Disorder effects on the coupling strength of coupled photonic crystal slab cavities

Abstract

We study the effects of disorder on the coupling strength of coupled photonic crystal slab cavities by considering fully-3D electromagnetic calculations. Specifically, we investigate two coupled L3 cavities at 30°and 60°configurations, where the coupling strength J (or photon hopping) is extracted from the simulations in the presence of disorder. We found that the relative fluctuations of the photon hopping are more sensitive to disorder effects than the corresponding fluctuations in the eigenfrequencies of the coupled cavities. Furthermore, for the typical range of disorder in state-of-the-art devices, the J fluctuations are found to increase linearly as a function of the disorder amplitude. This allows one to set upper bounds to the amplitude of fabrication imperfections, for which the coupling predicted by design can still be expected, on average, in a fabricated device.J of two coupled L3 PhC cavities in the presence of disorder, i.e., in the regime where the two cavities have different resonant frequencies. We find that the relative fluctuations of J with respect to their mean values, J J d á ñ, are more sensitive to disorder than the relative fluctuations of the normal mode frequencies, dW áWñ, of the coupled cavity system. We finally establish the scaling law of J J d á ñas a function of the disorder parameter and set an upper bound to the amplitude of random imperfections in the system, in order for the nominal coupling to be realized on average, i.e. J J 1 d á ñ  . The present results are of particular relevance for the design of state-of-the-art integrated PhC devices and for the rapidly growing research on quantum many-body phenomena in photonic arrays [35][36][37][38][39][40].The paper is organized as follows. In section 2 we discuss the resonant modes of the ideal (i.e. non disordered) system of two coupled PhC cavities, and explain the procedure to compute the coupling strength J, by combining GME with a two coupled-mode model in the presence of disorder. In section 3, we present results for the coupled cavity system in presence of disorder and discuss the scaling law for the relative fluctuations J J d á ñand dW áWñ. Finally, we draw conclusions in section 4.

Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array

“…Herein, we allow the occurrence of random fluctuations in the resonant frequency ( ω 0 + δ i ; i = 1, ···, 10) and the coupling strength between cavities ( C A/B + ε i ; i = 1, ···, 9). Based on our own experience in semiconductor fabrication, as well as the literature 39,40 , we limit the fluctuations in the resonant frequency to levels below 1% and those in the coupling strength to below 10%. The conditions can be formulated as δ i = 0.01 γξ i ω 0 and ε i = 0.1 γξ i C A/B , where γ (0 < γ <1) is the fluctuation factor that determines the overall degree of fluctuations and ξ i is a random number between −1 and +1.…”

Global optimization of an encapsulated Si/SiO2 L3 cavity with a 43 million quality factor

“…Realistic photonic devices are always subject to a small amount of intrinsic disorder, coming from unavoidable imperfections introduced at the fabrication stage. We model such effect by considering random Gaussian fluctuations in all hole positions and sizes of our PC, where the standard deviation of the Gaussian probability distribution σ is taken as the disorder parameter [44][45][46] . Results of this analysis are shown in Fig.…”

Global optimization of an encapsulated Si/SiO$$_2$$ L3 cavity with a 43 million quality factor

“…Realistic photonic devices are always subject to a small amount of intrinsic disorder, coming from unavoidable imperfections introduced at the fabrication stage. We model such effect by considering random Gaussian fluctuations in all hole positions and radii of our PC, where the standard deviation of the Gaussian probability distribution is taken as the disorder parameter 44 – 46 . Results of this analysis are shown in Fig.…”