The beam arrangement for the 3-TG and 5-TG experiments is presented schematically. (a) The incident excitation beams have been split into three components with wave vectors , , and generating the 3-TG signal, which appears at according to phase matching conditions, and the 5-TG signal that appears at . (b) An in-plane view [perpendicular to the perspective in (a)] of the beams after the sample including the 3-TG and 5-TG signals. Varying the relative time delays can be used to produce surface plots as shown in (c). The surface plot in (c) was obtained experimentally using the radius sample, capped with TOPO and dispersed in toluene. The axis of (c) (intensity) is presented on a log scale.
Calculated transient grating curves including (broken line) and omitting (unbroken line) the difference exponential terms arising from the homodyne nature of the measurement. The inset is a comparison of the two calculated curves at short probe delay times. The curves were generated using equal amplitudes, a time constant of for the damped cosine and the following exponential time constants: 100, 1000, 10 000, and .
The lines with markers correspond to values obtained for the exciton, biexciton, and triexciton population densities calculated using an equation of motion treatment. The population densities correspond to the same time after interaction with an optical field of different relative intensities. The parameters used in the equation of motion simulation correspond to an arbitrary quantum dot with a first transition of with , , and set to and , , and set to , , and , respectively. The lines without markers correspond to the predicted probability of forming an exciton, biexciton or triexciton as shown. All of the values are plotted vs total exciton occupancy on a log-log scale.
Time integrated transient grating data measured for (a) 3-TG (top) and the 5-TG (bottom) experiments on the 1.67 colloidal CdSe quantum dot sample dispersed in toluene. The traces are plotted on semilog scale with separate axes. Plot (b) is a close-up of the short time region after the coherent spike. The 3-TG data were fitted over the range of to the expanded function , where the parameters were found to be , , , , , , , , , and . The 5-TG data were fitted in a similar manner over the same range using the function for the third order plus two additional exponential terms inside the modulus squared bracket . The exponential parameters were found to be , , , , , , , , , and .
Time integrated transient grating data for 3-TG and the 5-TG experiments on a model two level dye system rhodamine 6G. The inset is a close-up of the traces at short probe delay times. The traces in both cases are plotted on semilog scale with separate axes and have been offset for clarity.
The power dependence of the fifth order (5-TG) signal direction is plotted against the power dependence of the third order (3-TG) signal direction on a log-log scale.
The nanocrystal size dependence of (a) the time constants assigned to relaxation from an exciton excited state and (b) biexciton recombination. Both graphs are presented on a log-log scale with a line that corresponds to a cubic radius dependence.
(a) A simplified state level representation of the few level model. (b) Double sided Feynman diagrams for the third order signal that appears in the normal time ordered direction. Each diagram corresponds to a response function associated with ground state recovery (GSR), stimulated emission (SE), and excited state absorption (ESA). (c) The double sided Feynman diagrams for the fifth order signal in the normal time ordered signal direction. For the fifth order, a pair of diagrams contributes to each of the response functions associated with GSR, SE, and ESA.
Average parameters obtained from 3-TG and 5-TG CdSe traces.
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