Analysis of light propagation in slotted resonator based systems via coupled-mode theory.

Optical devices with a slot configuration offer the distinct feature of strong electric field confinement in a low refractive index region and are, therefore, of considerable interest in many applications. In this work we investigate light propagation in a waveguide-resonator system where the resonators consist of slotted ring cavities. Owing to the presence of curved material interfaces and the vastly different length scales associated with the sub-wavelength sized slots and the waveguide-resonator coupling regions on the one hand, and the spatial extent of the ring on the other hand, this prototypical system provides significant challenges to both direct numerical solvers and semi-analytical approaches. We address these difficulties by modeling the slot resonators via a frequency-domain spatial Coupled-Mode Theory (CMT) approach, and compare its results with a Discontinuous Galerkin Time-Domain (DGTD) solver that is equipped with curvilinear finite elements. In particular, the CMT model is built on the underlying physical properties of the slotted resonators, and turns out to be quite efficient for analyzing the device characteristics. We also discuss the advantages and limitations of the CMT approach by comparing the results with the numerically exact solutions obtained by the DGTD solver. Besides providing considerable physical insight, the CMT model thus forms a convenient basis for the efficient analysis of more complex systems with slotted resonators such as entire arrays of waveguide-coupled resonators and systems with strongly nonlinear optical properties.

Analytical modal analysis of bent slot waveguides.

We analyze modal properties of dielectric optical bent slot waveguides by using the multilayer formulation of the well-known classical analytical model of bent waveguides based on the Bessel-Hankel functions. Unlike the previously studied approximate model based on the Airy functions, this model is valid for all values of bend radii. The present approach allows quick and accurate computations of propagation constants, mode profiles, and field-power densities for the 2D bent slot waveguides with very small radii. Using this model we characterize the optimal slot position inside the bent core to maximize the field enhancement in the slot. Such modal analysis is quite useful for the design of devices involving bent slot waveguides. Moreover the results obtained by the present 2D rigorous analytical model can also be used for benchmarking other numerical tools.

Perturbations of whispering gallery modes by nanoparticles embedded in microcavities.

The effects of perturbations of whispering gallery modes (WGMs) in cylindrical microcavities by embedded particles are studied by FDTD modeling. The principal effects are: i) spectral shift of the WGM-related peaks caused by the variation of the average index, ii) broadening of the WGM peaks introduced by the scattering, and iii) splitting of the WGM peaks due to formation of symmetric (SSW) and antisymmetric (ASW) standing waves. The focus of this work is on the last effect. We show that it can be maximized by placing the nanoparticle inside the cavity at a position corresponding to the antinode of the radial distribution of intensity of WGM. It is demonstrated that in this case the magnitude of splitting reaches several angstroms for cavities with moderately high quality (Q approximately = 10(5)) WGMs. We show that for relatively small particles with radius <70 nm and index contrasts <0.2 the magnitude of SSW/ASW splitting is linearly dependent on the size and index of the nanoparticle. This allows developing biomolecular sensors based on measuring this splitting in porous cavities. It is predicted that a similar effect of splitting can occur in semiconductor microdisks and pillars where the role of embedded dielectric nanoparticles can be played by self-assembled quantum dots.