Laser-seeding dynamics with few-cycle pulses: Maxwell-Bloch finite-difference time-domain simulations of terahertz quantum cascade lasers

We implement a Maxwell-Bloch simulation for a two-level system within the finite-difference time-domain method to simulate the seeding of lasers by broadband pulse injection. The model does not make the slowly varying envelope approximation, and the full electromagnetic field is simulated so that we are able to obtain time-resolved seeding by few-cycle pulses. The model is compared to recent results on seeding of THz quantum cascade lasers to aid in the interpretation of their complex signals. The simulations are found to be in good agreement with the data when gain recovery times of 15 ps are used. Furthermore, we find that the emission from the laser depends only weakly on the seed used to initiate laser action. The model is readily applicable to any seeded laser system where few-cycle seed pulses are used.

Figure 1

Schematic of the simulation. The active region has a relative permittivity of ${\epsilon }_r=12.9$, a waveguide loss of 3 cm${}^{-1}$, and an unsaturated gain of 21 cm${}^{-1}$. The absorber regions have a relative permittivity of ${\epsilon }_r=1$, a loss of $3\times {10}^4{\mathrm{cm}}^{-1}$, and zero gain. The seed is launched at $t=0$ on the left facet and the signal is probed just outside the right facet.

Figure 2

Stills from a video of a simulation for a 1.5 mm cavity using a gain recovery time of 20 ps, showing the simulation after (a) 230 ps and (b) 440 ps. The video is available in the Supplemental Material.

Figure 3

Numerical simulations for (a) 1.5 mm and (b) 3 mm cavities using gain recovery times of $T_1=5$, 20, and 50 ps. The simulations are normalized and offset for clarity.

Figure 4

A comparison between experimental data and simulation for 1.5 and 3 mm cavities. Parts (a) and (b) show experimental data for 1.5 and 3 mm cavities, respectively. Parts (c) and (d) show the corresponding simulations. The value of gain recovery time used in these simulations is 15 ps.

Figure 5

A comparison of different seed pulses for a 3 mm cavity. Blue (upper): The cavity is seeded by a narrow-band pulse resonant with the laser transition and is 50 ps long. Red (middle): A short seed pulse, as in Fig. 4. Black (lower): A random perturbation is made to the cavity and evolves. (a) The first 500 ps after the seed arrives. (b) Simulation after 1 ns. In this figure, the time delay of each trace has been shifted to facilitate comparison.