Nonadiabatic Dynamics of the Electromagnetic Field and Charge Carriers in High-$Q$ Photonic Crystal Resonators

We address, both experimentally and theoretically, phase and amplitude dynamics of the electromagnetic field in a two-dimensional photonic crystal when femtosecond pulses are injected. We demonstrate that the usual adiabatic approximation underlying the dynamics of field and carriers in a semiconductor resonator is no longer valid, since in general the photon lifetime cannot be neglected with respect to the carrier recombination lifetime. Parameter regions where adiabaticity is broken are shown, and the ubiquity of the observed dynamical scenario in the new generation of active photonic microresonators is predicted.

Figure 1

Electric field (solid line), second order phase (dashed line), and carriers dynamics (solid line with shadow) for typical pump and probe delay. The shadow represents that the medium is active. Traces correspond to Eqs. (3, 4) with $N_0=0.5$ and $\gamma =0.02$.

Figure 2

Experimental optical spectra. Pumping levels are $N_0=0.3$ in (a), 0.6 in (b), and 0.9 in (c). Each curve corresponds to a pump-probe delay; positive delays mean pump arriving after the probe. Normalized delays are: (a) $t_0=4.4,1.8,1.36,0.78,0.56,0.19,-0.67,-26$; (b) $t_0=4.4,2.17,0.78,0.63,0.4,0.28,0.06,-0.3,-0.74$; (c) $t_0=4.4,2.1,-0.09$ (also in the inset), $-0.15,-11.5,-26.7$ from the front curve to the back curve.

Figure 3

Theoretical optical spectra. (a) $N_0=0.3$ and (b) $N_0=0.6$ are calculated from Eq. (6); (c) $N_0=0.9$ is the power spectrum of Eq. (5) with (3, 4). Normalized delays are the same as the experimental ones. Inset: $t_0=0$.

Figure 4

Parameters map for (a) $\gamma =0.02$ and (b) $\gamma =1$, showing regions where type 2 oscillations are visible (dark regions), and those where they disappear (light regions). Dark lines correspond to contour plots of $r$ defined in the text. White line is ${\varphi }^{(2)}=\pi$ ($\delta t_E=t_a$); well below this line means ${\varphi }^{(2)}\ll \pi$, then the adiabatic approximation becomes valid.