Analysis of Terahertz-Regime Electromagnetic Waves in Photonic Crystals Generating Fano Resonances
Authors
Schjøtt, Andreas Grøndal ; Vejen, Laurits ; Hjorth, Veronica Elze
Term
4. term (FYS10)
Education
Publication year
2023
Submitted on
2023-06-01
Pages
135
Abstract
Dette projekt undersøger og karakteriserer Fano-resonanser i terahertz-området i fotoniske krystaller bestående af siliciumstænger på en siliciumplade. For at beregne transmissionsspektre udvikles tre tredimensionelle Fourier-modalemetoder, som adskiller sig i behandlingen af permittivitet: en simpel direkte formulering, en formulering baseret på Lifeng Lis faktoriseringsregler samt en formulering med tensorbeskrivelse. Alle tre modeller konvergerer til samme resultat, hvor Li-formuleringen konvergerer hurtigst, og resultaterne valideres yderligere med en todimensionel Fourier-modalemetode. Resonansernes oprindelse kortlægges ved at beregne ledede bølgetilstande, som den indkommende bølge kan koble til. Undersøgelserne omfatter ændringer i indfaldsvinkel og -polarisation, stanggeometri (firkantet eller cirkulært tværsnit), stanghøjde og tværsnitsareal, periodicitetslængde samt pladetykkelse. I en endimensionel periodisk struktur kan alle resonanser relateres til ledede tilstande, mens der i todimensionelle strukturer optræder resonanser uden direkte korresponderende tilstand, forklaret ved superposition af S- og P-polariseret lys. Transmittansen påvirkes kun svagt af stangens form, hvis tværsnitsarealet holdes konstant. Øget indfaldsvinkel splitter resonanser i to og kan i praksis udvaske dem for ikke-parallelle stråler. Lavere stanghøjde flytter resonanser mod højere frekvens og gør dem smallere (højere Q-faktor), mens meget små eller meget store tværsnitsarealer også øger Q-faktoren; større stangareal og tykkere plade flytter resonanser mod lavere frekvens, og større periode flytter dem mod længere bølgelængder. Samlet giver arbejdet et konsistent beregningsgrundlag for analyse af Fano-resonanser i terahertz-fotoniske krystaller.
This project investigates and characterizes Fano resonances in the terahertz range in photonic crystals composed of silicon rods on a silicon plate. To compute transmittance spectra, three three-dimensional Fourier modal method formulations are developed that differ in how the permittivity is treated: a simple direct approach, a formulation using Lifeng Li’s factorization rules, and a tensor-based formulation. All three converge to the same results, with the Li-based approach converging fastest, and the models are further validated by comparison to a two-dimensional Fourier modal method. The origin of resonances is probed by calculating guided modes that the incident field can couple to. Parameter studies vary incidence angle and polarization, rod geometry (square or circular cross-section), rod height and cross-sectional area, the lattice period, and the plate thickness. In a one-dimensional periodic structure, all resonances can be traced to guided modes, whereas in two dimensions some resonances lack a direct counterpart and are explained by superposition of S- and P-polarized light. Transmittance is nearly unchanged by rod shape if cross-sectional area is fixed. Increasing incidence angle splits resonances and can wash them out for non-parallel beams. Reducing rod height shifts resonances to higher frequency and narrows them (higher Q-factor); very small or very large areas also raise the Q-factor, while larger area and thicker plate shift resonances to lower frequency, and increasing the period shifts them to longer wavelengths. Overall, the work provides a consistent computational basis for analyzing terahertz Fano resonances in photonic crystals.
[This summary has been generated with the help of AI directly from the project (PDF)]
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