Three-dimensional carrier-dynamics simulation of terahertz emission from photoconductive switches

A semi-classical Monte Carlo model for studying three-dimensional carrier dynamics in photoconductive switches is presented. The model was used to simulate the process of photoexcitation in GaAs-based photoconductive antennas illuminated with pulses typical of mode-locked Ti:Sapphire lasers. We analyzed the power and frequency bandwidth of THz radiation emitted from these devices as a function of bias voltage, pump pulse duration and pump pulse location. We show that the mechanisms limiting the THz power emitted from photoconductive switches fall into two regimes: when illuminated with short duration $(<40\mathrm{fs})$ laser pulses the energy distribution of the Gaussian pulses constrains the emitted power, while for long $(>40\mathrm{fs})$ pulses, screening is the primary power-limiting mechanism. A discussion of the dynamics of bias field screening in the gap region is presented. The emitted terahertz power was found to be enhanced when the exciting laser pulse was in close proximity to the anode of the photoconductive emitter, in agreement with experimental results. We show that this enhancement arises from the electric field distribution within the emitter combined with a difference in the mobilities of electrons and holes.

Figure 1

(Color online) Diagram of the boundary conditions used. On the plane $z=0$ the boundary conditions are set as 0 for $y<10\mu \mathrm{m}$, $V_b$ for $y>20\mu \mathrm{m}$ and Neumann boundary condition is assumed in the region $10\mu \mathrm{m}<y<20\mu \mathrm{m}$ as well as on all other boundaries.

Figure 2

(Color online) Graphs of the THz waveform (upper panel) for $10\mathrm{fs}$ pump pulses at different voltages, and their Fourier transforms (lower panel). The width of the pulse decreases with voltage and this effect gives as a result an increase of the bandwidth.

Figure 3

(Color online) Graph of full widths at half maximum (circles) for $10\mathrm{fs}$ pump pulses as a function of the bias voltage showing the narrowing of the THz transient with voltage. The power of the signal emitted (triangles) is also shown as a function of the applied voltage. The inset shows the evolution of the effective mass of electrons as a function of time for 0, 10, 20 and $30\mathrm{V}$ of bias voltage.

Figure 4

(Color online) Graphs of THz waveforms (upper panel) for different widths of the pump pulse durations. The THz pulse sharpens as the pump pulse width becomes smaller. The spectra of the previous signals is shown in the lower panel, there is a significant effect on the high frequency components.

Figure 5

(Color online) Graph of the spectral width at $-10\mathrm{dB}$ as a function of the pump pulse width (circles) at a bias voltage of $30\mathrm{V}$. The width of the distribution increases as the pump pulse decreases caused by carriers being photogenerated in a shorter period of time. The power of the signal emitted is also plotted (triangles) as a function of the pump pulse duration, the dotted curve shows the power calculated taking into account the number of photogenerated carriers and their effective mass, the dashed line includes additionally the effective bias electric field. The inset is a schematic with two curves (not drawn to scale) of the energy distributions of a short and a long pulse: A) are the photons with not enough energy to transfer carriers into the conduction band, B) is the band-gap energy, C) is the band-gap energy plus the L-valley offset and D) are the photons with enough energy to inject carriers directly into the L valley

Figure 6

(Color online) Graph of electric potential as function of $x$ and $t$. The surface show the screening of the electric field in the gap region after the arrival of the pump pulse (at $t=0$) as the separation of electrons and holes form a dipole.

Figure 7

(Color online) Simulation results showing “anode enhanced” THz emission. (a) and (b) are contour plots of the change in charge density, $\Delta \rho$, for simulations where the laser pulse arrived near the cathode $(x=-3\mu \mathrm{m})$ and anode $(x=3\mu \mathrm{m})$, respectively. $\Delta \rho$ is the change in charge density between $t=0$ to $t=300\mathrm{fs}$ projected onto the $x-y$ plane. $\Delta \rho$ was averaged over all slices in the $z$ direction. A summary of 11 simulations is shown in (c) where the peak THz electric field (triangles) and FWHM (circles) are plotted as a function of laser spot position.