Comprehensive numerical investigation of intrinsic mechanical modes of one-dimensional optical waveguides

Typical suspended one-dimensional waveguides, tapered optical fibers (TOFs), combine sub-wavelength optical confinement with mechanical flexibility, enabling applications in optomechanics, quantum optics, atomic physics and sensing. However, the intrinsic mechanical modes (IMMs) of TOF, including flexural, longitudinal, and torsional modes, remain underexplored. Through analytical formulations and simulations, we comprehensively and explicitly explore the classification of various mechanical modes of a TOF. The characteristics of various TOF IMMs are investigated in detail, including frequencies, displacements, and vibration patterns. Novel degenerate IMMs are confirmed, and these modes result from dynamic coupling between the modes in the tapered and waist regions. It is also revealed that the IMMs are strongly geometry-dependent. The frequencies scale with the length and diameter of the waist, whereas linear tapers exhibit stronger energy localization than exponential tapers. The elaborate design and engineering of TOFs allow for precise mechanical resonance tuning and seamless integration with nanophotonic systems, positioning them as a versatile platform for quantum precision metrology and advanced optomechanical technologies.