Experimental Evidence of Thermal Capillary Waves Excitation on a Microsphere Surface

Abstract

Whispering-gallery-mode (WGM) microsphere resonators have emerged as a versatile platform across various photonic applications. Despite significant progress, their performance at short wavelengths is fundamentally limited by scattering-induced optical losses that restrict achievable quality factors (Q-factor). Although surface roughness has long been recognised as the leading cause of these losses, its physical origin has remained unclear, with current understanding attributing it to unavoidable fabrication imperfections. Here, we show that thermally excited capillary waves are the fundamental source of scattering losses in microsphere cavities. Using high-resolution atomic force microscopy (AFM) combined with rigorous statistical analysis, we quantitatively identify the characteristic signatures of frozen capillary fluctuations at the sub-nanometre level. The experimentally extracted roughness parameters show close agreement with theoretical predictions based on capillary wave theory. These findings fundamentally revise the prevailing interpretation of surface scattering losses and establish thermodynamic fluctuations, rather than fabrication defects, as the limiting roughness mechanism. By identifying frozen capillary waves as the limiting factor, this work opens new pathways for engineering ultra-high-Q microsphere resonators through fabrication management strategies, particularly for visible- and ultraviolet-photonic applications where scattering losses are most severe.