DSFDs of directional phase-matching photon echo signal. The straight arrows indicate the interactions with the light field while the dashed lines indicate the exit field.
DSFDs for a TLS interacting with (a) a -pulse directional phase-matching photon echo. The labels indicate the vector acquired with each interaction with light field and the final direction that the echo signal exits at, and (c) a three collinear phase coherent pulse for a photon echo specific population. The labels indicate the phase acquired with each interaction with the light field and the final phase of the photon echo specific population. The 2D Fourier transform of the response function associated with (a) and (c) gives the 2D spectra of (b) and (d), respectively. The gray box denotes the regions of the 2D spectra that are usually presented. The peaks in (d) appear in the rotating frame of the laser center frequency and hence appear near the origin.
DSFDs of collinear phase coherent photon echo signal. The label numbers are analogous to the diagrams presented in Fig. 1.
DSFDs for a vibrational manifold of populations induced by (a) the third-order 2Q-2D process and (b) the 1Q-2Q process.
Simulation of the 2D photon echo spectra from three pulse phase-cycling experiments of a model system that consists of two coupled TLSs. (a) Without any phase cycling. The spectrum is dominated by lower-order processes. (b) With a phase-cycling scheme. This scheme produces the desired photon echo 2D spectrum with no aliasing and (c) with a phase-cycling scheme. The 2D spectrum also contains the aliasing signal . (d) With a phase-cycling scheme. The 2D spectrum also contains the aliasing signals and .
Simulation of three pulse experiment with a phase-cycling scheme of a system that consists of two coupled anharmonic oscillators. This scheme allows 2D spectra from various FWM processes to be obtained simultaneously. Each spectrum is obtained with the appropriate weighted summation dictated by Eq. (15). (a) Photon echo 2D spectrum, . (b) Third-order 2Q-2D spectrum, . (c) 1Q-2Q correlation 2D spectrum, .
Simulation of four pulse phase-cycling experiments with a phase-cycling scheme of a system that consists of two coupled TLSs. (a) Real valued rephasing (echo) 2D spectrum, . (b) Real valued nonrephasing (antiecho) 2D spectrum . (c) A pure 2D absorption spectrum is obtained by reflecting about the axis and adding it to .
Allowed values of , , and , indicating the interactions by the first, second, and third pulses, respectively, of a three pulse pulse train, subjected to the conditions and . The row in bold denotes the values for the photon echo specific population .
Summary of various phase-cycling schemes needed for different three and four pulse experiments.
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