Mode Coupling and Cavity-Quantum-Dot Interactions in a Fiber-Coupled Microdisk Cavity

A quantum master equation model for the interaction between a two-level system and whispering-gallery modes (WGMs) of a microdisk cavity is presented, with specific attention paid to current experiments involving a semiconductor quantum dot (QD) embedded in a fiber-coupled, AlGaAs microdisk cavity. In standard single mode cavity QED, three important rates characterize the system: the QD-cavity coupling rate g, the cavity decay rate kappa, and the QD dephasing rate gamma_perpendicular. A more accurate model of the microdisk cavity includes two additional features. The first is a second cavity mode that can couple to the QD, which for an ideal microdisk corresponds to a traveling wave WGM propagating counter to the first WGM. The second feature is a coupling between these two traveling wave WGMs, at a rate beta, due to backscattering caused by surface roughness that is present in fabricated devices. We consider the transmitted and reflected signals from the cavity for different parameter regimes of {g,beta,kappa,gamma_perpendicular}. A result of this analysis is that even in the presence of negligible roughness induced backscattering, a strongly coupled QD mediates coupling between the traveling wave WGMs, resulting in an enhanced effective coherent coupling rate g = sqrt(2)*g0 corresponding to that of a standing wave WGM with an electric field maximum at the position of the QD. In addition, analysis of the second-order correlation function of the reflected signal from the cavity indicates that regions of strong photon antibunching or bunching may be present depending upon the strength of coupling of the QD to each of the cavity modes. Such intensity correlation information will likely be valuable in interpreting experimental measurements of a strongly-coupled QD to a bi-modal WGM cavity.Comment: rev4: updated references and added additional correlation function calculations; to appear in Phys. Rev. A in Feb 200

Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals

Building upon the results of recent work [1], we use momentum space design rules to investigate high quality factor (Q) optical cavities in standard and compressed hexagonal lattice photonic crystal (PC) slab waveguides. Beginning with the standard hexagonal lattice, the results of a symmetry analysis are used to determine a cavity geometry that produces a mode whose symmetry immediately leads to a reduction in vertical radiation loss from the PC slab. The Q is improved further by a tailoring of the defect geometry in Fourier space so as to limit coupling between the dominant Fourier components of the defect mode and those momentum components that radiate. Numerical investigations using the finite-difference time-domain (FDTD) method show significant improvement using these methods, with total Q values exceeding 10^5. We also consider defect cavities in a compressed hexagonal lattice, where the lattice compression is used to modify the in-plane bandstructure of the PC lattice, creating new (frequency) degeneracies and modifying the dominant Fourier components found in the defect modes. High Q cavities in this new lattice geometry are designed using the momentum space design techniques outlined above. FDTD simulations of these structures yield Q values in excess of 10^5 with mode volumes of approximately 0.35 cubic half-wavelengths in vacuum

Momentum space design of high-Q photonic crystal optical cavities

The design of high quality factor (Q) optical cavities in two dimensional photonic crystal (PC) slab waveguides based upon a momentum space picture is presented. The results of a symmetry analysis of defect modes in hexagonal and square host photonic lattices are used to determine cavity geometries that produce modes which by their very symmetry reduce the vertical radiation loss from the PC slab. Further improvements in the Q are achieved through tailoring of the defect geometry in Fourier space to limit coupling between the dominant momentum components of a given defect mode and those momentum components which are either not reflected by the PC mirror or which lie within the radiation cone of the cladding surrounding the PC slab. Numerical investigations using the finite-difference timedomain (FDTD) method predict that radiation losses can be significantly suppressed through these methods, culminating with a graded square lattice design whose total Q approaches 105 with a mode volume of approximately 0.25 cubic half-wavelengths in vacuum

Polarization properties of dipolelike defect modes in photonic crystal nanocavities

Far-field measurements of the in-plane polarization properties of spontaneous emission from optical nanocavities formed in two-dimensional photonic crystal slab waveguides are presented. A strong polarization signature, even subthreshold, is found for a pair of highly localized dipolelike resonant modes. This polarization signature is used to study the effects of symmetry lowering within the cavity

Nonlinear Oscillations and Bifurcations in Silicon Photonic Microresonators

Silicon microdisks are optical resonators that can exhibit surprising nonlinear behavior. We present a new analysis of the dynamics of these resonators, elucidating the mathematical origin of spontaneous oscillations and deriving predictions for observed phenomena such as a frequency comb spectrum with MHz-scale repetition rate. We test predictions through laboratory experiment and numerical simulation.Comment: Main text: 5 pages, 6 figures. Supplemental material: 12 pages, 8 figure