FDTD Pulse Propagations

As already discussed, we have been developing time-resolved THz spectroscopy (TRTS) in order to characterize changes in the low frequency spectrum upon photoexcitation. Early on in this endeavor, we realized that several technical challenges existed in interpreting TRTS experiments. These challenges occur whenever the response of the system to the visible pump pulse evolves on the same time scale as the propagation of the THz pulse, in other words where the slowly varying envelope approximation (SVEA) fails. In these cases, the usual frequency domain techniques can not be used to interpret TRTS experiments.

For example, consider an excitation pulse and a THz probe pulse, both travelling from left to right through a sample. Three different pump-probe delay times are shown to the right. The THz pulse is shown in black and the induced polarization from the visible excitation is shown in red. In each of the three panels the THz delay is the same. 1. The pump pulse arrives at the sample after the arrival of the THz pulse, in this case the induced polarization only effects the trailing part of the THz pulse. 2. The pump pulse arrives at the same time as the THz pulse, in this case the induced polarization causes a large distortion of the THz pulse. 3. The pump pulse arrives well before the THz pulse, in this case every part of the THz pulse experiences an excited medium. The induced polarization is seen to decrease from panel 1 to 3, which is due to the absorption of the visible pulse as it penetrates the sample.

Finite-difference time-domain (FDTD) methods are commonplace for solving complex electromagnetic problems. We have extended previous work to simulate TRTS experiments. This is achieved by simultaneously propagating the visible pulse and the THz pulse, keeping track of the transient polarization induced by the visible pulse. Herein lies the power of the FDTD-TRTS method: the polarization may be modified transiently during the propagation of the THz pulse.

A TRTS experiment is inherently non-linear because there are two temporal variables that must be considered: the arrival of the pump pulse relative to the arrival of the THz pulse, and the propagation time of the THz pulse. The arrival of the visible pulse introduces a transient polarization in the sample, which will affect the propagation of the THz pulse.

In the static case, the response of the system to an applied field is given by the time-domain response function c(t), however, the response function is expressed as c(t,t") when the sample has been photoexcited at time t". The goal of the FDTD-TRTS method is to obtain the response function from a TRTS measurement. We do this by assuming a form of c(t,t") and perform a non-linear least squares fit of the model to the measured data. We have applied this method to several problems of current interest in our group, including transient photoconductivity in wide bandgap semiconductors, visible pump-THz probe of a dye/solvent system, and generation of a THz transient from a coherently induced charge transfer event. The figure below shows a fit of the model using FDTD propagation to the measured data of photoexcitation of the dye TBNC dissolved in toluene.

The horizontal "THz Delay" axis corresponds to scanning delay line # 2 in the experimental schematic. The vertical "Pump-Delay" axis corresponds to scanning delay line #3. The FDTD propagation is able to accurately reproduce the experimentally measured features.