Whispering gallery modes in deformed hexagonal resonators



Optical resonances in polygonal resonators are due to whispering gallery modes (WGM). We investigate WGM in regular and deformed hexagonal ZnO microwire resonators. Four types of geometries are investigated: regular hexagonal and dodecagonal cross sections, hexagonal cross section elongated for one pair of facets and hexagonal cross section deformed by bending (uniaxial stress). Experimental data on mode energies and angular dispersion are correlated with model calculations and Poincaré surfaces of section. Hexagonal (ϕ = 60°), square (ϕ = 45°), triangular (ϕ = 30°), and Fabry–Pérot modes (ϕ = 0°) are observed in the various investigated geometries, ϕ being the angle of incidence at the facets with respect to the normal direction.

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Hexagonal WGMs (green, 6-WGM), triangular (red, 3-WGM), and double-triangular (blue, D3-WGM) rays in regular hexagons, elongated hexagons and hexagons deformed by bending. Triangular WGMs are stable modes in all three resonators. Hexagonal modes are not stable in the bent hexagon.