Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide

Abstract

A deterministic design of an ultrahigh Q, wavelength scale mode volume photonic crystal nanobeam cavity is proposed and experimentally demonstrated. Using this approach, cavities with Q> 10 6 and on-resonance transmission T>90% are designed. The devices fabricated in Si and capped with low-index polymer, have Q=80,000 and T=73%. This is, to the best of our knowledge, the highest transmission measured in deterministically designed, wavelength scale high Q cavities.Photonic crystal (PhC) The large computational cost, in particular the computation time, needed to perform the simulation of high-Q cavities make this trial based method inefficient. Inverse engineering design, in which the physical structure is optimized by constructing specific target functions and constraints, was also proposed[14] [15]. A design recipe based on the desired field distribution is proposed in [16]. In this letter, we propose and experimentally demonstrate a deterministic method to design an ultrahigh Q, sub-wavelength scale mode volume, PhC nanobeam cavity( Figure.1) that is strongly coupled to the feeding waveguide(i.e. near unity on resonance transmission). The design approach is deterministic in the sense that it does not involve any trial-based hole shifting, re-sizing and overall cavity re-scaling to ensure ultra-high Q cavity. Moreover, the final cavity resonance has less than 2% deviation from a predetermined frequency. Our design method requires only computationally inexpensive, photonic band calculations (e.g. using plane wave expansion method), and is simple to implement.The Q factor of a PhC nanobeam cavity can be maximized by reducing the out-of plane scattering(Q sc ) due to the coupling to the radiation modes. As shown previously [3][16], scattered power (P sc ) can be expressed as an integral of spatial fourier frequencies within a light cone, calculated over the surface above the cavity:. The integral is minimized when major fourier components are tightly localized (in k-space) at the edge of the first Brillioun zone [4]. We start by considering the ideal field distribution on this surface which would minimize P sc . A general property of these nanobeam cavities is that it consists of the waveguide region of length L, that sup- * Electronic address: quan@fas.harvard.edu ports propagating modes, surrounded by infinitely long Bragg mirror on each side( Figure.1a). Without the loss of generality, we consider the TE-like cavity mode with Hz as a major field component. In the case of conventional periodic Bragg mirror, evanescent field inside the mirror can be expressed as sin(β Bragg x) exp(−κx), where κ is attenuation constant. The cavity field inside the waveguide region can be represented as sin(β wg x). As mentioned above, scattering loss decreases in mirror section when β Bragg = π/a, while phase matching between mirror and waveguide [7], β Bragg = β wg , minimizes the scattering loss at cavity-mirror interface. The spatial fourier transform of such cavity field is approximately a Lorentzian in the vicinity of π/a. As ...

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