Phase-conjugate Degenerate Four-wave Mixing Research Articles

Measurement of lithium isotope ratio in various concentration samples using degenerate four-wave mixing.

Phase-conjugate degenerate four-wave mixing (PCDFWM), as a sub-Doppler spectroscopy technique, can be employed to selectively analyze Li isotopes. It is necessary to explore the optimal incident powers in order to measure the Li isotope ratio accurately. In this case, the power condition of PCDFWM signal is first investigated using samples with various concentrations. The results indicate that the power characteristic is intimately related to the sample concentration, and the optimal incident power conditions for different sample concentrations are different. Under their own optimized power conditions, we measured the Li7/Li6 isotope ratio in Li standard solutions of 500, 300, and 200ng/ml. The corresponding results are, respectively, 11.571±0.003, 11.552±0.003, and 11.582±0.004, which are in good agreement with the value calculated by atomic absorption spectroscopy. The information obtained from this study suggests that PCDFWM can be used to measure isotope ratios accurately in samples with different concentrations under suitable power conditions.

Measurement of 7Li/6Li Isotope Ratio Using Phase-Conjugate Degenerate Four-Wave Mixing in a Graphite Furnace

To obtain a Doppler-free resolution, we employ phase-conjugate degenerate four-wave mixing (PCDFWM) to isotope selectively analyze <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> Li and <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> Li in a graphite furnace atomizer. After the investigation of concentration and power dependences of PCDFWM, the optimal sample concentration and power conjugation are determined. Under the optimized conditions, we measured <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> Li/ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> Li isotope ratio in Li standard solution with PCDFWM to be 11.571 ± 0.003, which is in good agreement with the value calculated by atomic absorption spectroscopy but has a preferable resolution. The detection limit as 15.54 ng/mL is achieved. The information obtained from this paper suggests that PCDFWM is a reliable laser spectroscopic technique with high resolution in isotope ratio measurement and trace analysis for various applications such as geochemical exploration.

Resolution for Forward and Phase-Conjugate Degenerate Four-Wave Mixing in Hot Atomic Media

Resolutions of degenerate four-wave mixing with forward and phase-conjugate configurations (FDFWM and PCDFWM) are investigated and compared theoretically and experimentally in hot rubidium (Rb) atomic vapor. The theoretical simulations indicate that PCDFWM is of much higher resolution than FDFWM. The resolution of PCDFWM is less dependent on Doppler broadening. The experimental results are in good agreement with the theoretical expectation. PCDFWM can resolve the hyperfine transitions and crossover resonances of 87Rb which cannot be achieved by FDFWM. Additionally, with sample temperature increasing, the linewidth of FDFWM spectrum obviously broadens. In comparison, no obvious broadening can be observed in the PCDFWM spectrum.

Kinetic temperature and electron density measurement in an inductively coupled plasma torch using degenerate four-wave mixing

Laser wave mixing is presented as an effective technique for spatially resolved kinetic temperature measurements in an atmospheric-pressure radio-frequency inductively coupled plasma. Measurements are performed in a 1 kW, 27 MHz radio-frequency plasma using a continuous-wave, tunable 811.5 nm diode laser to excite the 4s3P2→4p3D3 argon transition. Kinetic temperature measurements are made at five radial steps from the center of the torch and at four different torch heights. The kinetic temperature is determined by measuring simultaneously the line shape of the sub-Doppler backward phase-conjugate degenerate four-wave mixing and the Doppler broadened forward-scattering degenerate four-wave mixing. The temperature measurements result in a range of 3,500 to 14,000±150 K. Electron densities measured range from 6.1 (±0.3)×1015 cm−3 to 10.1 (±0.3)×1015 cm−3. The experimental spectra are analyzed using a perturbative treatment of the backward phase-conjugate and forward-geometry wave-mixing theory. The Stark width is determined from the collisional broadening measured in the phase-conjugate geometry. Electron density measurements are made based on the Stark width. The kinetic temperature of the plasma was found to be more than halved by adding deionized water through the nebulizer.

Calculations of Stark-broadened line shapes in phase-conjugate degenerate four-wave mixing laser spectroscopy

The Stark-broadened line shapes for phase-conjugate degenerate four-wave mixing (PCDFWM) laser spectroscopy are studied. The line profiles are calculated for high-density (N(e) > 10(21) m(-3) plasma conditions and for different contributions of the Doppler broadening. Calculations are performed in the limit of low laser intensities using the perturbation approach. The theoretical model takes into account the Stark effect together with the ion dynamics, the electron collisions, and the Doppler effect. The resultant PCDFWM spectral profiles are significantly less broadened and less asymmetric than the emission profiles but shifted by similar magnitudes. Moreover, the results of our calculations show the sub-Doppler character of the PCDFWM profiles and also their strong dependence on the geometric configuration of the pump and the probe laser beams.

Detailed velocity-dependent line shapes for degenerate four-wave mixing spectra in a two-level atomic system

We study phase-conjugate degenerate four-wave mixing in an optically pumped, two-level atomic system (the ${3s}^{2}{S}_{1/2},$ $F=2,$ ${m}_{\mathrm{F}}=\stackrel{\ensuremath{\rightarrow}}{2}{3p}^{2}{P}_{3/2},$ $F=3,$ ${m}_{\mathrm{F}}=3$ transition in a diffuse, collision-free, thermal beam of sodium). In this investigation, we study the detailed line shape and strength of the four-wave mixing signal as a function of the intensity of the cw pump waves, and of the velocity of the atoms. Our technique allows us to examine the four-wave mixing interaction under conditions in which the Doppler shift, the natural linewidth of the transition, and the Rabi frequency for the interaction are each comparable with one another. From our experimental measurements and computational results, we show that the line shapes are very complex in this regime, and that they depend sensitively upon the atomic velocity, especially in the case when the intensity of the forward and backward pump beams exceeds the saturation intensity for the transition.

