Three wave mixing is investigated with respect to its spectroscopic applications under fully resonant conditions. A theoretical study of the appropriate second order susceptibility χ(2) reveals interesting features both for sum and difference frequency generation. For difference frequency generation two different mechanisms are possible one of which allows the observation of resonances between excited states and the study of dephasing induced coherent emission. The coherence decay rate between the two excited states may be measured and also its pure dephasing rate. The line-narrowing characteristics of the fully resonant χ(2) are studied with respect to correlation between the inhomogeneous distribution for different levels. The line-narrowing capabilities are found to be partly complementary for the sum—and the two difference frequency resonance configurations. This leads to the suggestion of new line-narrowing techniques which could provide information about type and amount of correlation in inhomogeneously broadened systems.
Three wave mixing is investigated with respect to its spectroscopic applications under fully resonant conditions. A theoretical study of the appropriate second order susceptibility χ(2) reveals interesting features both for sum and difference frequency generation. For difference frequency generation two different mechanisms are possible one of which allows the observation of resonances between excited states and the study of dephasing induced coherent emission. The coherence decay rate between the two excited states may be measured and also its pure dephasing rate. The line-narrowing characteristics of the fully resonant χ(2) are studied with respect to correlation between the inhomogeneous distribution for different levels. The line-narrowing capabilities are found to be partly complementary for the sum—and the two difference frequency resonance configurations. This leads to the suggestion of new line-narrowing techniques which could provide information about type and amount of correlation in inhomogeneously broadened systems.
We explain the utility of third-order nonlinear susceptibility, χ (3) (ω 2 ; ±ω 1 , ∓ω1, ω 2 ), for the observation of resonances with homogeneous widths from inhomogeneously broadened distributions in three-level systems related to Raman or two-photon allowed electronic transitions. The line narrowing and high resolution capabilities are demonstrated theoretically using a model for inhomogeneous distributions of transitions in which we regard an absorption spectrum as the composition of some inhomogeneously broadened substructures. The experimental methods to separate a signal having frequency ω 2 from ingoing beam at the same frequency are outlined.
A comprehensive theory of a new type of three-wave optical mixing (${\ensuremath{\omega}}_{3}=2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$) is given for the spectroscopic purpose of determining ultra-short relaxation times (picoseconds or less) associated with excited states of condensed matter. Two incident light frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ are chosen so that they are both resonant with an inhomogeneously broadened optical transition and $|{\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}|$ is in the vicinity of inverse relaxation times. The theory is developed for its major application to broad-band electronic transitions. The nonlinear susceptibility ${\ensuremath{\chi}}_{R}^{(3)}$ for this process (named resonant Rayleigh-type mixing) is calculated by a density-matrix formalism with the model of a two-level atomic system incorporating the distribution of resonance frequencies and longitudinal (T1) and transverse (T2) relaxation times. The result shows a frequency characteristic depending only on T1, T2, and ${\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}$ in a broad-band limit, which serves for the determination of T1 and T2 in the frequency domain. The analysis is further extended to include the various effects as follows. The calculation of the saturation effect in the lowest order reveals that it modifies the shape of the frequency characteristic of the nonlinear susceptibility but does not affect seriously the determination of relaxation times. The effect of spectral cross relaxation within the inhomogeneous broadening is incorporated by a generalized density-matrix formalism. The resultant ${\ensuremath{\chi}}_{R}^{(3)}$ consists of two terms. The dominant term is the same as before except that T1 is replaced by a combined relaxation time ${T}_{1}^{\ensuremath{'}}={({T}_{1}^{\ensuremath{-}1}+{T}_{3}^{\ensuremath{-}1})}^{\ensuremath{-}1}$, where T3 is the cross-relaxation time. The other term originates from the inverse spectral-diffusion process. The effect of other energy levels located between the two levels under study is analyzed with a simple three-level model. The resultant ${\ensuremath{\chi}}_{R}^{(3)}$ also consists of two terms, the dominant one being the same as that for the two-level model except that ${T}_{1}^{\ensuremath{-}1}$ should be interpreted as total population decay rate of the upper level. For accurate derivation of ${\ensuremath{\chi}}_{R}^{(3)}$ from experiment, we discuss the interference between the resonant and nonresonant susceptibility terms and the light-wave propagation effect. Finally, the close analogy between this type of optical mixing and the photon echo is discussed.
