Hybrid coupled mode modelling of the evanescent excitation of a dielectric tube by semi-guided waves at oblique angles
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Hybrid coupled mode modelling of the evanescent excitation of a dielectric tube by semi‑guided waves at oblique angles Manfred Hammer1 · Lena Ebers1 · Jens Förstner1 Received: 12 July 2020 / Accepted: 8 October 2020 © The Author(s) 2020
Abstract A dielectric step-index optical fiber with tube-like profile is considered, being positioned with a small gap on top of a dielectric slab waveguide. We propose a 2.5-D hybrid analytical/numerical coupled mode model for the evanescent excitation of the tube through semiguided waves propagating in the slab at oblique angles. The model combines the directional polarized modes supported by the slab with analytic solutions for the TE-, TM-, and orbital-angular-momentum (OAM) modes of the tube-shaped fiber. Implementational details of the scheme are discussed, complemented by finite-element simulations for verification purposes. Our results include configurations with resonant in-fiber excitation of OAM modes with large orbital angular momentum and strong field enhancement. Keywords Photonics · Integrated optics · Dielectric resonators · Modes of dielectric fibers/ tubes · Orbital angular momentum modes · Oblique excitation by semi-guided waves
1 Introduction Slab-coupled microstrips (Hammer et al. 2019), when considered in a context of photonic microresonators (Chremmos et al. 2010), can exhibit rather remarkable filtering properties. In the most basic configuration, a simple dielectric strip, positioned at some distance above a slab waveguide, is evanescently excited, at oblique angles of incidence, by the semiguided waves supported by the slab. Narrow transmission resonances can be observed; the essentially lossless system is characterized by a Q-factor factor that grows exponentially with the gap between slab and strip, accompanied by a strong enhancement of the field in the cavity strip. Similar effects have been predicted for filter configurations that involve two bus waveguides, and one or two potentially coupled microstrip cavities (Ebers et al. 2019). The rectangular microstrips considered previously by the authors support resonances of standing-wave type (Manolatou et al. 1999), as opposed to the traveling-wave resonances of ring- or disk-shaped optical microresonators (Hiremath and Hammer 2010). One might thus be interested in what happens if one replaces the former rectangular strip cavity by a * Manfred Hammer manfred.hammer@uni‑paderborn.de 1
FG Theoretical Electrical Engineering, Paderborn University, Warburger Straße 100, 33098 Paderborn, Germany
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hollow-core optical fiber, a dielectric “tube”, with circular cross section. Figure 1 shows a respective configuration. On the one hand, a system as in Fig. 1 can be simulated readily by numerical means, solving a scattering problem in the frequency domain, on a 2-D cross-sectional (x-z-) computational window, equipped with transparent-influx-boundary conditions, and assuming a uniform harmonic dependence of all fields on the tube-axis-coordinate (Çi
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