We present a theoretical description of the generation and detection of photon echoes, stimulated from an accumulated frequency grating in the inhomogeneous distribution. We show that detection of the echoes takes place via interference in the sample between a properly phased and directed probe pulse and the echo polarization. In this description the echo phenomenon emerges as an induced transparency of the sample rather than a burst of coherent radiation. By solving simultaneously the optical Bloch and Maxwell equations, an expression is obtained which correlates quantitatively the echo intensity to the decay parameters, pulse intensity, and the transition moment. As an application of the theory we present results on the intersystem crossing of pentacene in naphthalene at 1.5 K.
We present a theoretical description of the generation and detection of photon echoes, stimulated from an accumulated frequency grating in the inhomogeneous distribution. We show that detection of the echoes takes place via interference in the sample between a properly phased and directed probe pulse and the echo polarization. In this description the echo phenomenon emerges as an induced transparency of the sample rather than a burst of coherent radiation. By solving simultaneously the optical Bloch and Maxwell equations, an expression is obtained which correlates quantitatively the echo intensity to the decay parameters, pulse intensity, and the transition moment. As an application of the theory we present results on the intersystem crossing of pentacene in naphthalene at 1.5 K.
A theory has been developed describing probe pulse-detected accumulated stimulated photon echo experiments on inhomogeneously broadened electronic transitions. This theory gives a more quantitative description of these experiments than the theory previously developed by Hesselink and Wiersma [J. Chem. Phys. 75, 4192 (1981)]. At the same time, the present theory provides numerical instead of analytical results. A better founded insight is obtained in the possibilities and limitations of the accumulated photon echo method. The main conclusion is that the measured echo decay curves are still expected to give T2 directly, thus maintaining the value of the accumulated echo technique as a convenient method to determine picosecond dephasing times. It is concluded that the probe pulse detected accumulated echo method is not readily applied to accurate determinations of intersystem crossing yields.
The three pulse stimulated echo, long known in magnetic resonance (1), has more recently been demonstrated on optical transitions(2). An interesting way of looking at the stimulated-echo-formation relies on the fact that the first two excitation pulses create an "ordered" population as a function of detuning .This ordered population can also be looked upon as a " grating " in frequency space from which a probe pulse can "reflect" an echo. Since a grating in only one of the levels suffices, a corollary is that the echo may be stimulated at some entirely different frequency ω2 than the one ω1, at which the grating was prepared. We report the observation of such a connected two-color stimulated echo(C2CSE) in a solid and use it to confirm the relaxation out of the 747 cm−1 vibrational state of the S1 manifold of pentacene in naphthalene. It has also been realized (3) that after redistribution of the initially excited population grating, that the echo may be stimulated from any state into which the grating has relaxed. We report here the first observation of such a relaxed two-color stimulated echo(R2CSE) and note that this echo can be seen as the optical analogue of the cross-relaxation peak in a two-dimensional nmr spectrum. The rise and fall of this relaxed echo can be used as a probe for the vibrational deactivation pathway(s) subsequent to excitation of various vibrational levels in the S1 manifold. Prior to discussing briefly some of the results we note that from an analysis of this echo effect it is clear that a necessary prerequiste to observation of such two-color photon echoes is that the inhomogeneous broadening on the selected transitions is strongly correlated. Furthermore we note that in these echo effects interference with stimulated emission and super -fluorescence must be avoided by using small-angle excitation pulses. Some of the results are shown in Fig.1. In (A) the decay of the C2CSE is presented with the solid line being a fit to a population decay parameter of the 747 cm-1 level of 33 psec. In (B) the rise of the R2CSE is shown where the probe wavelength is at the pure electronic transition. The dashed line is the expected echo-intensity rise if the initially excited vibration would directly decay into the vibrationless state. The mismatch between the dashed curve and the experimental one shows that intermediate levels in the relaxation pathway must exist. The solid line in (B) is a fit to a model where one intermediate bottleneck level is assumed with a lifetime of 16±2 psec. Other examples will be presented at the meeting.
