Achromatic critically coupled racetrack resonators

Abstract

In this paper, we investigate the spectral response of whispering-gallery-mode (WGM) resonators coupled to their access waveguide 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 singlemode and unidirectional devices. A coupled-mode treatment of the coupling region enables 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 Si3N4 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 1550nm, whereas the proposed new designs demonstrate critical bandwidths larger than 330nm, i.e. exhibit bandwidths enhanced by more than one order of magnitude.

Numerical study on Kerr frequency comb generation in Si3N4 microresonators with frequency-dependent access coupler properties

“…This iterative approach combines at each iteration two models: the Generalized NonLinear Schrödinger Equation (GNLSE) that describes intra-cavity light propagation and a transfer matrix model that describes propagation through the coupler. The use of the Ikeda map to model the optical cavity allows an interesting degree of latitude as it can be applied to any optical cavity regardless of its finesse or quality factor, thus providing a reliable tool for the implementation of the information about frequency-dependent coupling provided by Arlotti et al in [23] in the simulation of KFC generation.…”

“…Arlotti et al have designed in [23] three different access coupling regions intended for Si3N4 resonators with 220 GHz FSR to operate in the critical coupling regime over a large frequency bandwidth when pumped in the optical C-band. In reference [23] the parameters that are modified to achieve the desired coupling properties are the access waveguide cross-section dimensions and the separation distance between the Si3N4 cavity and the underlying access waveguide. The size, shape and material properties of the cavity remain unchanged.…”

“…Absolute values of coupling ( 1,2 ) and transmission ( 1,2 ) coefficients for each coupler (labelled 1, 2 and 3) as a function of simulated optical mode numbers. Labels 1 and 3 (left vertical axis) refer to PMM structure whereas label 2 (right vertical axis) refers to QPM structure (see [23]).…”

“…The effects of intra-cavity dispersion alone are also represented with a dashed curve 4 for comparison purposes. The importance of taking coupler dispersion into account in our simulations becomes apparent as the mode structure of each resonator is strongly shaped by its access coupler design, further highlighting the importance of the work performed in reference [23].…”

“…All along this paper we will compare three specific designs of vertically coupled Si3N4/SiO2 resonators with the same resonant ring but different coupling designs that were theoretically studied in [23] in order to obtain critical coupling over a spectral range larger than 30 nm at 1550 nm pump wavelength. Section 1 of this paper is dedicated to the description of the numerical model.…”