Modeling of grating assisted standing wave, microresonators for filter applications in integrated optics

Abstract

A wide, multimode segment of a dielectric optical waveguide, enclosed by Bragg reflectors and evanescently coupled to adjacent port waveguides, can constitute the cavity in an integrated optical microresonator. It turns out that the device can be described adequately in terms of an approximate coupled mode theory model which involves only a few guided modes as basis fields. By reasoning along the coupled mode model, we motivate a simple design strategy for the resonator device. Rigorous two dimensional mode expansion simulations are applied to verify the predictions of the approximate model. The results exemplify the specific spectral response of the standing wave resonators. As refinements we discuss the single resonance of a device with nonsymmetrically detuned Bragg reflectors, and the cascading of two Fabry-Perot cavities, where the coupling across an intermediate shorter grating region establishes a power transfer characteristic that is suitable for an add-drop filter.

Hybrid Analytical/Numerical Coupled-Mode Modeling of Guided-Wave Devices

“…From Ref. [16] we adopted a resonator concept and the related Bragg reflectors as examples for contradirectional coupled mode theory. The resonator (Figure 8) consists of a piece of a wide multimode waveguide that is terminated on both ends by Bragg gratings.…”

“…For a unit TE excitation of the 5th order mode in the left half infinite part of the waveguide, the plot shows the relative power R reflected back into that mode, versus the vacuum wavelength λ. Continuous curve: rigorous calculations by bidirectional eigenmode propagation [12,16], reference; dashed line: the present HCMT model. Ref.…”

“…Ref. [16] provides a an alternative coupled mode model for the resonator that combines separate solutions for codirectional propagation of evanescently coupled waves along the cavity segment z ∈ [0, L] and for contradirectional wave interaction in the reflector gratings. There questions arise whether, for the computation of modal reflectivities and the net coupling effect along the cavity, the interaction between the outer channels and the central core needs to be taken into account also in the regions of the Bragg reflectors.…”

“…Plots: relative power fractions P B , and P A , P C , P D (largely superimposed) transfered to the guided outward propagating modes in port B and in ports A, C, D, versus the vacuum wavelength λ; overview (left) and the region around one of the major resonances at λ = 1.55 µm. Continuous line: simulations by bidirectional eigenmode propagation[12,16], dashed curve: the present HCMT model. [−10, 10] µm.…”

Analytical Approaches to the Description of Optical Microresonator Devices

“…A variant as proposed in Ref. [32] could be somewhat more realistic, where waveguide Bragg gratings constitute the cavity reflectors. Entirely different regimes of parameters apply, with significantly lower refractive index contrast at the cost of an increased device length.…”