Nature of relaxation processes revealed by the action signals of intensity-modulated light fields

Abstract

We present a generalized theory and experimental results of the action signals induced by the absorption of two photons from two phase-modulated laser beams. In our experiment, the phases of the laser beams are modulated at the frequencies ${\ensuremath{\phi}}_{1}$ and ${\ensuremath{\phi}}_{2}$, respectively. Their collinear combination leads to the modulation of the total intensity at the frequency $\ensuremath{\phi}=\left|{\ensuremath{\phi}}_{2}\ensuremath{-}{\ensuremath{\phi}}_{1}\right|$. The action signals, such as photoluminescence and photocurrent, which result from the absorption of two photons, are isolated at frequencies $m\ensuremath{\phi}, m\ensuremath{\in}{0,1,2,\ensuremath{\cdots}}$. We demonstrate that the ratio of the amplitudes of the secondary ($m=2$) and the primary ($m=1$) signals ${A}_{2\ensuremath{\phi}}:{A}_{\ensuremath{\phi}}$ is sensitive to the type of relaxation processes in the media. Such sensitivity originates from the cumulative effects of the nonequilibrated state of the matter between the pulses. When the cumulative effects are small, i.e., the relaxation time is much shorter than the laser repetition rate or the laser intensity is high enough to dominate the system behavior, the ratio achieves the reference value of $1:4$. This ratio decreases monotonically as the relaxation time increases. Our experimental results from fluorescent molecules rhodamine 6G and rubrene support these theoretical findings. In the case of a second-order relaxation process, the ratio changes rapidly with the excitation intensity. When the recombination rate in the second-order process is significantly slower than the repetition rate of the laser, we observe nonmonotonic behavior of the ratio as a function of excitation population at low excitation intensity, and when the recombination rate and the excitation intensity are high, the ratio approaches the value of $1:4$. We also use the model to determine the value of the recombination rate of charge carriers in a GaP photodiode.