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arXiv:1210.2869 · Physical Review A

All-optical delay of images by backward four-wave mixing in metal-nanoparticle composites

Kwang‐Hyon Kim, Anton Husakou, Joachım Herrmann

Published Apr 26, 2013• 2 citations
arXivHTMLPDF

Abstract

We theoretically study a method for all-optical delay of images based on backward four-wave mixing in composites containing metal nanoparticles. In this approach a delayed phase-conjugate probe pulse is generated by the interaction of two counterpropagating pump beams and a noncollinear shaped probe pulse in the nanocomposite. The fractional delay and the reflectivity for the phase-conjugate signal pulses are studied as functions of the input pump intensity. It is shown that this scheme can be used for delayed imaging combined with the elimination of optical diffraction. The advantages of this method include miniaturized design, tunable wavelength range up to the telecommunication range, and wide bandwidth.

DOI
10.1103/physreva.87.045805

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We theoretically study a method for all-optical delay of images based on backward four-wave mixing in composites containing metal nanoparticles. In this approach a delayed phase-conjugate probe pulse is generated by the interaction of two counterpropagating pump beams and a noncollinear shaped probe pulse in the nanocomposite. The fractional delay and the reflectivity for the phase-conjugate signal pulses are studied as functions of the input pump intensity. It is shown that this scheme can be used for delayed imaging combined with the elimination of optical diffraction. The advantages of this method include miniaturized design, tunable wavelength range up to the telecommunication range, and wide bandwidth.
A slowing down of light pulses using backward-wave four-wave mixing is achieved in photorefractive crystals with different coupling strength. The delay and width of the output pulse are studied as a function of the input pulse width and pump intensity ratio for the amplified transmitted beam and for the phase-conjugated beam. The delay characteristics are compared with those of the two-beam coupling. It is demonstrated that the four-wave mixing process ensures a larger slowing down of short pulses (pulses with width shorter than the photorefractive response time) as compared to the photorefractive two-beam coupling scheme and guarantees the elimination of forerunners. The delay of long pulses in the four-wave mixing configuration is almost the same as the one that can be reached with two-beam coupling. The effect of absorption on the nonlinear shape transformation of the output pulses is discussed qualitatively.
The slowing down of light pulses is achieved using backward-wave four-wave mixing in a medium with local response. A Bi12TiO20 crystal with an external dc field is used in the experiment as a proof-of-concept material. The delay and shape transformation of output pulses are studied and compared for the transmitted and phase conjugate channels. It is shown that the phase conjugate pulse achieves a longer delay under typical experimental conditions with equal intensities of the pump beams. This advantage of the phase conjugate beam is especially pronounced for short pulses with half-widths smaller than the response time of the medium. The agreement of the experimental results with numerical calculations confirms the validity of the previously developed theoretical model. Analytical solutions are derived for input pulses with triangular shapes.
We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the 3s2S1∕23s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}3s2S1∕2​, F=2F=2F=2, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, F=3F=3F=3, mF=3{m}_{F}=3mF​=3 transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.
The nonlinear phase shift per unit length acquired by the transmitted and phase conjugate waves in backward-wave four-wave mixing may be considered as an effective refractive index. Consequently, a narrow spectrum of the nonlinear phase shift in non-degenerate frequency interaction corresponds to natural dispersion and such interaction may be used for temporal manipulation of light pulses. Analysis of the narrow spectra of the nonlinear phase shift shows high potential of the backward-wave four-wave for slowing down of light pulses. The slowing down is achieved using backward-wave four-wave mixing in media with local and nonlocal response. The delay and shape transformation of output pulses are studied and compared for the transmitted and phase conjugate channels. It is shown that the phase conjugate pulse achieves a longer delay under typical experimental conditions.
This paper presents an exact solution to the slowly varying envelope equations for the probe and signal fluxes in degenerate four-wave mixing in Kerr media. The analysis is performed for a noncollinear geometry, and all beams have the same linear polarization in the nonlinear medium. It is assumed that the angle separating the directions of the counterpropagating pumps and probe and signal beams is large enough so that cross-coupled waves do not contribute to the envelope equations describing the spatial evolution of the pump, probe, and signal beams. Multiple values of the transmitted probe are obtained for equal pump fluxes above a threshold determined by the nonlinear phase shift in the medium. Significant pump depletion occurs in this regime, but it can also occur without the appearance of multiple solutions. Since exact optical phase conjugation occurs only in the limit where the pumps are undepleted in Kerr media, this result implies that there are fundamental upper limits on the pump intensity that can be used to increase signal reflectivities in optical phase conjugation.