  Solitons, arising from nonlinear wave-matter interactions, stand out for
their intrinsic stability during wave propagation and exceptional spectral
characteristics. Their applications span diverse physical systems, including
telecommunications, atomic clocks, and precise measurements. In recent years,
significant strides have been made in developing cavity-optomechanics based
approaches to generate optical frequency combs (FCs). In this study, we present
an innovative approach, never explored before, that leverages elastomer
membrane (EM)-cavity optomechanics to achieve the generation of soliton FCs, a
highly sought-after phenomenon in the realm of nonlinear wave-matter
interactions. Our method represents a significant breakthrough due to its
streamlined simplicity, relying on a single continuous-wave (CW) laser pump and
an externally applied acoustic wave exciting an EM-cavity, which gives rise to
phonons, quantized vibrational energy states intrinsic to the elastomer's
crystalline lattice structure. The mechanical resonator and electromagnetic
cavity resonance are parametrically coupled within the microwave frequency
range, collectively orchestrate the process of soliton FCs formation with
remarkable efficiency. Numerical simulations and experimental observations
demonstrate the emergence of multiple stable localized opto-mechanical wave
packets, characterized by a narrow pulses time-domain response. Crucially, by
setting the acoustic wave frequency to match the natural frequency of the EM
resonator, the solitons' teeth are precisely spaced, and the EM's motion is
significantly amplified, giving rise to a Kerr medium. The successful
realization of optomechanical stable solitons represents a monumental
advancement with transformative potential across various fields, including
quantum computing and spectroscopy.
