Confined modes in finite-size photonic crystals

Abstract

The real band structure of finite-size photonic crystals ͑PCs͒ is different from the band structure of infinite PCs derived using Bloch's theorem. There are isolated instead of a continuum of modes around a band edge. We use the envelope function approximation ͑EFA͒ method to derive simple formulas to describe the frequency and field pattern of the modes in finite-size PCs. The results are compared with those from finitedifference time-domain ͑FDTD͒ method. We observe that the agreement between the results from EFA with a vanishing boundary condition and FDTD is sensitive to the boundary orientation. In addition, although a simple group-velocity-based analysis explains the long lifetime of the confined modes, this explanation is inappropriate for certain structures. In particular, we find boundary orientations, for which the lifetime of the confined modes can be enhanced by orders of magnitude compared with that anticipated from group velocity analysis. We explain this by total internal reflection. Our results demonstrate the utility of the EFA approach in studying the modes in finite-size PCs and reveal the importance of boundary conditions to develop an EFAbased tool for cavity lasers and for studying nonlinear interactions.

Lasing action from photonic bound states in continuum

“…This is of utmost importance in device design as fabrication tolerances will have less impact on resonance-trapped BIC than on modes that rely on symmetry protection. Moreover, designing a mode with a high quality factor in a large region of k-space is of practical importance because fabricated devices, which are never infinite, always sample the dispersion relation in a finite neighborhood in k-space [22]. Therefore, for a given quality factor, we can achieve a much smaller device footprint with a resonance-trapped BIC mode than with symmetry-protected modes.…”

Nanowire array based photonic crystal devices

“…Due to the small group velocity around the band edge 6, 7 and an effective total internal reflection (TIR) condition at the boundary of specific orientation as analyzed in Ref. 8, microcavities operating around the band edge (without the introduction of defects) can have high Q values, which is similar to the concept of DFB cavity. Despite the similarity, PCs microcavities can be extended to 2-D and 3-D, which will yield confining and coupling mechanism unattainable in traditional 1-D ones.…”

Developing 1D nanostructure arrays for future nanophotonics

“…We found that PCs consisting of semiconductor nanowire arrays grown by VLS are excellent candidates for photonic elements and devices, such as microcavities, due to the high dielectric constant contrast and high aspect ratio [110]. In addition, it is easy shows the normalized change in transmission of the THz pulse through the sample as a function of delay time with respect to 400 nm, 100 fs pump pulses at various fluences.…”