New dynamic mechanism of interplay between nonlinearity and Bragg scattering in a femtosecond all-optical photonic crystal switch

Abstract

We have studied a femtosecond (fs) ultrafast all-optical photonic crystal (PhC) switch, and a new dynamic mechanism of the interplay between nonlinearity and Bragg scattering is revealed. Almost all phenomena observed in the experiments are reproduced in our numerical simulations. Completely different from the traditional band-gap shift mechanism, we propose a new dynamic mechanism that can explain the considerable increase of transmission and almost all other complex transmission behaviors of the switch. First, the fs-level ultrashort-lifetime nonlinearity generated by the fs pumping pulse, which cannot generate a band-gap shift, only causes a sudden phase change on the signal field that is still inside the PhC. Second, such a phase change can partially destroy the destructive interference of Bragg scattering, which is the physical reason for the low transmission in the photonic gap of the PhC. The study by Fourier transform of the temporally transmitted field can clearly support our new explanation. New phenomena, such as the larger than unity sum of transmission and reflection, are predicted. The new dynamic mechanism could be widely used in other systems as a new method to amplify nonlinear effects, or as a detector for ultrafast (femto- or attosecond) electronic processes.

Ultra‐fast dynamic nonlinear mechanism of Fabry–Perot cavity with femtosecond pumping

“…In our simulation, the nonlinearity of the polystyrene electronic system was represented by a two‐level electronic system, as described in Section 2. Theoretically, it is easy to prove that when the electronic system is pumped by a time‐independent power, it corresponds to a Kerr‐like nonlinear material owing to the variation in the population difference $${\rm{\Delta }}N(x,t)={N}_{1}(x,t)-{N}_{2}(x,t)={N}_{1}^{0}-2{N}_{2}(x,t)$$, 21 where $${N}_{1}(x,t)$$ and $${N}_{1}^{0}$$ are the populations at the lower level with and without pumping, respectively, and $${N}_{2}(x,t)\propto | E{| }^{2}$$ is the population at the upper level. Here, we set $${N}_{1}^{0}=5\times 1{0}^{25}\,{{\rm{m}}}^{-3}$$, while the lifetime of electrons on the upper level is set as $$1{0}^{-14}$$ s, which is a typical value for intraband electronic processes.…”

“…, 21 where N x t ( , ) 2 , respectively; t p is the pumping start time and τ is the effective lasting time of nonlinearity upper level is set as 10 −14 s, which is a typical value for intraband electronic processes. The temporal variation curves of the electron population on the lower level N x t ( , )…”

“…13,14 Similarly, FP cavities combined with graphene, magnetic plasmons, and metal nanocavities can also be used to realize an electrical switching effect, 15 plasmonic biosensors, 16 or label-free biosensing. [17][18][19][20] In our previous studies on the ultrafast dynamic nonlinear mechanism of PhCs with femtosecond (fs) pumping, 21,22 we only focused on the transmission change of a certain frequency at the edge of the gap region and ignored strange phenomena caused by the ultrafast dynamic nonlinear effect in other frequency regions, especially in the band region (e.g., the transmission is sloped from the original flat structure). This phenomenon was observed through numerical simulation for the first time, and the transmission of certain frequencies was significantly larger than unity, which has great application prospect.…”