Interplay of plasma-induced and fast thermal nonlinearities in a GaAs-based photonic crystal nanocavity

Abstract

We investigate the nonlinear response of GaAs-based photonic crystal cavities at time scales which are much faster than the typical thermal relaxation rate in photonic devices. We demonstrate a strong interplay between thermal and carrier induced nonlinear effects. We have introduced a dynamical model entailing two thermal relaxation constants which is in very good agreement with experiments. These results will be very important for Photonic Crystal-based nonlinear devices intended to deal with practical high repetition rate optical signals.

Oscillatory dynamics in nanocavities with noninstantaneous Kerr response

“…Assuming, for instance, a response time τ phys ∼ 30 ps [29], which yield τ = (τ phys /2t c ) ∼ 0.75 in a cavity with Q ∼ 25000 (t c ∼ 20 ps at λ = 1.55µm), assuming n 2I ∼ 10 −17 m 2 /W and a nonlinear modal volume V = 3(λ/n) 3 , the threshold power P = 10 in Fig. 4 corresponds to a real-world power P in = (γ/Γ 2 0 )P ∼ 10 mW in the waveguide coupled to the nanocavity, where γ = ω 0 n 2I c/(n ef f nV ) is the overall nonlinear coefficient [24]. Here we have assumed a refractive index n ∼ n ef f ∼ 1.5 and Q to be essentially determined by the coupling itself.…”

“…They implicitly assume that the nonlinearity is dominated solely by the Kerr effect with relaxation time τ , while other possible nonlinear contributions, e.g. two-photon absorption along with the free-carrier dispersion [13,18,20,24]), are neglected. Here P is the normalized power injected in the cavity through coupling with the waveguide, and |a| 2 is the normalized intracavity energy, which can be easily rescaled into real-world units by comparison with widely used dimensional models (see, e.g., Ref.…”

“…However SP and so-called weak turbulence occurs also in the opposite (say short cavity) limit, where the delay can be averaged out to end up with a differential mean-field model [2]. This regime becomes important nowadays where nano-cavities are employed for many modern photonic applications [16], including bistability [17], demonstrated in photonic crystal (PhC) membranes which offer great flexibility of design as well as high nonlinear performances in semiconductors [18][19][20][21][22][23][24][25]. In these cavities, transverse effects are absent and their dimensions are so small that the response time of the medium can be much larger than the light transit time in the cavity, yet being comparable with the photon lifetime which is strongly enhanced on account of the large quality factor Q. SP in such nano-cavities has * andrea.armaroli@unife.it been recently predicted, owing to the free-carrier dispersion induced by two-photon absorption [13].…”

Silicon photonic devices for mid-infrared applications

“…We performed time domain measurements in order to separate these effects and established that our nonlinearity was primarily thermal [35,36,38]. By modulating the input laser signal with a sine wave and looking for distortion in the output signal [35,38] due to bistablity, we were able to establish that 200 kHz was the modulation frequency at which all bistability-induced distortion disappeared, indicating that instantaneous χ3 effects could not be the cause of our bistability [11]. The corresponding thermal time constant, 5 µs, is also consistent with finite-element modeling of thermal effects in our cavities.…”

Experimental demonstration of a four-port photonic crystal cross-waveguide structure

“…4 Featuring small modal volume and large quality-factor (Q-factor), PhC nanocavity devices may enhance nonlinearities due to Kerr or carrier effects, [5][6][7][8] thus realizing ultra-compact and integrated devices facilitating ultra-fast, low-energy optical signal processing.…”