Abstract

In this paper, we investigate the spectral response of whispering-gallery-mode (WGM) resonators coupled to their access waveguides with a view to design their constitutive waveguides to promote critical coupling over a wide spectral range and thereby facilitate their use for high-sensitivity sensing or nonlinear frequency-conversion applications. The carried-out theoretical analysis is based on the universal response functions of single-mode and unidirectional devices. A coupled-mode treatment of the coupling region enables us to derive two sets of favorable designs. The identified resonator/access waveguide systems exploit waveguides with mismatched propagation constants, forming a coupling section exhibiting either an achromatic beat length or an achromatic power-transfer coefficient. This generic model is followed by a numerical case study of vertically coupled ${\mathrm{Si}}_3{\mathrm{N}}_4$ racetrack resonators. The conventional (quasi-)phase-matched configuration, treated as a reference case, is shown to display a critical-coupling bandwidth of 23 nm at a wavelength of 1550 nm, whereas the proposed new designs demonstrate critical bandwidths larger than 330 nm, i.e., bandwidths enhanced by more than 1 order of magnitude.

© 2017 Optical Society of America

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