Microring resonators are a rapidly-developing area of research in photonic devices with a wide range of applications including signal processing, filters, sensors, lasers, modulators, switches, memory and slow-light elements [1]. Generally speaking, microring resonators represent frequency selective elements that can perform a variety of functions such as add-drop filtering, switching, and modulating in wavelength-division systems. In coupled-resonator structures, one of the most critical issues is the precise control of the resonance frequency, which depends on both the resonator and cladding material and the resonator geometric parameters (radius, width, height). Also, it has been shown that when single microring is coupled to access waveguides or another rings, the resonance frequency will deviate from its original isolated resonator value. This effect, known as coupling-induced resonance frequency shift (CIFS), which is recently investigated more systematically in [2], causes resonance frequency mismatches between individual resonators and thus significantly impacts the performance of the coupled-resonator systems. By the nature of the problem this effect is most obviously manifested in system eigenspectra, although it is shown [2], [3], that CIFS can be related to the phase responses of the coupling region in the resonator coupling structure. Several methods are used for calculating the response of a microring resonator such as the prominent FDTD or modeling in terms of semi-analytic coupled-mode theory, usually in two space dimensions (2D) and rarely in 3D. Although 2D calculations are sufficient to explain some concepts and phenomena, the rigorous 3D simulations are necessary to determine the parameters of the devices intended to be used in real WDM systems, especially when the dimensions of the system are comparable with the light wavelength. For many reasons, finite element method (FEM) is the method of choice for accurate and fast simulations of photonic systems. It enables rigorous treatment of full Maxwell's equations in complicated geometries and inhomogeneous domains. Arbitrary high-order methods for faster convergence and the error control through automatic adaptive mesh refinement are available in many commercial and academic FEM packages. In our previos paper [4] we analysed eigenspectra and CIFS in finite length microring resonator arrays (systems without access waveguides) using 2D FEM method. Here we present a detailed investigation of CIFS effects in coupled microring resonators system configured as the high order serial filter based on eigenspectra analysis using full 3D vectorial FEM method. Such calculations are computationaly much more demanding, and require careful devising of adaptive mesh refinement strategy, in order to make it feasible, even on the most powerful workstation.VI International School and Conference on Photonics and COST actions: MP1406 and MP1402 : PHOTONICA2017 : August 23 - September 1, 2017; Belgrade
