2D photon echo spectroscopy is a powerful method to elucidate the electronic structure of complex systems on an ultrafast time scale. Unfortunately, 2D PES requires extreme environmental control especially in the visible and ultraviolet regions of the spectrum owing to stringent phase stability requirements. Fluctuations in the environment that leads to changes in the signal are called multiplicative noise and lead to broadened line widths and reduced sensitivity. The relevant time scale of these fluctuations vary depending on the source such as laser instability, temperature gradients, relative humidity changes, and mechanical vibrations - all of which are important when performing a multi-scan experiment such as in two-dimensional spectroscopy. Such parametric sampling typically takes several minutes although some recent work in the IR using pulse shapers can reduced this to several seconds in special circumstances. Nonetheless, any fluctuations that occur on the second to minute or longer time scale can lead to multiplicative noise and severely degrade the quality of 2D spectra even with efforts to actively or passively phase lock the pulse pairs. Another approach that instantly solves this problem is to capture the entire spectrum in a single laser shot in which all fluctuations are effectively frozen except those that are being measured. GRadient-Assisted Photon Echo Spectroscopy or GRAPES effectively does just that - captures the entire 2D spectrum in a single laser shot by employing a spatial encoding of the coherence times that would otherwise have to be recorded separately.

The basic principle behind GRAPES is to capitalize on the spatial, rather than solely on the temporal, properties of the light. For a well-collimated beam in the absence of angular dispersion and spatial chirp, the wave front is approximately flat. As a result, when two beams cross at an angle, the relative timing between the pulse envelops along a particular direction becomes roughly proportional to the crossing angle (for small angles) and linear along the beam waist. In this way, a temporal gradient has been encoded in space simply by tilting one pulse relative to the other. Typically, this effect is not beneficial for four-wave mixing experiments involving short pulses because it results in temporal gradients all pulse pairs and an undesirable temporal smearing (i.e. loss of temporal resolution). However, if one carefully designs the phase-matching condition, one can achieve a controlled timing of all pulse pairs. For 2D PES, this is achieved by keeping pulses 2 and 3 parallel along the beam waist and titling pulse 1 relative to pulse 2. The sample is kept roughly parallel to beams 2 and 3. As can be seen in Figure 1, this scheme is identical to the one in which the timing between the pulses are sampled parametrically, except that now all the coherence times are sampled simultaneously. To insure that the gradient only occurs along one axis and to maintain sufficient laser intensity at the sample, the beams are focused along one direction but remain unfocused along an orthogonal axis aligned with the sample. The photon echo signal is now emitted as a line rather than a point, necessitating the use of a two-dimensional detector after spectral dispersion in the orthogonal direction.

Figure 1: Left - typical 2D PES pulse sequence. The coherence time is parametrically sampled and the experiment is repeated. Right - GRAPES pulse sequence. The coherence time is now spatially encoded along an axis of the sample. All the coherence times are sampled simultaneously without any loss in signal and reduced overall noise (due to improved phase stability).

A schematic of the GRAPES experiment is shown in Figure 2. Four pulses are reflected off of a three-mirror assembly and directed towards a cylinder mirror (not shown) before being focused onto a line at the sample. To ensure that beams 2 and 3 are focused to parallel lines, they are reflected off a common mirror. Beam 1 is reflected off a mirror angled up by a small angle and beam 4 is positioned in such a way as to ensure the phase-matching condition. Notice that the familiar boxcar geometry has been replaced by a parallelogram geometry. The pulse wavefront tilt and, hence, the strength of the temporal gradient is controlled by the angle of mirror 1. The signal is emitted in the rephasing direction and imaged onto the slit of spectrometer. Reflection off a diffraction grating leads to angular dispersion in the horizontal direction. The resultant two-dimensional spectrally resolved signal field is heterodyned with the local oscillator and detected by cooled 2048 x 2048 CCD detector.

See gallery for GRAPES movie and details of the optical setup.

Figure 2: GRadient-assisted photon echo spectroscopy (see text for details).