The three-pulse stimulated photon echo has been considered as one of the most fundamental transient four wave mixing processes1, where each of the three excitation pulses induces a single elementary interaction process between a laser field and an inhomogeneously broadened two-level system., resulting in a burst of the fourth wave, i.e., echo. Now if four or more optical pulses are applied to a medium, a number of photon echoes should be expected, in general. At low excitation intensities where the perturbation theory is applicable, however, the dominant nonlinear process is still the three-pulse stimulated echo and consequently each echo signal is generated only by three of the preceding pulses. It is rather a remarkable result that the echo intensity is unaffected by the presence of all the rest of the pulses other than its three generators. With this in mind, it is theoretically and experimentally shown that by applying a single optical pulse (#1) propagating along k1 followed by N pairs of counter-propagating pulses (#2j (k2j) and #3j− (k3j = −k2j); j=1,…N) in various directions, it is possible to obtain N photon echoes along the direction -k1 opposite to the first pulse #1. We will call this degenerate photon echoes, degenerate in. the sense that the echoes are spatially overlapping and temporally simultaneous. When N=l, this scheme is reduced to the ordinary backward photon echo2,3. The doubly degenerate case (N=2) is illustrated in Fig. 1. The j-th echo will be generated by the set of pulses (#1, #2j, #3j) and appear at t = t3j + t2j − t1 where t1, i2j and t3j are the arrival times of the pulses #1, #2j and #3j, respectively.
A gaseous atomic or molecular system with four energy levels Ea<Eb<Ec<Ed which is stimulated by resonant laser pulses at frequencies ${\ensuremath{\omega}}_{1}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{ba}}$, ${\ensuremath{\omega}}_{2}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{cb}}$, ${\ensuremath{\omega}}_{3}\ensuremath{\simeq}{\ensuremath{\omega}}_{\mathrm{dc}}$ is considered. The six photon echoes which are stimulated by first and second pulses at frequencies ${\ensuremath{\omega}}_{1}$, ${\ensuremath{\omega}}_{2}$, ${\ensuremath{\omega}}_{3}$ are discussed. For wave fronts which are described by ${e}^{i(\ensuremath{\phi}\ensuremath{-}\ensuremath{\omega}t)}$ the echo phase is described by ${\ensuremath{\phi}}_{E}=\ensuremath{\Sigma}(2{\ensuremath{\phi}}_{m}^{\mathrm{II}}\ensuremath{-}{\ensuremath{\phi}}_{m}^{\mathrm{I}})$ at the sum frequency ${\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}+{\ensuremath{\omega}}_{3}$ with m=1,2,3, at ${\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$ with m=1,2, at ${\ensuremath{\omega}}_{1}$ with m=1, etc. For waves in the z direction where $\ensuremath{\phi}=\ensuremath{\kappa}(x,y,z)+kz$ the gradient of the phase yields the wave-vector direction ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{E}=\ensuremath{\Sigma}(2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{m}^{\mathrm{II}}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{m}^{\mathrm{I}})$ in a physically thin sample. A probe pulse at ${\ensuremath{\omega}}_{2}$ and ${\ensuremath{\omega}}_{3}$ after the second pulse can generate a probe-pulse echo at ${\ensuremath{\omega}}_{1}$ with phase ${\ensuremath{\phi}}_{1}=\ensuremath{\Sigma}(2{\ensuremath{\phi}}_{m}^{\mathrm{II}}\ensuremath{-}{\ensuremath{\phi}}_{m}^{\mathrm{I}})\ensuremath{-}{\ensuremath{\phi}}_{2}^{S}\ensuremath{-}{\ensuremath{\phi}}_{3}^{S}$, etc., for other frequency arrangements. Transverse phases ${\ensuremath{\kappa}}_{m}(\mathrm{xy})$ can be added and subtracted, but no application is suggested for this novel feature. When all ${\ensuremath{\kappa}}_{m}$ except one are zero, phase conjugation or phase-adaptive optics can occur.
An analytical study of the photon echoes associated with the three-level system interacting resonantly with optical pulses possessing two different frequencies is performed. It is predicted that photon echoes arise at anomalous times corresponding to the correlation between the inhomogeneous broadenings for the different spectral lines as well as at the normal time expected in a simple two-level system. This new effect is caused by the coupling of the two resonant transitions through the common energy level. Furthermore, if the particle does not have inversion symmetry, the echoes with the sum or difference frequency of the exciting optical pulses can be observed in such a system. The quantitative analysis is also given for intensities, direction of propagation and polarizations of the anomalous echoes which depend upon the exciting pulses with different frequency.
A theory of optical echo spectroscopies of large polyatomic molecules in condensed phases is developed. Using phase space correlation functions, we examine the interrelationships among the following optical measurements: ordinary photon echo, stimulated photon echo, accumulated photon echo, incoherent accumulated photon echo, and pump–probe absorption. Conditions for the elimination of inhomogeneous broadening in these experiments are specified. A multimode Brownian oscillator model is used to account for high frequency molecular vibrations, as well as solvent modes, and electronic dephasing processes. The effects of quantum beats, spectral diffusion, and homogeneous dephasing on the echo signals are studied and compared in detail with pump–probe and hole burning spectroscopy.