Abstract
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.
Highlights
A popular strategy for solving Maxwell’s equations for a system with complex geometries and/or material response is to develop flexible and versatile all-purpose methods that allow for their direct numerical solution
We will demonstrate below that a Discontinuous Galerkin Time-Domain (DGTD) method [5,6,7,20] enhanced with curvilinear finite elements [4] is able to address these challenges in a satisfactory manner
In order to further reduce the computational efforts within the Coupled-Mode Theory (CMT) approach, we employ a speed-up technique which is based on analytical arguments and interpolation
Summary
A popular strategy for solving Maxwell’s equations for a system with complex geometries and/or material response is to develop flexible and versatile all-purpose methods that allow for their direct numerical solution. Such slotted configurations exploit the fact that the introduction of a sub-wavelength slot in conventional ridge/slab waveguides leads — for an appropriately polarized mode — to an extremely high electric field confinement inside the (low-refractive index) slot region [15]. We will demonstrate below that a Discontinuous Galerkin Time-Domain (DGTD) method [5,6,7,20] enhanced with curvilinear finite elements [4] is able to address these challenges in a satisfactory manner Even such sophisticated computational tools require long simulation times, it makes perfect sense to develop a dedicated semi-analytical model that takes into account the characteristic physical properties of the resonators and waveguides under consideration.
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