Quasi-normal-modes description of transmission properties for photonic bandgap structures

Abstract

Quasi-normal-modes description of transmission properties for photonic bandgap structures Settimi, A.; Severini, S.; Hoenders, B. J. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. We use the "quasi-normal-modes" (QNM) approach for discussing the transmission properties of double-side opened optical cavities: in particular, this approach is specified for one-dimensional (1D) "photonic bandgap" (PBG) structures. Moreover, we conjecture that the density of the modes is a dynamical variable that has the flexibility of varying with respect to the boundary conditions as well as the initial conditions; in fact, the electromagnetic (e.m.) field generated by two monochromatic counterpropagating pump waves leads to interference effects inside a quarter-wave symmetric 1D-PBG structure. Finally, here, for the first time to the best of our knowledge, a large number of theoretical assumptions on QNM metrics for an open cavity, never discussed in literature, are proved, and a simple and direct method to calculate the QNM norm for a 1D-PBG structure is reported.

Modeling electromagnetic resonators using quasinormal modes

“…The one-dimensional problem was also investigated by Settimi in Refs. [32,33], and Doost et al have treated slabs [34], cylinders [35] and spheres [36] by a QNM expansion of the Green tensor. For modeling using a bi-orthogonal basis in one dimension, see also Refs.…”

Constructing a partially transparent computational boundary for UPPE using leaky modes

“…In this section we will design asymptotic formulas for all solutions ξ, ξ 0 to equations (16), (18), and thus determine all modes for the system and their respective dispersion laws. Let us start by observing that ξ 0 = 0 is a solution to equation (18) and that the corresponding solution vector to the linear system (16) is given by…”

On the Theory of Coupled Modes in Optical Cavity-Waveguide Structures

“…In many practical applications of QNMs, and in the present case in particular, we are not interested in a full expansion of the field. Rather, we seek an expansion in terms of at most a few QNMs in each cavity, which can be treated analytically and often provide a surprisingly accurate description [35,36,51,[53][54][55][56][57][58][59]. In such an approach, at frequencies close to the cavity resonance and positions in or near the cavity, we assume that the Green tensor may be well approximated as [59] …”

“…Similarly, to calculate the reflected light in the limit of high Q-values, we can set Φ = −1 in Eq. (36) and use the expression for the coupling in Eq. 30 to write…”

“…Similar ideas were introduced for transmission calculations in a one dimensional system in Ref. [36], and very recently a scattering matrix approach to the CMT was presented in Ref. [37].…”