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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Four-wave mixing theory for two-photon generation of excitons in thin films of cuprous oxide

Igor V. Beloussov, John B. Ketterson, Yanyong Sun

Published Sep 10, 2010• 0 citations
Publisher

Abstract

We propose and theoretically investigate a two-photon four wave mixing experiment to probe for BEC of excitons in Cu2O thin films. A relatively simple set of equations describing the dynamics of the system is obtained for a particular configuration of the exciting beams, and numerical and approximate analytical solutions are found. The resulting phase-conjugated signal vs. the delay time between the pump and probe pulses yields a direct measure of the time evolution of the exciton condensate, and exhibit peaks when the film thickness is a multiple of a half wavelength of light.

DOI
10.1117/12.881329

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We propose and theoretically investigate a two-photon four wave mixing experiment to probe for BEC of excitons in Cu2O thin films. A relatively simple set of equations describing the dynamics of the system is obtained for a particular configuration of the exciting beams, and numerical and approximate analytical solutions are found. The resulting phase-conjugated signal vs. the delay time between the pump and probe pulses yields a direct measure of the time evolution of the exciton condensate, and exhibit peaks when the film thickness is a multiple of a half wavelength of light.
We propose and theoretically investigate a two-photon four-wave mixing experiment to probe for Bose-Einstein condensation of excitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O thin films. A relatively simple set of equations describing the dynamics of the system is obtained for a particular configuration of the three incident beams, and numerical and approximate analytical solutions are found. When one takes into account the boundary conditions, which result in reflections from the interfaces, the characteristics of the resulting phase-conjugated signal will exhibit Fabry-Perot-type oscillations. For film thicknesses equal to a multiple of a half wavelength in the film the resulting signal is enhanced by more than an order of magnitude relative thicknesses that are an odd multiple of a quarter wavelength. In this case the contribution from accompanying excitonic condensates with wave vectors $\ifmmode\pm\else\textpm\fi{}2\mathbf{k}$ is minimal. Therefore, the resulting phase-conjugated signal vs the delay time between the pump and probe pulses yields a direct measure of the time evolution only of the exciton condensate with wave vector k=0\mathbf{k}=\mathbf{0}k=0.
We propose and examine theoretically a four-wave-mixing experiment in which excitons in Cu2O{\text{Cu}}_{2}\text{O}Cu2​O are pumped directly into a state with wave vector k=0\mathbf{k}=\mathbf{0}k=0 by two counter-propagating cross-polarized laser pulses and which is subsequently probed by a third time-delayed pulse. Approximate analytical solutions of the time evolution equations are found which describe the time dependence of the exciton and photon densities. Most importantly, we obtain the dependence of the resulting phase-conjugated signal versus the delay time td{t}_{d}td​ between the probe and pump pulses. It is shown that the total number of photons generated in the course of the experiment is proportional to the areas of all three incoming pulses. The dependence of the resulting time-integrated signal on the delay time td{t}_{d}td​ is the same as the exciton density dependence on the time ttt. Hence, one may directly study the time evolution of the exciton condensate. The approximate analytical results are compared with a numerical solution of the evolution equations for a wide range of incident pulse intensities. It is noted that an exciton condensate arising by an alternate route can also be probed through a phase-conjugated two-photon process.
The experimental situation in which excitons in Cu 2 O are pumped directly into a state with wave vector k → = 0 → by two counter-propagating laser pulses , and subsequently probed by a third, time-delayed, pulse has been theoretically investigated. It has been shown that additional electromagnetic waves are excited in the system. A specific configuration of two pump pulses and one probe pulse has been found to generate only one additional electromagnetic wave. The dependence of the time-integrated photon number in this wave on the delay time between pump and probe pulses for some values of the detuning has been investigated.
The experimental situation in which excitons in Cu2O are pumped directly into a state with wave vector = k0 by two counter-propagating laser pulses, and subsequently probed by a third, time-delayed, pulse has been theoretically investigated. It has been shown that additional electromagnetic waves are excited in the system. A specific configuration of two pump pulses and one probe pulse has been found to generate only one additional electromagnetic wave. The dependence of the time-integrated photon number in this wave on the delay time between pump and probe pulses for some values of the detuning has been investigated.
We demonstrate the possibility of ultrafast optical control of excitons confined in GaAs thin films. The intensity of a two-beam degenerate four-wave-mixing signal changes with an increase in the power of each pulse. The signal intensity monotonically decreases after reaching the maximum. Peaks appear at different excitation powers for k 1 and k 2 pulses, which suggests that the decrease in the signal intensity is caused by excitonic Rabi oscillations. Our results demonstrate the possibility of ultrafast control of the exciton population by using optical pulses.
Abstract We present a study of optical phase conjugation through degenerate four-wave mixing in CuCl, as a function of light frequency, intensity, polarization and sample temperature. The phase-conjugate signal exhibits two maxima at the frequencies of the T5 exciton (one-photon resonance) and of the biexciton (two-photon resonance). By appropriate combinations of the input beam polarizations, it is possible to single out the various terms contributing to the signal (small-spaced, large-spaced population grating and two-photon coherent excitation). The absolute value of X(3) responsible for the two-photon resonance has been determined ( x(3) (-w,w,w, -w) = 3.10-7 e.s.u.). It leads to ‘mirror’ efficiencies of the order of 10% for input pump intensities I0 » 105 W cm -2 and sample thickness d» 10-4 cm. At higher I0, a saturation of the reflection takes place. The variation of the conjugate beam with temperature has been studied in the range 15 K < T <70 K. Finally, the phase-conjugate nature of the signal has been verified by inserting an aberrator in the path of the input probe beam, and by checking the reconstruction of the reflected beam.