Potentials with partly constant FSR: semiclassical theory and applications to SNAP microresonators

TL;DR

This paper develops a semiclassical theory for SNAP microresonators with partly constant free spectrum range (FSR), analyzing their properties and potential advantages for applications like frequency combs and signal processing.

Contribution

It introduces a novel semiclassical approach to model SNAP microresonators with localized constant FSR potentials, expanding the understanding of their spectral properties.

Findings

Potentials with localized constant FSR are feasible and useful.

Semiclassical analysis reveals key properties of these potentials.

Applications include improved frequency comb generation and signal processing.

Abstract

Propagation of whispering gallery modes in Surface Nanoscale Axial Photonics (SNAP) microresonators, fabricated at the optical fiber surface, is commonly described by a one-dimensional wave equation, resembling the Schr\"odinger equation, where the fiber cutoff frequency (CF) varying along the fiber length plays the role of potential and the light frequency plays the role of energy. Of particular importance for applications including frequency comb generation, frequency conversion, and signal processing are SNAP microresonators with constant free spectrum range (FSR). Here we note that, in addition to CF potentials with a globally constant FSR, the potentials having constant FSR confined within a specific spectral region may be sufficient or, in certain cases, preferable for a range of applications. We describe such potentials in semiclassical approximation and analyze their properties considering representative examples.