Theory of forward degenerate four-wave mixing in two-level saturable absorbers

A theoretical description for a forward degenerate four-wave mixing process in homogeneously broadened two-level absorbers with arbitrary intensities of all four beams is presented. Assuming no pump absorption and depletion, we obtain an analytical solution of forward degenerate four-wave mixing signal intensity in the limit of the strong pumps and weak probe and signal. In the case of low absorption or large detuning, this solution is shown to become equivalent to that of the phase-conjugate degenerate four-wave mixing derived by Abrams and Lind [Opt. Lett.2, 94 (1978)]. For arbitrary beam intensities and absorption parameters, the signal intensity is numerically calculated by solution of the coupled equations of complex wave amplitudes. Comparing the results of the numerical calculation with those of the analytical solution, we discuss the validity of using the analytical solution in practical experiments and show the saturation behavior that is due to the strong probe beam. The line shapes under the various ratios among the input beams and absorption parameters are also obtained and discussed.

Degenerate phase-conjugate four-wave mixing in a nearly-Doppler-free two-level atomic medium

We present experimental observations of phase-conjugate degenerate four-wave mixing in a two-level atomic system (the ${3s}^{2}{S}_{1/2}, F=2, {m}_{F}=\stackrel{\ensuremath{\rightarrow}}{2}{3p}^{2}{P}_{3/2}, F=3, {m}_{F}=3$ transition in a diffuse, collision-free, thermal beam of atomic sodium) driven by cw, narrow-band $(\ensuremath{\sim}250 \mathrm{kHz}),$ stabilized pump and probe fields. The primary measurements that we report are of the peak signal strength of the four-wave-mixing interaction and the bandwidth of the four-wave-mixing spectrum (as the laser frequency is tuned through the resonant frequency) as a function of the intensity of the pump field. We compare these measurements with the predictions of a theoretical analysis in which extension to include the effect of the small transverse velocity $(\ensuremath{\sim}3 \mathrm{m}/\mathrm{s}\mathrm{e}\mathrm{c})$ of the atomic beam is critical. These measurements provide a direct verification of the theory of this important nonlinear interaction.

On the interpretation and rotational assignment of degenerate four-wave mixing spectra: Four-photon line strengths for crossover resonances in NO A 2Σ+–X 2Π

We present here a set of equations specifically adapted to simulation of fully resonant, high-resolution, phase-conjugate degenerate four-wave mixing (DFWM) in molecular gases. Signal-intensity dependence on molecular wave functions, lifetimes, and laser beam polarizations is explicitly included in these equations. The emphasis of the presentation is on both physically intuitive interpretation and a practical, ‘‘cookbook’’ approach to spectral simulation. We present experimental verification of our calculations drawn from the spectrum of dilute NO in N2 at low pressures. Both degenerate two-level and three-level (crossover) resonances were observed. The experimental spectral intensities are accurately reproduced by the expressions presented here. We point out some of the subtleties of DFWM spectra that could be used as aids to interpretation, especially the use of laser polarization as a probe for spectral line assignments.

Phase conjugate degenerate four-wave mixing in molecular aggregates

Abstract We investigate phase conjugate degenerate four-wave mixing (DFWM) in molecular aggregates consisting of N interacting, homogeneously broadened two-level systems in a cyclic configuration with a dimension much smaller than an optical wavelength. The interaction includes both the static dipole-dipole coupling and superradiant coupling. We show that, in general the size dependence of χ(3) is determined by the relative magnitudes of the homogeneous dephasing rate and the superradiant decay rate. We predict the existence of a narrow dephasing-induced resonance superposed on the broader superradiant exciton lineshape.

Nonlinear susceptibilities of molecular aggregates: Enhancement of chi (3) by size.

We investigate the third-order nonlinear-optical susceptibility ${\ensuremath{\chi}}^{(3)}$ in molecular aggregates and its scaling with aggregate size. The aggregate is modeled as a collection of N-interacting, homogeneously broadened two-level systems, where the interaction includes both the static dipole-dipole coupling and superradiant coupling. Our expression for ${\ensuremath{\chi}}^{(3)}$, derived using Liouville-space Green-function techniques, contains contributions from excitons as well as biexcitons. The scaling of ${\ensuremath{\chi}}^{(3)}$ with aggregate size and its dependence on the laser detuning and homogeneous and inhomogeneous dephasing rates are analyzed. ${\ensuremath{\chi}}^{(3)}$ contains terms that scale as \ensuremath{\sim}${N}^{2}$ and \ensuremath{\sim}N(N-1). However, under off-resonant conditions these terms interfere destructively, resulting in a linear \ensuremath{\sim}N scaling, which is precisely what is expected for N monomers. Detailed calculations of phase-conjugate degenerate four-wave mixing and pump-probe spectroscopy are performed. In the first case we predict the existence of a narrow dephasing-induced resonance superposed on the broader superradiant exciton line shape. Pump-probe spectroscopy shows a series of biexciton absorption lines, some of which are superradiantly broadened.