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Journal of the Optical Society of America B

Interference effects in time-delayed degenerate four-wave mixing with broadband noisy light

Valery P. Kozich, Leonardo de S. Menezes, Cid Bartolomeu de Araujo

Published Jun 1, 2000• 11 citations
Publisher

Abstract

Femtosecond beats in time-delayed forward degenerate four-wave mixing (DFWM) with incoherent light in liquid and solid materials have been observed, and their origin is discussed. It is shown that the oscillations are due to the interference between pure DFWM signal and Rayleigh scattering from the excitation beams. It is also shown that, if this effect is not taken into account, incorrect conclusions can be reached.

DOI
10.1364/josab.17.000973

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Femtosecond beats in time-delayed forward degenerate four-wave mixing (DFWM) with incoherent light in liquid and solid materials have been observed, and their origin is discussed. It is shown that the oscillations are due to the interference between pure DFWM signal and Rayleigh scattering from the excitation beams. It is also shown that, if this effect is not taken into account, incorrect conclusions can be reached.
Signal intensity as a function of mutual delay time of three incoherent pump beams in the degenerate four-wave mixing (DFWM) process has been calculated with the second-order correlation time of the fields being much shorter than both the dephasing time T 2 and the inverse of the inhomogeneous broadening width δω. The results show that when broadening is purely homogeneous and extremely inhomogeneous, the curve of the DFWM signal intensity as a function of the delay time τ shows no peak shift, while when the inhomogeneous broadening is finite, the peak shift is related to the dephasing time T 2 and the inhomogeneous width δω, and can thus be used to estimate T 2.
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.
This dissertation presents experimental and theoretical studies of transient degenerate four wave mixing (DFWM) in organic dyes. Chapter 1 is an introduction to DFWM. Chapter 2 describes DFWM experiments that were performed in the gain medium of a dye laser. Chapter 3 presents the theory of DFWM of short pulses in three level saturable media. Chapter 4 presents DFWM experiments of femtosecond pulses in the saturable absorber of a passively modelocked ring dye laser. Chapter 5 presents the theory of DFWM of ultrashort pulses in resonant media.
Time-resolved three-beam degenerate four-wave mixing with incoherent light for observation of population relaxation, originally proposed by Morita . [ J. Opt. Soc. Am. B4, 1269 ( 1987)] is examined both theoretically and experimentally. Theoretical calculation shows that a large part of the decaying signal in the time-resolved profile originates from the ground-state relaxation if the excited-state relaxation is faster than the ground-state relaxation. It is also shown that the use of a nonzero delay time between the k2 and k1 beams, in addition to that between the k3 and k1 beams (ks = k1 − k2 + k3, where k1–3 and ks are the wave vectors for the incident and the scattered beams, respectively), provides information on population relaxation, especially when the population-relaxation time is far longer than the correlation time of the incoherent light. These theoretical considerations are verified experimentally with the use of a triphenylmethane dye in solution.