Analytical Approaches to the Description of Optical Microresonator Devices

Abstract

Optical ring resonators are commonly discussed on the basis of a frequency-domain model, that divides a resonator into coupler elements, ring cavity segments, and the straight port waveguides. We look at the assumptions underlying this model and at its implications, including remarks on reciprocity/symmetry arguments, the general power transfer characteristics, the resonance condition, the spectral distance and width of the resonances, the quantities that describe the resonator performance, and a few remarks about tuning. A survey of bend mode properties and a coupler description in terms of coupled mode theory fills the abstract notions of the model. As an example for devices that rely on a standing wave principle, in contrast to the traveling waves found in the microrings, we consider in less detail microresonators with square or rectangular cavity shapes. Also here a frequency domain coupled mode theory can be applied that opens up simple possibilities to characterize resonant configurations. Abstract resonator modelThe "standard" model covers the propagation of light at fixed angular frequency ω = kc, usually specified by the vacuum wavelength λ , vacuum wavenumber k = 2π/λ , and vacuum speed of light c. All optical fields vary in time according to ∼ exp(iωt). The list of underlying assumptions and approximations includes the following items:• Single polarization operation is considered, none of the waveguide segments and coupler elements couples waves of different polarization; all waveguides are unimodal per polarization orientation.

Analysis and modeling of a silicon nitride slot-waveguide microring resonator biochemical sensor

“…The resonance wavelength incremental change (Δλ r /Δn eff ) can be analytically estimated by using the analysis of tuning of microresonators proposed in [21]. For our slot-waveguide microring sensor the cavity mode phase propagation constant (β) in the unperturbed state (n B =n B0 , λ r =λ r0 ) can be written as:…”

Controlling group delay in single and multi-stage slotted ring resonator with fabrication tolerances

“…The total ring loss comes from the imaginary part of propagation constant, bend loss of circular ring, and also from coupling between straight and circular waveguides. The resonance peaks are separated by FSR which is calculated according to equation 1 [23] as below:…”

“…Since the propagation and bending loss are low for high index waveguides, the Q factor is approximately as below according equation 2 to [23]:…”

Analysis of light propagation in slotted resonator based systems via coupled-mode theory

“…In what follows, we work in the frequency-domain and limit ourselves to a linear optics setting [23]. Within this standard approach, the waveguides-coupled slotted resonator is conceptually divided into two bent-straight waveguide couplers (the boxes (I) and (II) delineated by dashed lines in Fig.…”