Quantitative measurements of the vibrational eigenmodes in ultra-high-Q silica microspheres are reported. The modes are efficiently excited via radiation-pressure induced dynamical back-action of light confined in the optical whispering-gallery modes of the microspheres (i.e. via the parametric oscillation instability). Two families of modes are studied and their frequency dependence on sphere size investigated. The measured frequencies are in good agreement both with Lamb's theory and numerical finite element simulation and are found to be proportional to the sphere's inverse diameter.Silica microcavities[1] such as microspheres [2] or microtoroids[3] possess ultra-high-Q optical whispering gallery modes (WGMs), while simultaneously exhibiting mechanical modes which lie typically in the radio frequency range. Owing to the resonant buildup of light within these cavities the effect of radiation pressure is enhanced, leading to mutual coupling between the mechanical and optical modes, as first predicted by Braginsky in the context of the Laser Interferometer Gravitational Wave Observatory, LIGO [4]. When entering the regime where the photon lifetime is comparable to the mechanical oscillation period and the cavity is pumped with a laser whose frequency slightly exceeds the WGM resonance (i.e. blue-detuned excitation), this mutual coupling gives rise to a parametric oscillation instability [4] which is characterized by regenerative mechanical oscillation of the mechanical eigenmodes. This phenomenon has been first reported in toroid microcavities [5,6,7]. On the other hand, red-detuned light can induce cooling of the mechanical mode, as recently reported [8,9,10]. In this letter, parametric oscillation instability in ultra-high-Q silica microspheres is observed and the mechanical resonant frequencies and mode patterns studied. In contrast to earlier studies of acoustic modes of nanospheres [11,12] using Raman or Brillouin scattering from ensembles, the present method allows measurement of the mechanical modes of single microspheres in a larger diameter regime (35-110 µm in our case). Furthermore, the mechanical Q-factors are determined.

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The concept of corporate social responsibility (CSR) is an ever-evolving concept in the field of business management. Even in 2021, its boundaries are evolving and researchers are linking the concept of CSR to different variables to achieve different outcomes. However, the concept of CSR in the healthcare sector is not well-explored in prior literature. The current study is an application of social identity theory to induce electronic word-of-mouth (eWOM) from consumers for a specific brand, through its CSR engagement on social media (CSRS) and consumer-company identification (CCI) in the healthcare sector of an emerging economy. The data of the current survey were collected from different patients of four large hospitals in a large city through a self-administered questionnaire (paper-pencil technique). To validate different hypotheses of the current study, the authors employed the structural-equation-modeling (SEM) technique using AMOS software. The output of SEM analysis confirmed that CSRS positively influences eWOM, and CCI mediates this relationship. The findings of the current study will be helpful for policymakers in the healthcare industry to improve their understanding of CSRS and CCI, inducing eWOM through the lens of social identity theory.

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