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(a) Schematic of a nanobeam PhC with a conventional Bragg mirror. (b) SEM image of a silicon nanobeam PhC with a “modulated Bragg mirror.” (c) for a model cavity with exponential attenuation in the mirrors. (d) for a model cavity with Gaussian attenuation in the mirrors. (e) The fraction of the Fourier components that are within the light line, assuming a refractive index ratio of 2.5 between the waveguide and the surroundings.
(a) Schematic of a modulated nanobeam cavity. and refer to energy loss due to the coupling to the feeding waveguide and scattering/radiation losses, respectively. (b) TE band diagrams for and 0.07. The green line denotes the light line. The resonance of cavity mod40 is about 1.5% lower than the dielectric band edge of the central section with , due to the modulation. (c) Mirror strength for different FFs. An approximately linear increase is observed in the shaded region. (d) Simulated profile at the middle of the nanobeam cavity for fundamental mode A and second mode B . (e) Experimental transmission spectrum of the mod40 cavity with input power . The signal is normalized by the band edge modes (shaded region), which have unity transmission, as verified by 3D-FDTD simulations shown in the inset. Due to the very large photon life time of our ultrahigh cavity , it becomes nearly impossible to model transmission through the cavity (resonant tunneling) using the 3D-FDTD method directly. Hence, the high- cavity mode does not appear in the simulated spectrum shown in the inset. (f) Zoom-in of the transmitted signal of the fundamental mode at different input power levels (measured at the fiber tip). The dots are experimental data and the lines are the fitted curves using Eq. (1).
3D-FDTD simulation results of a waveguide-coupled cavity with 40 and 50 modulated mirror segments on each side of the cavity. The FF is changed from 0.15 at the center of the cavity to 0 at the edge. To calculate partial quality factors, we monitored the power flowing outside the cavity through closed surface enclosing the cavity. was found by monitoring the power coupled into the waveguide and projecting it onto the fundamental mode of the waveguide. found using partial Qs was in good agreement with calculated directly by monitoring time decay of the cavity field. The transmission is obtained using . is the mode volume normalized by where for silicon.
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