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Physical Review A

Delayed four-wave-mixing spectroscopy in molecular crystals: A nonperturbative approach

D. P. Weitekamp, Koos Duppen, Douwe A. Wiersma

Published Jun 1, 1983• 30 citations
Publisher

Abstract

The delayed or time-domain four-wave-mixing experiment is treated in the regime of intense near-resonant pulses. The interaction with the radiation during both pump and probe pulses is considered to all powers of the electric field amplitude. Analytical results are obtained for an effective four-level system. These include the dependence of the coherence amplitudes on the ratio of the pump-field intensities when there is a large vibrational discrepancy between ground and excited electronic states and a general solution for the unitary time development during the probe pulse. For the first time, delayed coherent anti-Stokes Raman scattering is detected from highly dilute (10-ppm) guest molecules. Illustrative examples are presented for the system of pentacene in benzoic acid at low temperature. Vibronic-free induction decay and the effect of field inhomogeneity across the beam profile are found to be essential for understanding the observed intensity and spectral distribution of the signal beam in the region of optimum pulse intensity.

DOI
10.1103/physreva.27.3089

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We predict that the four-wave mixing (FWM) excitation spectrum for a two-level system becomes extremely asymmetrical when steady-state excitation is replaced by pulsed excitation, using temporally nonoverlapping probe and pump pulses. We also show that when a resonant probe pulse precedes the detuned pump pulse, the FWM signal may become more intense than when the pulses overlap. These effects are attributed to free-induction decay (FID): the coherence induced in the two-level system by a short resonant probe pulse survives the pulse (FID) and replaces it in producing a strong nonlinear signal on interaction with the strong pump pulse. Moreover, by plotting the FWM signal intensity as a function of the delay between the probe and pump pulses, an efficient method is proposed for determining short transverse relaxation times or fast chemical reaction rates.

The Journal of Physical Chemistry A•Nov 1, 1998•2 citations
The delayed or time-domain four-wave-mixing experiment is treated in the regime of intense near-resonant pulses. The interaction with the radiation during both pump and probe pulses is considered to all powers of the electric field amplitude. Analytical results are obtained for an effective four-level system. These include the dependence of the coherence amplitudes on the ratio of the pump-field intensities when there is a large vibrational discrepancy between ground and excited electronic states and a general solution for the unitary time development during the probe pulse. For the first time, delayed coherent anti-Stokes Raman scattering is detected from highly dilute (10-ppm) guest molecules. Illustrative examples are presented for the system of pentacene in benzoic acid at low temperature. Vibronic-free induction decay and the effect of field inhomogeneity across the beam profile are found to be essential for understanding the observed intensity and spectral distribution of the signal beam in the region of optimum pulse intensity.
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 general theory of transient stimulated Raman scattering and the phase-matching diagrams are developed based on an interaction Hamiltonian which includes all the possible competing interaction channels. In a Raman system pumped by multiple crossing beams with multiple Stokes and anti-Stokes components, these channels are defined by the interactions among fields at different frequencies and/or k vectors of the pump pairs and Stokes and anti-Stokes fields. An ensemble-averaged equation of motion for the active phonon mode is derived within the Markovian approximation in which the phonon-phonon coupling (pressure effect) is reduced to an energy relaxation and a phase fluctuation. A complete set of transient coupled equations including phase modulation, Stark shift, medium (anharmonic) saturation, and all the possible four-wave-mixing channels is presented. In the transient regime, it is found that the effects of the Stark shift on the Raman efficiency are mainly governed by the input pump energy in contrast to the steady-state theory where the pump intensity plays the main role. Both analytic and numerical methods are developed in describing the nonlinear effects due to the energy feedback mechanism in the strong pump-depletion regime. Twelve possible four-wave-mixing channels are analyzed for nonlinear phase diagrams characterized by the angles among pump pairs, and Stokes and anti-Stokes fields. Finally, numerical examples are shown for the effects of the coherence lengths of high-order Stokes fields and pump pairs on the generation of low-order Stokes fields.
New radiation-matter phenomena in four-wave mixing spectroscopies, given a theoretical basis in the preceding paper [Dugan and Albrecht, Phys. Rev. A 43, 3877 (1991)], are examined experimentally here. A new class of Rabi detuning oscillations is recorded in interferometric coherent Stokes Raman scattering (CSRS). Two identical nanosecond incoherent light fields are mutually delayed, while simultaneously mixing in a nonlinear medium with a narrow-band field of a different color. Spectral filtering of the CSRS signal is essential. From such signals the frequencies and the dephasing rate constants can be a measure of the Raman-active vibrations in both the electronic ground state and the electronic excited state of the scattering chromophore. In principle, analogous probing of vibronic transitions is possible. Detuning oscillations for multimode systems are presented. It is shown how they are transformed into quantum beats, exactly those seen with femtosecond CSRS, when the narrow-band field is made broad and/or the detection is ``white.'' Finally, an example of the sub-Raman linewidth spectral feature, predicted in the preceding paper, is presented. It determines a Raman frequency, but does not carry its linewidth.
Resonance-enhanced four-wave-mixing processes were studied in molecular iodine by detection of a wave generated at frequency ${\mathrm{\ensuremath{\omega}}}_{3}$=2${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$ for a wide range of Raman frequencies (${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$). On the basis of known spectroscopic constants of the two electronic states involved, the electronic ground state X1{\mathit{X}}^{1}X1${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ and the electronic excited state B3{\mathit{B}}^{3}B3${\mathrm{\ensuremath{\Pi}}}_{\mathit{u}0}^{+}$, an interpretation of the spectral features in terms of three essentially different four-wave-mixing processes is given. Resonance enhancement through bound states with discrete energy levels and the enhancement effect by dissociative continuum states are considered. In addition to resonance-enhanced coherent anti-Stokes Raman-scattering (CARS) processes, in which the Raman resonances are in the electronic ground state, two resonant schemes are identified in I2{\mathrm{I}}_{2}I2​, in which Raman resonances in an excited state are probed: excited-state parametric and nonparametric CARS. The latter process is an example of electronic population transfer in a four-wave-mixing cycle.
A theory of quantum beats in a Stokes signal observed in pump-probe experiments upon excitation of four-level atoms with two close upper lying levels by femtosecond laser pulses is developed. Quantum beats arise in the intensity of the Stokes field due to the interference of two atomic wave packets generated by ultrashort pump and probe pulses. An analytical solution of the non-steady-state Maxwell-Bloch equations is obtained, and the dependence of the Stokes radiation intensity on the delay time between two laser pulses is investigated. The theoretical results describe qualitatively well the observed features of quantum beats.
We predict that the four-wave mixing (FWM) excitation spectrum for a two-level system becomes extremely asymmetrical when steady-state excitation is replaced by pulsed excitation, using temporally nonoverlapping probe and pump pulses. We also show that when a resonant probe pulse precedes the detuned pump pulse, the FWM signal may become more intense than when the pulses overlap. These effects are attributed to free-induction decay (FID): the coherence induced in the two-level system by a short resonant probe pulse survives the pulse (FID) and replaces it in producing a strong nonlinear signal on interaction with the strong pump pulse. Moreover, by plotting the FWM signal intensity as a function of the delay between the probe and pump pulses, an efficient method is proposed for determining short transverse relaxation times or fast chemical reaction rates.