Four-wave mixing processes with double and triple resonances are discussed in detail. Explicit expressions for the resonant nonlinear susceptibilities of various cases are derived. It is shown that in some cases, four-wave mixing can yield a spectrum with reduced inhomogeneous broadening. Possible applications of multiresonant four-wave mixing as a spectroscopic technique are considered. They include high-resolution spectroscopy, deduction of transition matrix elements, study of transitions between excited states, measurement of longitudinal relaxation times, distinction between resonant Raman scattering and resonant fluorescence, etc. Selective polarization arrangement allows us to suppress the nonresonant background, separately measure the real and imaginary parts of the resonant nonlinear susceptibility, minimize the effects of absorption and laser intensity fluctuations, and greatly enhance the signal-to-noise ratio.
Recent research has expanded the capabilities of four-wave mixing by providing it with component selectivity, site selectivity, and mode selectivity. The selectivity is achieved by taking advantage of the three resonance enhancements that occur in a four-wave mixing process. New spectral scanning strategies allow one to scan a single resonance while maintaining the other two resonances at constant values. The constant resonances can be used to select a specific component, a specific site within an inhomogeneously broadened envelope of a component, and/or a specific vibrational or vibronic mode of that site. The scanned resonance will then contain enhanced features corresponding to the particular component, site, and/or mode that was chosen by the constant resonances. These component and site selective capabilities of the four-wave mixing complement the single vibronic level fluorescence methods. The relative transition intensities from a specific component or site reflect the mode coupling between the vibrational and vibronic modes. Since the four-wave mixing is fully resonant in these experiments, saturation effects play a dominant role and cannot be ignored. This review presents a complete discussion of the theoretical and experimental factors that control the fully resonant four-wave mixing. It shows examples of the component selectivity and the line narrowing capabilities. It also provides examples of how mode selection can identify mode coupling through the relative intensities of different vibrational features.
Until the advent of laser, optical spectroscopy was limited to absorption and emission. These linear techniques often provided incomplete information because of the presence of inhomogeneous broadening, which arises in gases from Doppler shifts and in solids from random crystal elds or structural disorder (Figure 10.1). Lasers provided the high intensity needed to implement nonlinear spectroscopic techniques, which can make measurements “below” the CONTENTS 10.1 Introduction 371 10.1.1 Physical Description of TFWM for a Two-Level System 373 10.1.2 Overview of Variants and Extensions of TFWM 375 10.1.3 Use of TFWM Spectroscopy in Solids, Semiconductors, and Complex Systems 376 10.2 Theory 377 10.2.1 TFWM Signal from an Inhomogeneously Broadened Ensemble of Two-Level Systems 378 10.2.2 Phenomenological Inclusion of Many-Body Effects 381 10.3 Experimental Details of TFWM 382 10.3.1 Basics of Excitation Pulse Generation, Alignment, and Signal Detection 382 10.3.2 Time-Integrated Two-Pulse TFWM 385 10.3.3 Time and Spectrally Resolved Two-Pulse TFWM 386 10.3.4 Three-Pulse TFWM 386 10.3.5 Co-Linear TFWM 387 10.4 Case Study: TFWM from Excitons in GaAs Quantum Wells 387 10.4.1 Dephasing 388 10.4.2 Many-Body Effects 389 10.4.3 Disorder 391 10.4.4 Quantum Beats 391 10.4.5 Polarization Dependence 392 10.5 Multidimensional Fourier Transform Spectroscopy 392 10.6 Summary 393 References 393 inhomogeneous line width and determine the underlying homogeneous line widths. Often the homogeneous width is more interesting because it reects dynamics such as scattering and/ or radiative decay.
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.
Frequency domain laser spectroscopy has been most often used to provide information on the internal Hamiltonian of the resonant system. In recent work, however, we have shown that by analysis of frequency domain four-wave mixing (FWM) line shapes, it is possible to obtain relaxation rates which reflect how the resonant system interacts with its environment. In addition, these experiments are performed with low-intensity cw lasers and give experimental information quite distinct from information obtained with high-intensity pulsed lasers.
A new technique for overcoming inhomogeneous broadening in condensed matter is reported. Phase-matchinginduced frequency selectivity associated with multiresonant four-wave mixing is explored in detail for the first time to our knowledge and shown to give laser-limited linewidths that are more than 10 times narrower than the inhomogeneous width of an intermediate resonance in LiTbF (4). The anomalous dispersion associated with the resonance. was also measured, and model calculations suggest that significantly greater narrowing is feasible.