Geometry of the 2-D square-lattice phoxonic crystal structure. (a) Phoxonic crystal with a line defect, (b) unit cell of square lattice, and (c) first Brillouin zone.
Calculated frequency band structure of photonic TM mode in the 2-D square lattice phoxonic crystal without the line defect. Gray range denotes the full photonic band gap.
(a) Guided optical defect bands and (b) transmission spectrum of TM waves propagating through the line-defect phoxonic crystal. The transmission shows a peak in the full photonic band gap at frequency foa/c = 0.2448.
Optical wave field of TM modes at foa/c = 0.2448. The optical waves are confined to the line defect. (a) Electric field Ez , (b) x-component magnetic field Hx , and (c) y-component magnetic field Hy.
Calculated dispersion curves of mixed acoustic modes (x-y polarization modes) in the 2-D square lattice phoxonic crystal without the line defect. Gray range denotes the full phononic band gap.
Defect bands of acoustic cavity modes in the full phononic band gap. There are four acoustic cavity modes in the band gap (labelled as A, B, C, and D). The flat bands show the localization characteristics of the modes that can reach amplified acoustic wave fields.
Eigenmode shapes and the induced refractive index distributions of the four acoustic cavity modes (modes A–D) in the line-defect phoxonic crystal, where is the total displacement.
Variations in refractive indices nx (solid curves) and ny (dashed curves) along the length of the line defect induced by the four acoustic cavity modes. (a) Mode A (y = 0.2a), (b) mode B (y = 0), (c) mode C (y = 0.2a), (d) mode D (y = 0).
Frequency shift of the guided optical TM modes presented in Fig. 3(a) under the action of the four acoustic cavity modes A (a), B (b), C (c), and D (d). The contributions of photoelastic effect (dotted-dashed curves), interface effect (dashed curves), and simultaneous effects (solid curves) to AO interaction are displayed separately. The frequency shift under the action of modes D is one order of magnitude larger than the shift under the action of the other three modes. The curves in regions I and II correspond to the shift of the lower and higher optical defect bands, respectively.
Transmissions of guided optical TM wave mode with action of the acoustic cavity mode D. Solid curve denotes the case without the AO interaction, and dashed and dotted-dashed curves denote cases with the action of acoustic cavity mode D at phases 0° and 180°, respectively.
Material constants of silicon used in the simulations. 22
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