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Journal of the Optical Society of America B

Degenerate four-wave mixing of femtosecond pulses in an absorbing dye jet

Jean‐Claude Diels, Ian C. McMichael

Published Apr 1, 1986• 28 citations
Publisher

Abstract

Intracavity measurements of degenerate four-wave mixing have been performed with femtosecond laser pulses to determine the phase relaxation time of the absorbing dye, diethyloxadicarbocyanine iodide (DODCI), in ethylene glycol. The influence of various broadening mechanisms (homogeneous, inhomogeneous, cross relaxation) and pulse parameters (frequency, pulse shape, phase modulation, and energy) is investigated. The dependence of the signal energy on probe delay is found to be strongly affected by the phase modulation of the pulse; hence determination of the phase relaxation time requires accurate diagnostics of the laser source. The rise of the signal provides an upper limit of 10 fsec for the phase relaxation time of the main absorption band of the dye DODCI. The decay of the signal is found to be related to the phase relaxation time of a two-photon absorption in the same dye. Accurate fitting of the data with the theory yields 50 ± 10 fsec for the dephasing time of the two-photon excitation in DODCI.

DOI
10.1364/josab.3.000535

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We study exciton dephasing in 8 nm GaAs quantum wells (QW) at 8 K by resonantly exciting the excitons at low densities. For this, we perform femtosecond degenerate four-wave mixing (DFWM) measurements using two laser beams. The excitons in the QWs are inhomogeneously broadened, with a photoluminescence linewidth of 1.8 meV. We investigate how the time integrated DFWM signal and its decay rate $\ensuremath{\eta}$ change as the average intensity of either of the two exciting beams is varied separately. We find that the dependence of $\ensuremath{\eta}$ on the intensity of the first pulse is about twice as that for the delayed pulse. We compare the results with a theory based on optical Bloch equations and relaxation rate approximation, accounting phenomenologically for dephasing due to exciton-exciton scattering.

Physical review. B, Condensed matter•Dec 22, 2000•2 citations
Intracavity measurements of degenerate four-wave mixing have been performed with femtosecond laser pulses to determine the phase relaxation time of the absorbing dye, diethyloxadicarbocyanine iodide (DODCI), in ethylene glycol. The influence of various broadening mechanisms (homogeneous, inhomogeneous, cross relaxation) and pulse parameters (frequency, pulse shape, phase modulation, and energy) is investigated. The dependence of the signal energy on probe delay is found to be strongly affected by the phase modulation of the pulse; hence determination of the phase relaxation time requires accurate diagnostics of the laser source. The rise of the signal provides an upper limit of 10 fsec for the phase relaxation time of the main absorption band of the dye DODCI. The decay of the signal is found to be related to the phase relaxation time of a two-photon absorption in the same dye. Accurate fitting of the data with the theory yields 50 ± 10 fsec for the dephasing time of the two-photon excitation in DODCI.
The saturable absorber dye jet of a femtosecond ring dye laser provides an ideal candidate for the study of fast transients in de- generate four-wave mixing (DFWM). Since the counterpropagating pulses in the ring laser meet at the absorber jet, the problem of timing the DFWM pump pulses is solved. The energy of the pulses inside the cavity is such that the absorber is saturated. This meets one of the conditions for efficient DFWM in saturable media.1 Since the dye jet is thin, fast transients in DFWM are not masked by propagation effects.
The nonlinear absorption of intense laser light is used to obtain information about the times required for spectral cross relaxation (T3{T}_{3}T3​) and collisional dephasing (T2{T}_{2}T2​) in organic-dye solutions. The steady-state transmission experiment of Huff and DeShazer indicates that T2{T}_{2}T2​ is in the range 0.1-1 psec for cryptocyanine-methanol, while T3{T}_{3}T3​ is in the range 1-10 psec. For DDI-glycerin (1, 1\ensuremath{'}-diethyl-2, 2\ensuremath{'}-dicarbocyanine-iodide-glycerin), measurements of ultrashort-pulse transmission as a function of incident energy and optical polarization suggest a value ${T}_{2}=0.4\ifmmode\pm\else\textpm\fi{}0.2$ psec for that system. These results are based on a new set of rate equations for absorption by inhomogeneously broadened organic-dye solutions. The equations display the effects of spectral cross relaxation and are not limited to light intensities less than those at which coherent interaction effects become important. For the case of ultrashort incident pulses, the equations are extended to account for excited-state absorption, the dependence of absorption on optical polarization, and the existence of a multiplicity of interacting excited states.
A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.
A novel transient three-pulse scattering technique for measuring ultrafast dephasing times in condensed matter is analyzed using a perturbative solution of the density matrix equation. The advantages of this technique include subpulsewidth resolution, a clear distinction between homogeneous and inhomogeneous broadening, and sensitivity to spectral cross-relaxation. Its application to the case of a multilevel resonance is also considered. We report results of femtosecond dephasing experiments with dye molecules in liquids and in a polymer host. The dephasing time is determined to be less than 20 fsec for dyes in solution at room temperature. At low temperatures in polymers, a transition from homogeneous to inhomogeneous broadening has been observed and studied as a function of temperature.
We study exciton dephasing in 8 nm GaAs quantum wells (QW) at 8 K by resonantly exciting the excitons at low densities. For this, we perform femtosecond degenerate four-wave mixing (DFWM) measurements using two laser beams. The excitons in the QWs are inhomogeneously broadened, with a photoluminescence linewidth of 1.8 meV. We investigate how the time integrated DFWM signal and its decay rate $\ensuremath{\eta}$ change as the average intensity of either of the two exciting beams is varied separately. We find that the dependence of $\ensuremath{\eta}$ on the intensity of the first pulse is about twice as that for the delayed pulse. We compare the results with a theory based on optical Bloch equations and relaxation rate approximation, accounting phenomenologically for dephasing due to exciton-exciton scattering.