A review of theoretical and experimental works on the polarization photon-echo spectroscopy (PPE spectroscopy) is carded out. The main attention is payed to the following advantages of the PPE spectroscopy. First, the PPE spectroscopy, free of the influence of the inhomogeneous spectral line broadening, allows to make the high precision measurements within the envelope of a inhomogeneously broadened spectral line. Second, the high resolution ability of the PPE spectroscopy, directly in the temporal field, unables to accomplish the investigations of the fast relaxation processes, when ultrashort nano- and picosecond exciting pulse are used. Third, in the PPE spectroscopy the investigated relaxation processes are not subjected to the perturbing action of the intensive laser radiation. Farther, it is necessary to note the flexibility of the PPE spectroscopy consisting in the existence of a great number of various methods used for receiving different spectroscopic information. Finally, as far as the signal intensifies of the photon echo and of its variants are proportional to the squared number of the resonant atoms (molecules), it secures the definite advantages for the PPE spectroscopy as compared to the spectroscopk methods based on the non-coherent phenomena (especially for low pressure a gas considered). The possibilities of new experiments on photon echo and its variants aimed for obtaining a detailed new spectroscopic information are discussed.
A review of theoretical and experimental works on the polarization photon-echo spectroscopy (PPE spectroscopy) is carded out. The main attention is payed to the following advantages of the PPE spectroscopy. First, the PPE spectroscopy, free of the influence of the inhomogeneous spectral line broadening, allows to make the high precision measurements within the envelope of a inhomogeneously broadened spectral line. Second, the high resolution ability of the PPE spectroscopy, directly in the temporal field, unables to accomplish the investigations of the fast relaxation processes, when ultrashort nano- and picosecond exciting pulse are used. Third, in the PPE spectroscopy the investigated relaxation processes are not subjected to the perturbing action of the intensive laser radiation. Farther, it is necessary to note the flexibility of the PPE spectroscopy consisting in the existence of a great number of various methods used for receiving different spectroscopic information. Finally, as far as the signal intensifies of the photon echo and of its variants are proportional to the squared number of the resonant atoms (molecules), it secures the definite advantages for the PPE spectroscopy as compared to the spectroscopk methods based on the non-coherent phenomena (especially for low pressure a gas considered). The possibilities of new experiments on photon echo and its variants aimed for obtaining a detailed new spectroscopic information are discussed.
Summary form only given. A very high temporal resolution and a broad bandwidth are but two advantages provided by the use of extremely short sub-5-fs pulses in a nonlinear spectroscopic experiment. However, the applicability of the standard theoretical description becomes questionable for the pulses that consist merely of a couple of optical oscillations. Far instance, the conventionally employed slowly varying envelope approximation, implying that the change of the pulse amplitude on the duration of an optical cycle is negligible compared to the magnitude of the amplitude itself, can no longer be maintained. Furthermore, the phase-matching bandwidth that is limited due to dispersion in the nonlinear medium rapidly gains importance with the increase of the spectral width of the pulse. Another point of serious concern is the frequency-dependent variation in the sensitivity of signal photodetectors. In combination, these features result in what is known as a spectral-filter effect. Finally, artificial lengthening of the experimental transients is a direct consequence of the noncollinear geometry employed in spectroscopic experiments. We present a theoretical analysis which thoroughly reexamines the formalism of ultrafast photon echo spectroscopy. We obtain a general expression for the echo signal, which is valid even for single-cycle-pulse applications. The derived formalism is applied to photon-echo spectroscopy on the hydrated electron with 5-fs pulses.
