Observation of Whispering Gallery Modes (WGM’s) in SrS:Eu octahedrons

We report on the observation of optical Whispering Gallery Modes (WGM’s) in SrS:Eu octahedrons. At resonant wavelengths, light undergoes total internal reflection at the surface of the particle and becomes trapped for several nanoseconds. WGM's are mainly described in spheres and in hexagonal structures, but in this investigation we focus on octahedrons. SrS:Eu octahedrons with a broad band emission at 610nm were prepared using a solvothermal synthesis method(2). Cathodoluminescence (CL) in a scanning electron microscope was used to evaluate the emission characteristics of individual octahedrons. Three different resonance modes are considered: light traveling in the equatorial plane (a) striking each boundary at an angle of 45° (transversal electric and transversal magnetic mode) ,(b) striking two opposite sides (Fabry-Pérot mode), or (c) the Fabry-Pérot mode between two parallel planes. The calculation of the WGM phase shifts is obtained starting from Fresnel's formulas, which gives us four equations for the resonant wavelengths depending on the size of the particles and the refractive index of the material. The CL emission spectrum was measured of a large ensemble of particles and of a single particle, so that a difference plot could be made to identify the WGM’s. The sharp peaks in the individual CL spectra were identified using the calculated WGM mode equations and with the refractive index of the bulk material. To improve the fit to the experimental peak positions we took the dispersion of the refractive index into account using Cauchy’s dispersion functions. In conclusion, WGM's are observed in the CL emission spectrum of a single SrS:Eu octahedron with the Fabry-Pérot modes being of minor importance. Most peaks in the CL spectrum could be identified through the WGM mode equations and Cauchy’s dispersion functions. The refractive index of a micron-sized SrS:Eu octahedron is slightly different from that of bulk crystals. References: (1) Liu et al, Appl. Physics Letters 92, 263102 (2008) (2) J. E. Van Haecke, P.F. Smet, K. De Keyser, D. Poelman, J. Electrochem. Soc. 154, 278-282 (2007) (3) D. Poelman, P.F. Smet, J. Phys. D:Appl. Phys. 36,1850-1857 (2003