrangements of the three incoming beams. Relative line intensities and spectral broadenings are correctly reproduced for both OH and NO in atmospheric pressure flame conditions, that is, with comparable Doppler and collisional linewidths. In NO, unresolved principal and satellite lines were observed and these could be reproduced using a three J-level model. The validity of this last model will be discussed.

Experimental observation of all-optical deflection using forward degenerate four-wave mixing in ZnSe

We report on the use of forward degenerate four-wave mixing in a sample of ZnSe to demonstrate a variable controlled all-optical deflector. The measured deflection is in the range of 2.9 × 10 −3 to 1.73 × 10 −2rad. The dependence of the deflection on the intensities of input beams has been investigated.

Phase-matched gratings for enhanced forward degenerate four-wave mixing

A phase-matched grating to enhance the second-order diffracted signals generated by forward degenerate four-wave mixing has been proposed and demonstrated for the first time to the authors’ knowledge. Experiments have been performed with a cw Ar:Kr laser at λ = 488 nm, with a linear–nonlinear sandwich of glass slides and Alizarin Yellow-doped films of epoxy resin. Finite-difference simulations have been used to model the process successfully, with finite beam size effects and deviations from an ideal Kerr response of the material taken into account. The possibilities for optical processing applications are assessed in the light of these results.

Nonlinear optical properties of some mono- and bimetallic organometallic systems

The second molecular hyperpolarizabilities (γ) of a group of conjugated organometallic systems have been measured off-resonance (1.064 μm) using forward degenerate four-wave mixing. The effect on the optical properties of introducing more than one metal centre into a conjugated organic backbone was studied. The effect of changing the size of solubilizing substituents was also investigated. Results demonstrate that the presence of two metals in the backbone of a conjugated organic compound serves to enhance the third-order nonlinearity in comparison to monometallic systems.

Size dependence of the third-order susceptibility of copper nanoclusters investigated by four-wave mixing

We report on the observation of the forward degenerate four-wave mixing in four composite samples with Cu nanoclusters embedded in fused silica. The mean diameters of the copper particles in the four samples were 5, 7, 10, and 13 nm. The independent tensor elements of optical Kerr susceptibility were measured with different wave-mixing polarizations by use of 35-ps laser pulses from a mode-locked, frequency-doubled Nd:YAG laser. The measured third-order susceptibilities were on the order of 10−9–10−8 esu; the response time of the nonlinearity is faster than the laser pulse duration. The experimental results are consistent with a d−3 size dependence predicted for quantum-confined conduction band electrons in Cu nanoclusters.

Ultrafast nonlinear optical effect in CdTe-doped glasses fabricated by the laser evaporation method

Abstract The laser evaporation method is an attractive technology to synthesize composite materials. We tried to apply the laser evaporation method on fabrication of CdTe-doped glasses for the first time. CdTe microcrystallites embedded in SiO2 films were confirmed by transmission electron microscope images. The third-order nonlinear susceptibility χ(3) and the decay time τ of CdTe-doped glasses were measured by three-beam forward type degenerate four-wave mixing. The maximum value of χ(3) was estimated 4.2 x 10-7 esu when the absorption coefficient was 6000 cm-1. From the limitation of pulse duration of 5 ps, τ was not exactly measured but imagined to be shorter than 10 ps, which was much faster than the other semiconductor-doped glasses ever reported. The figure of merit defined as χ(3)/ατ is probably larger than 7.

Nonlinear optical studies of group 10 transition-metal thienyl systems

trans-Square-planar Group 10 metal thienyl complexes were synthesized and characterized. The linear and nonlinear optical properties were studied in solution, the latter by forward degenerate four-wave mixing at 1.064 μm. A strong dependence of the linear and nonlinear optical properties on the metal centre was observed, both the lowest energy absorption wavelength and second hyperpolarizability decreasing down the metal group. Abbenzothienyl analogue of the nickel complex was similarly synthesized and characterized, both structurally and optically. The fused ring is seen to have a favourable influence on the second hyperpolarizability. Polymeric analogues of the two nickel complexes were prepared by copolymerization. The lowest energy optical transitions are substantially higher than those of purely organic analogues and the measured second hyperpolarizabilities compare very favourably, being up to 25 times higher than poly[(3-butyl)thiophene].

