Butterfly-like phase shift: a novel gauge for critical coupling of add\u2013drop resonator

Mahdi Bahadoran,Preecha Yupapin

doi:10.1007/s40094-018-0291-2

Abstract

Optical transfer function for add–drop resonator is derived in the presence of coupling loss using the scattering matrix method. A critical coupling condition for ADR is calculated. The response of the ADR under variation of coupling losses and coupling coefficients is studied. The number of allowed states under the critical condition is determined. The full width at half maximum as sharp as 0.17 nm is achieved. It is found that the relative phase shifts of through and drop ports show the same responses under the critical coupling condition. This response emerges in a butterfly-like phase shift, which can be considered as a new evaluating factor for checking the system in critical coupling condition.

Highlights

Ring resonators have found versatile functionalities in optical switching [1, 2], optical filters, photonics sensors [3, 4] and optical communications [5, 6]
The light response versus spectrum can be investigated by the scattering matrix method [21, 22]
The results simulated for the add–drop resonator (ADR) from silicon microring resonators with 1.5 lm radius and the group refractive index of 4.2 [34]

Summary

Introduction

Ring resonators have found versatile functionalities in optical switching [1, 2], optical filters, photonics sensors [3, 4] and optical communications [5, 6]. Resonators benefit from low photon loss rate and have ability to store energy in a microsized volume [7]. These features have made the ring resonators as multipurpose components for photonics and. The input light undergoes some variations while passing through a resonator system. Two light beams can simultaneously be coupled into the add–drop resonator via two couplers. A fraction of input light beam passing via direct path waveguide is showpn ffibffiffiyffiffiffifficffiffiffiffi(ffiffiFffiffiiffiffigffiffi.ffiffiffi1ffiffi)ffiffi,ffiffiffiwffi hich can be calpculffiffiaffiffitffieffiffidffiffiffiffiffiffiffiffiffiffiffibffiffiffiyffiffiffiffiffiffiffiffiffi c1 1⁄4 ð1 À cÞð1 À k1Þ and c2 1⁄4. Based on the scattering matrix method, the relation between input and output signals in each coupler, k1 and k2, can be written by the following matrices:

Edrop c2 is2

À c1c2n ð6Þ

Results and discussion