Sharp bends in photonic crystal waveguides as nonlinear Fano resonators

We demonstrate that high transmission through sharp bends in photonic crystal waveguides can be described by a simple model of the Fano resonance where the waveguide bend plays a role of a specific localized defect. We derive effective discrete equations for two types of the waveguide bends in two-dimensional photonic crystals and obtain exact analytical solutions for the resonant transmission and reflection. This approach allows us to get a deeper insight into the physics of resonant transmission, and it is also useful for the study and design of power-dependent transmission through the waveguide bends with embedded nonlinear defects.Comment: 8 pages, 5 figures, submitted to Optics Expres

Engineering Fano resonances in discrete arrays

We study transmission properties of discrete arrays composed of a linear waveguide coupled to a system of N side defect states. This simple system can be used to model discrete networks of coupled defect modes in photonic crystals, complex waveguide arrays in two-dimensional nonlinear lattices, and ring-resonator structures. We demonstrate the basic principles of the resonant scattering management through engineering Fano resonances and find exact results for the wave transmission coefficient. We reveal conditions for perfect reflections and transmissions due to either destructive or constructive interferences, and associate them with Fano resonances, also demonstrating how these resonances can be tuned by nonlinear defects

Mapping individual electromagnetic field components inside a photonic crystal

We present a method to map the absolute electromagnetic field strength inside photonic crystals. We apply the method to map the electric field component Ez of a two-dimensional photonic crystal slab at microwave frequencies. The slab is placed between two mirrors to select Bloch standing waves and a subwavelength spherical scatterer is scanned inside the resulting resonator. The resonant Bloch frequencies shift depending on the electric field at the position of the scatterer. To map the electric field component Ez we measure the frequency shift in the reflection and transmission spectrum of the slab versus the scatterer position. Very good agreement is found between measurements and calculations without any adjustable parameters.Comment: 12 pages, 7 figure

Design of Optomechanical Cavities and Waveguides on a Simultaneous Bandgap Phononic-Photonic Crystal Slab

In this paper we study and design quasi-2D optomechanical crystals, waveguides, and resonant cavities formed from patterned slabs. Two-dimensional periodicity allows for in-plane pseudo-bandgaps in frequency where resonant optical and mechanical excitations localized to the slab are forbidden. By tailoring the unit cell geometry, we show that it is possible to have a slab crystal with simultaneous optical and mechanical pseudo-bandgaps, and for which optical waveguiding is not compromised. We then use these crystals to design optomechanical cavities in which strongly interacting, co-localized photonic-phononic resonances occur. A resonant cavity structure formed by perturbing a "linear defect" waveguide of optical and acoustic waves in a silicon optomechanical crystal slab is shown to support an optical resonance at wavelength 1.5 micron and a mechanical resonance of frequency 9.5 GHz. These resonances, due to the simultaneous pseudo-bandgap of the waveguide structure, are simulated to have optical and mechanical radiation-limited Q-factors greater than 10^7. The optomechanical coupling of the optical and acoustic resonances in this cavity due to radiation pressure is also studied, with a quantum conversion rate, corresponding to the scattering rate of a single cavity photon via a single cavity phonon, calculated to be 292 kHz.Comment: 18 pages, 10 figures. minor revisions; version accepted for publicatio

Investigation of defect cavities formed in three-dimensional woodpile photonic crystals

We report the optimisation of optical properties of single defects in three-dimensional (3D) face-centred-cubic (FCC) woodpile photonic crystal (PC) cavities by using plane-wave expansion (PWE) and finite-difference time-domain (FDTD) methods. By optimising the dimensions of a 3D woodpile PC, wide photonic band gaps (PBG) are created. Optical cavities with resonances in the bandgap arise when point defects are introduced in the crystal. Three types of single defects are investigated in high refractive index contrast (Gallium Phosphide-Air) woodpile structures and Q-factors and mode volumes ($V_{eff}$) of the resonant cavity modes are calculated. We show that, by introducing an air buffer around a single defect, smaller mode volumes can be obtained. We demonstrate high Q-factors up to 700000 and cavity volumes down to $V_{eff}<0.2(\lambda/n)^3$. The estimates of $Q$ and $V_{eff}$ are then used to quantify the enhancement of spontaneous emission and the possibility of achieving strong coupling with nitrogen-vacancy (NV) colour centres in diamond.Comment: 12 pages, 11 figure

Guided resonances in photonic quasicrystals

In this paper, we report on the first evidence of guided resonances (GRs) in aperiodically-ordered photonic crystals, tied to the concept of "quasicrystals" in solid-state physics. Via a full-wave numerical study of the transmittance response and the modal structure of a photonic quasicrystal (PQC) slab based on a representative aperiodic geometry (Ammann-Beenker octagonal tiling), we demonstrate the possibility of exciting GR modes, and highlight similarities and differences with the periodic case. In particular, we show that, as for the periodic case, GRs arise from the coupling of the incident plane-wave with degenerate modes of the PQC slab that exhibit a matching symmetry in the spatial distribution, and can still be parameterized via a Fano-like model. Besides the phenomenological implications, our results may provide new degrees of freedom in the engineering of GRs, and pave the way for new developments and applications.Comment: 12 pages, 8 figures, 1 table. Three figures added; Sec. 3.3 significantly expande