Nonlinear optical susceptibility of ultrasmall CdS particles by means of the polarization-discriminated forward degenerate four-wave mixing in a resonant region

We report results of degenerate four-wave mixing (DFWM) measurements of resonant nonlinearity for ultrasmall CdS particles having diameters of 26–39 Å. The values of χxyyx(3) obtained by means of forward DFWM operating under polarization-discriminated conditions are the same order of magnitude as the reported χ(3) at a nonresonant wavelength.

Two-wave mixing in thin nonlinear local-response media: a simple theoretical model

A systematic study of degenerate two-wave mixing in the stationary regime in thin nonlinear local-response media is presented. The model is based on the coherent interaction of four waves, the two incident beams, and the two main diffracted waves. Analytical results are obtained in all cases investigated under the assumption of weak-beam amplification. It is demonstrated that the energy transfer arises only from the forward degenerate four-wave mixing terms. In particular, the theoretical results show two new features: (1) the gain factor of the interaction is substantially reduced because of the phase change associated with the two-wave mixing terms and (2) a phase mismatch can compensate for this phase change, leading to an appreciable gain enhancement. Moreover, the general case is solved numerically. Particular attention is given to the influence of separate two-wave and forward degenerate four-wave mixing terms. Self-diffraction effects and the gain dependence versus the ratio of the pump-beam intensity to the signal-beam intensity are investigated.

Squeezing performance of a nonlinear symmetric Mach–Zehnder interferometer using forward degenerate four-wave mixing

A nonlinear symmetric Mach–Zehnder interferometer is analyzed. It performs squeezing and phase-sensitive amplification through forward degenerate four-wave mixing with automatic phase matching. Since the balanced interferometer is frequency insensitive, the operation is broadband. The squeezing performance is computed numerically by means of the quantum theory without approximation. This result is compared with the squeezing characteristics derived from the linearized representation. It is found that squeezed states can be produced without excess noise. Noise reduction of an interferometric measurement and phase-preserving amplification with this squeezer are also analyzed.

Large third-order optical nonlinearity of the organic metal α-[bis(ethylenedithio) tetrathiofulvalene] triiodide

The organic metal α-[bis(ethylenedithio) tetrathiofulvalene]2I3 shows a large third-order optical nonlinearity around 650 nm, as observed by forward degenerate four-wave mixing. Nonlinear susceptibilities of ‖χ(3)‖ ∼5×10−8 esu are observed along the direction of maximum conductivity. The frequency dispersion of the nonlinearity points to a plasma effect due to the conduction electrons.

Vector-field quantum model of degenerate four-wave mixing.

A quantum theory of degenerate four-wave mixing is presented in which the atomic medium consists of stationary four-level atoms, each with three degenerate excited states, and the interacting light beams are allowed to be in different states of polarization. This vector-field theory differs from the scalar-field theory of Reid and Walls [Phys. Rev. A 31, 1622 (1985)] in that there are new atomic variables in the Langevin equations which are related to the induced coherence between the upper atomic states. It is found, for the assumed set of atomic levels, that this seemingly different mechanism of four-wave-mixing gain does not circumvent the degrading effect of spontaneous emission on squeezing obtainable via degenerate four-wave mixing. The theory is applied to both forward and backward degenerate four-wave mixing with nearly collinear geometry, and specialized to the case in which the polarization states of the two pump modes are mutually orthogonal. It is found that for both forward and backward configurations, the range of pump intensity for which squeezing can be achieved in the vector-field case is larger than that in the scalar-field case, and the maximum amount of squeezing obtainable at a particular pump detuning is comparable in both cases.

