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The Journal of Chemical Physics

Optical density effects in photon echo experiments

Radley W. Olson, Howard W. H. Lee, Frank G. Patterson, M. D. Fayer

Published Jan 1, 1982• 79 citations
Publisher

Abstract

The effects of optical density (OD) on photon echo experiments is examined both theoretically and experimentally. The theoretical treatment involves coupled Maxwell-Optical Bloch equations, and the experiments are picosecond photon echo studies of the mixed molecular crystal, pentacene in naphthalene. Under high power excitation (π/2, π) in high OD samples, the echo decays are predicted and observed to be faster than decays arising solely from the intrinsic molecular T2. The increase in the echo decay rate vanishes in the limit of low power or low OD, permitting the intrinsic molecular T2 to be measured. Previously reported concentration effects are shown to actually be optical density effects. The experimentally determined intrinsic molecular T2 of pentacene in naphthalene is shown to be independent of concentration and temperature (below ∼2 K) and T2≠2T1. It is suggested that the difference between T2 and 2T1 is due to the static multiplet level structure arising from the electronic state-phonon coupling.

DOI
10.1063/1.442725

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High pressure photon echo results are presented for pentacene doped naphthalene, pentacene doped (triclinic and monoclinic) p-terphenyl, and rhodamine doped PMMA. Figure 1 illustrates typical photon echo intensity decays in a high pressure diamond anvil cell at variable low temperatures. The effect of pressure and temperature on the homogeneous dephasing is used to characterize the interactions between the impurity molecule and the host crystal, as well as provide a unique probe of local polymorphic phase changes.

International Conference on Ultrafast Phenomena•Jan 1, 1994•0 citations
The effects of optical density (OD) on photon echo experiments is examined both theoretically and experimentally. The theoretical treatment involves coupled Maxwell-Optical Bloch equations, and the experiments are picosecond photon echo studies of the mixed molecular crystal, pentacene in naphthalene. Under high power excitation (π/2, π) in high OD samples, the echo decays are predicted and observed to be faster than decays arising solely from the intrinsic molecular T2. The increase in the echo decay rate vanishes in the limit of low power or low OD, permitting the intrinsic molecular T2 to be measured. Previously reported concentration effects are shown to actually be optical density effects. The experimentally determined intrinsic molecular T2 of pentacene in naphthalene is shown to be independent of concentration and temperature (below ∼2 K) and T2≠2T1. It is suggested that the difference between T2 and 2T1 is due to the static multiplet level structure arising from the electronic state-phonon coupling.
In this paper we investigate the influence of optical density or superradiance on the photon echo decay using the coupled Maxwell–Bloch equations. Our theory applies to optically thick but dilute media, where the transition dipole–dipole interaction between nearby chromophores is negligible, but the far-field interaction is not. Corrections to the (normalized) echo decay in the optically thin limit, INe(tπ)=exp [−4tπ/T2] (tπ and T2 are the interpulse separation times and the coherence relaxation times, respectively), are found by expanding the polarization, excited state population and pulse electric fields in powers of ζ=αz, where α is the inverse Beer’s absorption length, and z is the coordinate along the pulse propagation axis. Numerical solutions for optically thick samples are also presented, and when ζ≫1 the normalized echo intensity is found to obey the simple analytic form: INe(tπ)=2 exp [−tπ/T1]−1, when tπ/T1<ln 2 and INe(tπ)=0 for longer times. (T1 is the population relaxation time.) In this limit the echo decay is independent of the coherence relaxation time T2, illustrating the profound effect intermolecular coupling may have on any nonlinear optical measurement. We show that at low temperatures, when T2=2T1, the echo decay rate increases as the optical density increases. However, for higher temperatures, when T2 is sufficiently shorter than 2T1, the opposite behavior results, that is, the echo decay rate decreases as the optical density increases.
Picosecond optical coherence techniques are employed to study dynamical intermolecular interactions in low concentration mixed molecular crystals, i.e., pentacene in naphthalene at 1.4 K. A concentration-dependent broadening of the optical homogeneous line is observed. Stimulated photon echo measurements rule out excited state transport as the broadening mechanism. The photon echo results exhibit a linear concentration dependence and a theory is proposed that accounts for the broadening in terms of phonon-induced fluctuations in guest–guest dipole–dipole interactions. Detailed considerations indicate that the system is best described in terms of localized excitations rather than delocalized impurity band states. In the low concentration limit, there is additional broadening of the homogeneous line beyond that produced by the lifetime. A model is presented describing this broadening in terms of phonon-induced modulation of the guest–host van der Waals interactions, i.e., in terms of a fluctuating crystal shift.
Abstract Photon echo decay time is measured for pentacence molecules introduced in naphthalene and p-terphenyl crystals with rather high concentrations (10−6–105 mol/mol) at temperatures between 1.6 K and 4.1 K, using a tunable picosecond laser system consisting of a mode-locked YAG laser and a parametric oscillator. In naphthalene echo decay time increases with lowering temperature approaching a constant value below 2 K, but in p-terphenyl it is almost constant. The phase relaxation time at very low temperature is much shorter than twice the population relaxation time in both crystals, indicating that pure dephasing processes exist. Analyzing the results it turns out that there exsists a pure dephasing process which is temperature-independent and is very probably due to interactions between pentacene molecules, in addition to the temperature-dependent dephasing process due to the scattering of pseudolocalized phonons.
We calculate the photon echo decay for a strongly coupled electron–phonon system, without making unrealistic assumptions about excitation pulse durations. We find that asymptotically, the photon echo decay is exponential, and we provide a formal expression for the decay rate 1/T2 which is independent of pulse duration. In contrast to the usual results, our expression for 1/T2 is nonperturbative in the electron–phonon interaction. We calculate the dependences of the echo amplitude on pulse power and duration, finding that the strong electron–phonon coupling modifies the simple two level system result. We also focus on the relationship between the zero phonon line shape in the homogeneous optical absorption spectrum, and the photon echo decay rate. We find that the zero phonon line shape is Lorentzian, with width 1/πT2. We show that the usual optical Bloch equation approach to analyzing time-domain experiments, which normally is only applicable if the electron–phonon coupling is weak, can be extended to the case of strong coupling. These strong coupling Bloch equations are adequate for analyzing the time dependence, but not the pulse power and duration dependences, of time-domain experiments. Our results indicate that within the Condon approximation, electron–phonon coupling cannot explain the very low temperature anomaly of recent photon echo experiments on impurities in molecular crystals.
Optical dephasing due to intermolecular interaction is studied for pentacence molecules introduced in naphthalene and p -terphenyl crystals by measuring the ordinary photon echo and the accumulated three-pulse echo. It is found that the reciprocal of pure dephasing time increases linearly with the guest molecule concentration at low temperature where pure dephasing is known to be temperature-independent. A new model based on virtual transfer of excitation energy, i.e. energy transfer without phonon asistance, between guest molecules is presented to interpret this dephasing process. It is shown that observed linear dependence of the line width representing pure dephasing is well interpreted by this model, and that the calculated relationship between the line width and concentration agrees with the experimental one within a factor of about two.
High pressure photon echo results are presented for pentacene doped naphthalene, pentacene doped (triclinic and monoclinic) p-terphenyl, and rhodamine doped PMMA. Figure 1 illustrates typical photon echo intensity decays in a high pressure diamond anvil cell at variable low temperatures. The effect of pressure and temperature on the homogeneous dephasing is used to characterize the interactions between the impurity molecule and the host crystal, as well as provide a unique probe of local polymorphic phase changes.