Strain effects and phase transitions in photonic resonator crystals

Abstract

Optical structures with periodic variations of the dielectric constant in one or more directions (photonic crystals) have been employed extensively for studying optical diffraction phenomena. Practical interest in such structures arises from the possibilities they offer for tailoring photon modes, and thereby the characteristics of light propagation and light-matter interactions. Photonic resonator crystals comprising two-dimensional arrays of coupled optical microcavities have been fabricated using vertical-cavity surface-emitting laser wafers. In such structures, the light propagates mostly normal to the periodic plane. Therefore, the corresponding lateral Bragg-periodicities are larger, a feature that is advantageous for device manufacture as it allows for larger lattice constants in the lateral direction. Here we investigate strain effects in a photonic resonator crystal by shifting neighbouring lattice rows of microcavities in opposite directions, thereby introducing an alternating square or quasi-hexagonal pattern of shear strain. We find that, for strain values below a critical threshold, the lasing photon mode is virtually locked to the corresponding mode supported by the unstrained photonic crystal. At the critical strain value, we observe a phase-transition-like switching between the square and quasi-hexagonal lattice modes. The tolerance of subcritical strains suggests that the resonator crystal may be useful for applications requiring high spatial coherence across the lattice, while the mode switching could potentially be exploited in free-space optical communications.

Phase synchronization and polarization ordering of globally coupled oscillators

“…͑9͒ Figure 1 shows the good agreement between the transition to phase synchronization obtained from numerical integration of (2) and (3) and the solution of the self-consistent Eq. (8).…”

Strain-tunable photonic bandgap microcavity waveguides in silicon at 1.55 μm

“…Sub-nanometer strain tuning has many potential applications such as tunable low-threshold microlasers, filters and signal routers in silicon microphotonics. Effect of static strain on the periodic lattice of coupled vertical microcavity resonators has been reported [2] and a theoretical design for shearmodulated 2-dimensional photonic crystals on bulk piezoelectrics has been proposed [4]. Herein we present piezoelectric strain-tuning towards a 1D photonic band gap microcavity to achieve active tuning of the resonant frequency.…”

“…Dynamic tunability is required not only for reconfiguration of the optical characteristics based on user-demand, but also for compensation against external disturbances and relaxation of tight device fabrication tolerances. Recent developments in photonic crystals have suggested interesting possibilities for static small-strain modulations to affect the optical characteristics [1][2][3] , including a proposal for dynamic strain-tunability 4 . Here we report the theoretical analysis, device fabrication, and experimental measurements of tunable silicon photonic band gap microcavities in optical waveguides, through direct application of dynamic strain to the periodic structures 5 .…”

Spatial coherence in VCSEL-based photonic crystal homostructures and heterostructures

“…New designs of phase-locked arrays of vertical cavity surface emitting lasers (VCSELs) providing high output power in a coherent beam can benefit from concepts related to active photonic crystals (PhCs) [1][2][3]. In particular, tailoring of the photonic envelope functions of the Bloch states in these structures would be useful for controlling the phase locking and the beam properties of these photonic structures.…”