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1. Excitation schemes for CARS, DFWM and LIF. Like CARS, DFWM is a four-wave mixing processes but is similar to LIF because it is a resonant process. The energy of the signal photon in each case is denoted by .

2. Interference of two frequency degenerate beams leads to a spatial modulation of the refractive index of a nonlinear medium. In regions where the electric field strength is high as a result of constructive interference the local refractive index is modified through the photo-refractive effect.

3. Schematic diagram of the phase conjugate geometry for DFWM. The grating planes formed by the interaction of the forward propogating pump and probe fields, E and E, are indicated. A similar but much more finely spaced grating can be formed by the interaction of the backward pump, E, and the probe field. Because of the ohase matching condition the singnal beam, E, back propagates along the line of the probe beam.

4. Schematic diagram of a coherence grating. Although the spatial poulation distribution in the excited state is not modulated by the interaction of the forward and backward propagating pump beams coherences are setup between the magnetic sublevels which modulate the birefringence.

5. Comparison of the HCO spectrum obtained by PHOFEX and DFWM following the 308 nm dissociation of ethanal. The upper trace is the PHOFEX spectrum recorded on the CO Q(30) transition obtained by Kable et al. [53]. The lower trace shows the corresponding DFWM spectrum obtained by Hall et al. [11]. The rotational distributions in the two spectra are not directly comparable because the PHOFEX spectrum was obtained in a molecular beam apparatus while the DFWM spectrum was obtained in a cell experiment. The important point, however, is the enhanced resolution observable in the DFWM spectrum (see section ).

6. Schematic view of the forward geometry arrangement used by Meijer and Chandler. Interference between the horizontal and vertical pairs of the input beams creates a population grating which will scatter the third beam through the hole in the exit mask whenever the frequency of the laser is resonant with an absorption in the gas phase sample. Adapted from ref. [55].

7. Schematic representation of the DFWM imaging geometry. Adapted from ref. [71].

8. Schematic representation of coherent imaging, showing the object, transform and image plane. The dots correspond to specific spatial frequencies or orders. Adapted from ref. [96].

9. Two-colour transient grating spectrum of I. Overlaid is the dispersed emission spectrum produced following excitation by the pump laser. Transitions from both the ground and excited states are evident, as indicated by the corresponding energy level diagrams. Reproduced from ref. [12]

10. Comparison of the LIGS spectra obtained by Butenhof and Rohlfing with the probe laser tuned to transitions out of the and rotational levels of NO state, with the PHOFEX spectrum obtained by Miyawaki et al. [78]. Because the LIGS spectra scale with number density squared the square of PHOFEX spectrum is shown. Adapted from ref. [9].

11. Comparison of the velocity profiles and their corresponding transient decay traces for various limiting values of the anisotropy parameter. A value of is expected for the limiting case (instantaneous dissociation) following a parallel transition, is the corresponding case for a perpendicular transition. An isotropic distribution, , is expected if the dissociation time is long compared to the rotational period of the parent molecule. Reproduced from ref. [10].

12. Transient grating decay traces recorded by Butenhoff and Rohlfing for various relative orientations of the pump and probe polarisation vectors and rotational states of the NO photofragment produced following the near threshold photodissociation of NO. The solid lines are fits to the data, from which the anisotropy parameter can be obtained. Reproduced from ref. [10].

13. Experimental setup used for SEP-DFWM. Adapted from ref. [7].

14. Comparison of the SEP spectrum of CS recorded by fluorescence dip (upper trace) and SEP-DFWM (lower trace). Notice that the DFWM signal is the square of the fluorescence dip spectrum. Reproduced from ref. [7].