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.
We have examined the effect of various phase-matching conditions on sum frequency generation in vapors. Using sodium vapor two resonant-enhancement routes for sum-frequency mixing (SFM) via a second-order magnetic-field-induced nonlinearity were explored. On one route the output is resonant with a quadrupole-allowed transition and the other a dipole-allowed resonance. We will show that the first route is preferential for SFM as phase matching on this route is easier to control and we present results detailing the important parameters and their effect in focused and unfocused cases. A second-order nonlinearity of 0.5--1 ${\mathrm{pmV}}^{\mathrm{\ensuremath{-}}1}$ is observed under optimum conditions. In the second route, variations in phase matching as one tunes across the transition may lead to a significant distortion of the spectroscopic line shapes. We show how the combination of different refractive-index sources can account for the different features seen.
This work contains theoretical and experimental studies of the properties of three-level atoms subjected to two single-frequency, continuous-wave laser sources with special emphasis on magnetic-field-induced sum frequency mixing (SFM) and electromagnetically-induced transparency (EIT). In sodium vapour, two resonant-enhancement routes for SFM were experimentally studied. In one route (3S-3P-3D) the output is generated on a quadrupole-allowed transition and on the other (3S-3P-4P), a dipole-allowed transition. Phase matching conditions are studied in detail. On the second route, the two contributions to the phase mismatch can combine to heavily distort the spectroscopic lineshapes observed. Doubly-resonant SFM is considered and two paths for excitation of the output coherence are identified. Control of their relative strength, via the input laser strengths, is predicted, as well as interference between them. These are both experimentally observed on the 3S1/2-3P1/2-3D3/2 transition scheme in sodium. Theory is presented to show how the use of a strong upper laser in resonant SFM can, by EIT, greatly reduce the absorption on the lower transition without similarly reducing the nonlinear process. A significant increase in conversion efficiency is predicted. Theory is also presented on the inclusion of the local field correction, which is relevant for high vapour densities, in the Bloch equations for the three-level atom. Nonlinear coherence cross-coupling terms arise and the generalised equations are then used for two case studies; one concerning EIT, the other SFM. EIT is experimentally studied using continuous-wave lasers in rubidium vapour. Focusing and de-focusing were observed on the probe laser beam as it tunes through the transparency window at close, but separate, detunings. This is attributed to the radial intensity profile of the coupling laser which imposes a spatial refractive index modulation on the medium at the probe laser wavelength.
Two-dimensional (2D) line shapes derived from four types of coherent third-order nonlinear spectroscopies as a function of two independent time or frequency variables are compared. The signals scattered into two wave-vector-matching directions in the limits of high-time or high-frequency resolution are calculated for an inhomogeneously broadened ensemble of two-level systems with phenomenological dephasing and population relaxation times. While one-dimensional (1D) line shape analysis for this model is ambiguous, the contours of these 2D line shapes are shown to be characteristic of the relative time scales of the three relevant line-broadening parameters. These broadening mechanisms are also apparent by comparing 2D spectral profiles along the diagonal and antidiagonal frequency axes. For time domain experiments, in analogy with NMR correlation spectroscopy, the radiated signal is observed as a function of the two coherence periods and is 2D Fourier transformed to obtain a line shape. For experiments based on the photon echo, the ellipticity of the absolute value 2D line shape is related to the ratio of the inhomogeneous width to the dephasing rate, whereas experiments based on the transient grating method are shown to be functionally 1D. For frequency domain experiments, the contours of the 2D line shape can yield information on static and both dynamic broadening mechanisms. While the addition of spectral diffusion to such calculations will modify these results for frequency domain experiments, characterizing these dynamics in the time domain naturally leads to a 3D experiment analogous to the spin diffusion experiment in NMR.