The behavior of the photon echo produced by an inhomogeneously broadened spectral line is analyzed, with particular emphasis on the effect of spatial degeneracy of the molecular energy levels. The theoretical results are used to aid in the identification of the states involved in the echoes produced from gaseous SF6 excited by pulses of CO2 laser radiation near 10.6 \ensuremath{\mu}. The analysis demonstrates that for the $|{\ensuremath{\Delta}}_{j}|=1$ transitions (P and R branches) the echo induced by two linearly polarized pulses propagating along the same direction, with an angle $\ensuremath{\psi}$ between their electric vectors, is polarized at an angle greater than $\ensuremath{\psi}$ with respect to the first pulse, and the echo intensity decreases to a minimum, but not zero, as $\ensuremath{\psi}$ approaches $\frac{\ensuremath{\pi}}{2}$. An exception is the $j=1\ensuremath{\leftrightarrow}j=0$ transition, for which the echo is always polarized along the second pulse and the intensity varies as ${cos}^{2}\ensuremath{\psi}$. For ${\ensuremath{\Delta}}_{j}=0$ transitions (Q branch) the echo polarization generally lies at an angle smaller than $\ensuremath{\psi}$, i.e., between the first two pulses, and its intensity also decreases as $|\ensuremath{\psi}|$ approaches $\frac{\ensuremath{\pi}}{2}$. The exceptions for the ${\ensuremath{\Delta}}_{j}=0$ transitions are the cases $j=\frac{1}{2}\ensuremath{\leftrightarrow}j=\frac{1}{2}$ and $j=1\ensuremath{\leftrightarrow}j=1$. In the former case, the echo is polarized at an angle $2\ensuremath{\psi}$ with respect to the electric field vector of the first pulse, and the echo intensity is independent of $\ensuremath{\psi}$; whereas in the latter case, the echo behaves like that for $j=1\ensuremath{\leftrightarrow}j=0$. The dependence of the echo behavior on the angular momentum of states involved in the transition can serve to identify the transitions when measurements of the echo polarization and intensity are possible.
Optical spectroscopy provides a useful tool for probing the structure and dynamics of solids. Over the years, optical methods have evolved from absorption spectroscopy to more complex methods such as spectral hole burning, photon echoes, and luminescence line narrowing. The absorption spectrum provides information about inhomogeneous broadening, while the latter approaches provide information about the systematics of the homogeneous line shape information that is often obscured by inhomogeneous broadening. When external perturbations such as strain or electric fields are applied, details of the local site can be obtained. Recently, the ultimate limit of optical spectroscopy has been attained, in which the spectral properties of individual single impurity molecules in a solid can be measured, with all ensemble averaging removed. This novel regime has provided additional, previously unobtainable, information on a highly local scale, such as the direct observation of the spectral shifting of a single molecule produced by configurational transitions of the host. It is to be expected that further surprises await us in this new frontier of single-molecule spectroscopy in solids.
A new method of picosecond and femtosecond transient spectroscopy yielding information about ultrafast relaxation processes without requiring ultrashort light pulses is presented. It is based on the present theoretical analysis of the resonant degenerate four-wave-mixing process excited by two temporally incoherent light beams with wave vectors ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}$ which are originated from a single beam at frequency $\ensuremath{\omega}$ but have mutual time delay $\ensuremath{\tau}$. Under the assumption that the incoherent light field has Gaussian random complex amplitude and that the resonant material consists of the usual two-level atoms, the statistically averaged intensity of the output light field with ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{3}=2{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{2}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{1}$ at $\ensuremath{\omega}$ is calculated as a function of $\ensuremath{\tau}$. Even with the light having a much longer duration than both T1 (the longitudinal relaxation time) and T2 (the transverse relaxation time), the correlation trace, i.e., output intensity versus $\ensuremath{\tau}$, represents a decay profile determined mainly by T2 for both homogeneously and inhomogeneously broadened transitions, as long as the light correlation time ${\ensuremath{\tau}}_{c}$ is much shorter than the relaxation times. The correlation trace does not always represent a single-exponential decay but is sometimes slightly deformed by the T1 effect. However, it does not cause a significant error in the determination of T2. Moreover, as $\frac{{T}_{2}}{{T}_{1}}\ensuremath{\rightarrow}0$, the trace becomes a single-exponential decay curve determined only by T2. The feature of the results obtained by the present method is similar to that obtained by the conventional coherent transient spectroscopy with short pulses, such as the photon echo. The time resolution in the present method, however, is limited only by ${\ensuremath{\tau}}_{c}$ much shorter than the light duration. By regarding the incoherent light as a series of random ultrashort pulses, the present four-wave-mixing process is also interpreted as the ensemble of numerous transient four-wave-mixing processes caused by various combinations of these pulses.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy. In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels. It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid. Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180° pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes. The role of pulse phase is extensively analyzed. Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters. The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem. Phys. Lett. 48, 256 (1977); Orlowski et al., ibid. 54, 197 (1978)]. The relative merits of fluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences. Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions. In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.
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.