Photonic Crystal Fano Laser: Terahertz Modulation and Ultrashort Pulse Generation

We suggest and analyze a laser with a mirror realized by Fano interference between a waveguide and a nanocavity. For small-amplitude modulation of the nanocavity resonance, the laser can be modulated at frequencies exceeding 1 THz, not being limited by carrier dynamics as for conventional lasers. For larger modulation, a transition from pure frequency modulation to the generation of ultrashort pulses is observed. The laser dynamics is analyzed by generalizing the field equation for conventional lasers to account for a dynamical mirror, described by coupled mode theory.

Figure 1

(a) Schematic of line-defect photonic crystal laser structure with right mirror formed by Fano interference between the waveguide mode and a side-coupled nanocavity. The upper waveguide is not essential to laser operation but significantly increases the laser output power. (b) Effective reflection coefficient (black line) and phase (blue line) for the nanocavity mirror as seen from the waveguide. The total quality factor of the nanocavity is $Q=500$ while the internal quality factor is $Q_i=14\hspace{0.17em}300$.

Figure 2

Variation of (a) laser frequency and threshold gain and (b) throughport $P_t$, and crossport $P_x$ power as a function of nanocavity resonance frequency. Nonlinear mirror cavity effects are neglected.

Figure 3

Temporal variation of power coupled out via throughport $P_t$ for fixed modulation frequency $f_{\text{mod}}=1\mathrm{GHz}$, fixed detuning, ${\omega }_C={\omega }_r$, and different resonance frequency modulation amplitudes: (a) $\epsilon =0.5$ (black), (b) $\epsilon =1.8$ (blue), and (c) $\epsilon =2$ (red). The instantaneous frequency (in units of $\epsilon {\gamma }_T$, right $y$ axis) is shown as a dashed line.

Figure 4

FM modulation amplitude (left axis) relative to mirror resonance modulation amplitude $\epsilon {\gamma }_T$ vs frequency for $J/J_{\text{th}}=2$ (blue circles) and $J/J_{\text{th}}=10$ (red circles) and the analytical result (black solid line). Power modulation index (right axis) for the throughport for $J/J_{\text{th}}=2$ (purple triangles) and $J/J_{\text{th}}=10$ (magenta triangles). The modulation amplitude is fixed at $\epsilon =0.2$ and the cavity is offset by ${\omega }_C-{\omega }_r=-0.08{\gamma }_T$ for $J/J_{\text{th}}=2$ and by ${\omega }_C-{\omega }_r=-0.82{\gamma }_T$ for $J/J_{\text{th}}=10$.