Picosecond study of near-band-gap nonlinearities in GaInAsP

From picosecond pump-probe and forward degenerate four-wave mixing (DFWM) experiments, we obtain the near-band-gap nonlinear absorption and refraction properties of GaInAsP for λ∼1.5 μm. Using a mode-locked color center laser, the nonlinear signals are studied in room-temperature samples as a function of time and wavelength for different pump energies and for materials with different band-gap energies. Nonlinear absorption cross sections σeh as large as −5.7×10−15 cm2 are obtained from the pump-probe results, while effective nonlinear cross sections σeff as large as 7.8×10−16 cm2 (corresponding to a steady state ‖χ(3)‖∼3.8×10−3 esu for a 20-ns relaxation time) are measured in the DFWM experiments. The spectral behavior of the data shows that above the band gap, the nonlinearity is due both to band filling and screening of excitonic effects. However, the effectiveness of the screening diminishes within one or two plasma frequencies of the band edge.

Quantum atomic-fluctuations reduction and squeezed-state generation via forward degenerate four-wave mixing

It is shown that correlation of quantum atomic fluctuations for coupled modes at forward degenerate four-wave mixing leads to atomic noise reduction from the in-phase quadrature variance of the mode which is a linear combination of the coupled signal and probe modes. Thus, quantum atomic fluctuations are not an obstacle for the squeezed-state generation via degenerate four-wave mixing.

Squeezed-state generation via forward degenerate four-wave mixing

Degenerate four-wave mixing has been suggested as a possible generation scheme for squeezed-state light. A recent analysis of the quantum effects of probe-conjugate loss in backward degenerate four-wave mixing has shown that such loss puts an absolute limit on the squeezing that can be obtained via this generation scheme. In this Rapid Communication we show that it is the counter-propagating beam geometry of backward degenerate four-wave mixing that makes it ill suited for squeezed-state generation. On the other hand, the nominally copropagating beam geometry of forward degenerate four-wave mixing is shown to alleviate the absolute probe-conjugate loss limit on squeezing.

Degenerate four-wave mixing in room-temperature GaAs/GaAlAs multiple quantum well structures

We report the first observation of forward degenerate four-wave mixing (DFWM) in room-temperature GaAs/GaAlAs multiple quantum well structures near the exciton resonances. In a sample 1.26 μm thick with sixty-five 96-Å GaAs quantum wells we observe ∼10−4 diffraction efficiency with ∼30 W/cm2 average intensity from a mode-locked laser. We measure nonlinear absorption and DFWM spectra, and also a change in refractive index, per carrier pair/cm3, of neh∼2×10−19 cm3 just below the heavy hole exciton peak. With 20-ns carrier lifetime this corresponds to an effective nonlinear coefficient for cw beams of ‖n2‖≂2×10−4 cm2/W. This is appreciably larger than previous estimates and encouraging for room-temperature all-optical devices.

Theoretical and experimental aspects of the nonlinear spectroscopy of biexcitons in CuCl

Forward degenerate fourwave mixing in CuCl in the vicinity of the two-photon absorption on the biexciton can be analyzed from two complementary theoretical points of view :(a) In terms of the traditional perturbational formulation of nonlinear optics, the low intensity observations can be accounted for in terms of interferences and re-normalizations among different-order elementary mixing processes (b) In terms of a perturbational scheme which provides directly an analytic expression for the intensity-dependent dielectric function of the material. This last approach points to a potentially bistable optical response when local field effects are included in the calculation.

Propagation analysis of forward degenerate four-wave mixing

We discuss the propagation problem associated with the forward four-wave degenerate mixing induced by the third-order non-linear susceptibility <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\chi_{(-\omega; \omega, \omega, -\omega)}^{(3)} = \chi_{1}^{(3)} + i\chi_{2}^{(3)}</tex> . Exact analytical solutions are presented of two-photon resonances, evidencing the influence of the Kerr effect on the efficiency of the process. Around a two-photon resonance, we solve the problem of the nearly parallel propagation of two beams undergoing auto and induced two-photon absorption (TPA). The resonant interaction is studied in detail and analytical solutions are provided with operational accuracy for current experimental conditions. We show by the way that in the two-beam two-photon experiments, when the phase matching condition is fulfilled, although TPA is governed by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\chi_{2}^{(3)}</tex> , the real part of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\chi^{(3)}</tex> must be considered in a substantial way. All the above solutions are put in a form simple enough that the numerical computations can be performed on a programmable calculator.