Whispering-gallery mode calculator

Any transparent sphere with a higher refractive index than its surroundings: silica microspheres (the classic, with very high Q), polystyrene beads, titanium dioxide and other high-index microspheres (stronger confinement in smaller spheres), and liquid droplets. Choose the material and diameter here to get every optical whispering-gallery mode in a range.

A microsphere, microdisk or droplet made of (or coated with) a gain medium lases on its whispering-gallery modes: their high Q keeps light circulating long enough for amplification, giving very low thresholds and narrow emission lines at the mode wavelengths this calculator lists. Silica and polystyrene microspheres are common hosts.

Light trapped by total internal reflection that circulates just inside the surface of a sphere or droplet. Each mode has a polarization (TE or TM), an angular number l (wavelengths around the circumference) and a radial number n (field maxima across the radius).

From the exact complex resonance (pole) of the sphere's Mie coefficient: Q is the resonance frequency over its linewidth, including radiation leakage and the material's absorption. Surface roughness, contamination and coupling to a fibre or prism lower the Q of a real resonator further.

How far each resonance shifts per unit change of the surrounding refractive index and of the radius: the sensitivities used in whispering-gallery mode sensing.

Neighbouring modes of the same family are spaced by about λ²/(π D n), for diameter D and refractive index n; the calculator lists every mode in the range, so the spacing can be read directly.