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The (a) nominal unit cell with and (b) defect unit cell with of the OMC nanobeam cavity. The (c) optical and (e) mechanical band structure for propagation along the x-axis in the nominal unit cell, with quasi-bandgaps (red regions) and cavity mode frequencies (black dashed) indicated. In (c), the light line (green curve) divides the diagram into two regions: the gray shaded region above representing a continuum of radiation and leaky modes, and the white region below containing guided modes with y-symmetric (red bands) and y-antisymmetric (blue bands) vector symmetries. In (e), modes that are y- and z-symmetric (red bands), andmodes of other vector symmetries (blue bands) are indicated. These mechanical simulations use the full anisotropic elasticity matrix, where , and assume a crystallographic orientation for the x-axis ( orientation simulations exhibit a small, frequency shift in the bands below 8 GHz). The bands from which the localized cavity modes are formed are shown as thicker curves. Tuning of the (d) X-point optical and (f) -point mechanical modes of interest as the unit cell is smoothly transformed from the nominal to the defect unit cell.
(a) Plot of the unit cell parameters, a (blue ○), (green dashed □), and (red □), along the length of the nanobeam, in units of . (b) The normalized optical field and (c) the normalized mechanical displacement field of the localized optical and mechanical modes, respectively. (d) The normalized surface density of the integrand in Eq. (1), showing the contributions to . (e) The normalized volumetric density of the integrand in Eq. (3), showing the contributions to . (f) Scanning electron microscope (SEM) image of the experimentally realized cavity.
(a) The unit cell of the phononic shield with parameters . (b) Full in-plane mechanical band diagram with complete phononic bandgap (red region) and frequency of the acoustic mode of the cavity indicated (black dashed line). (c) SEM image showing the phononic shield (green) around the nanobeam.
(a) Normalized optical transmission spectrum, centered at 1544.8 nm, showing the fundamental optical cavity mode of the nanobeam, with a measured intrinsic . (b) Optically transduced thermal noise power spectral density centered at the mechanical frequency, , of the breathing mode, taken at with the input laser red-detuned (; red curve) and blue-detuned (; blue curve) from the cavity. (c) Measured cooperativity, C, as function of intracavity photon number, , for red detuning .
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