Theinfinity-loop microresonator: A new integrated photonic structure working on an exceptional surface

Abstract

Exceptional points, where eigenvalues and eigenvectors coalesce, impact the behavior of different photonics components that show, e.g., enhanced sensing, coherent perfect absorption, unidirectional lasing, and chirality. However, only a few passive geometries have been developed that work on these points. Here, we introduce a novel non-Hermitian structure based on a microresonator shaped as the infinity symbol twice coupled to a bus waveguide: the infinity-loop microresonator. Unlike other structures working on an exceptional surface, the infinity-loop microresonator can achieve either high- or low-contrast unidirectional reflection with a negligible or identical reflection for counterpropagating light. It allows an easy walking through the Riemann sheet by simply controlling the phase of the light propagating in the bus waveguide, which makes it a tunable component to build more complex topological structures. Furthermore, the infinity-loop microresonator allows sensors that show the features of both an exceptional point device and a diabolic point device simultaneously.

Modeling the Non-Hermitian Infinity-Loop Micro-Resonator over a Free Spectral Range Reveals the Characteristics for Operation at an Exceptional Point

“…The low-frequency spectral peaks are similar to the results of [16], which were also shown to be independent of φ. However, the higher-frequency peaks (i.e., > ω 0 ) are strongly dependent on φ, which is a departure from the general conclusions of [16].…”

“…In [16], the transmission and reflection signals are reported to be independent of φ, and so the system apparently always operates at an EP (or on an ES). From the above analysis, we can see that, in reality, this is only the case for λ 1 and λ 2 under the strict condition µ CW a = µ CW−CCW 1 , which we consider in the subsequent discussion.…”

“…The 'Taiji'-type micro-resonator is another such implementation, in which unidirectional reflection has been demonstrated [13] and which has also been proposed for sensing applications [14]. More recently, the concept of an exceptional surface (ES) has arisen, whereby these rich spectral properties may be observed over a wide range (or entirely independent) of device operating characteristics [15,16]. Other recent examples are the Coupled-Ring Reflector (CRR) device incorporating a crisscrossing directional coupler [17] and the ILMR [16], which is comprised of a bus waveguide coupled (at two points) to a continuous loop waveguide in the shape of the infinity symbol, as shown in Figure 1.…”

“…More recently, the concept of an exceptional surface (ES) has arisen, whereby these rich spectral properties may be observed over a wide range (or entirely independent) of device operating characteristics [15,16]. Other recent examples are the Coupled-Ring Reflector (CRR) device incorporating a crisscrossing directional coupler [17] and the ILMR [16], which is comprised of a bus waveguide coupled (at two points) to a continuous loop waveguide in the shape of the infinity symbol, as shown in Figure 1. The propagation of resonant signals at the intersections is considered to be 'ideal', implying zero coupling or crosstalk with light circulating in the loops, as implied by Figure 1a.…”

“…However, this is difficult to realize in practice, and even very small degrees of crosstalk, e.g., due to fabrication imperfections, will result in clockwise and counterclockwise propagating optical fields, leading to new resonances (and resonance splitting) in the transmission and reflection spectra of such devices. Whilst this backward scattering of optical fields is dealt with separately in [16], by considering the ILMR to consist of two intersecting loops, each with clockwise (cw) and counterclockwise (ccw) mutually coupled resonant modes, as shown in Figure 1b, we can account for this behavior within a robust TCMT model based on a fourth-order matrix.…”