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Low-threshold bistability of slow light in photonic-crystal waveguides

Sergei F. Mingaleev, Andrey E. Miroshnichenko, and Yuri S. Kivshar

Open Access Open Access

Abstract

We analyze the resonant transmission of light through a photonic-crystal waveguide side coupled to a Kerr nonlinear cavity, and demonstrate how to design the structure geometry for achieving bistability and all-optical switching at ultralow powers in the slow-light regime. We show that the resonance quality factor in such structures scales inversely proportional to the group velocity of light at the resonant frequency and thus grows indefinitely in the slow-light regime. Accordingly, the power threshold required for all-optical switching in such structures scales as a square of the group velocity, rapidly vanishing in the slow-light regime.

©2007 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. Frequencies of localized cavity modes created by changing the radius r def of (a) single defect rod and (b) two neighboring defect rods in the photonic crystal created by a triangular lattice of rods with ε=12 and radius r=0.25a in air, a is the lattice spacing. (c) Dispersion of the W1 photonic-crystal waveguide created by removing a row of rods in the same photonic crystal. Results are calculated using 11 maximally localized Wannier functions [27] (blue lines) and the supercell plane-waves method [28] (red circles).

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Fig. 2.
Fig. 2. Single-defect waveguide-cavity structure with the radius of the defect rod r def: (a) Electric field at the resonance reflection for r def=0.102a; (b) Transmission spectra for different values of r def: 0.1a (black), 0.101a (blue), 0.102a (red), 0.1025a (green). For convenience, in addition to the light frequency on the bottom axis, we indicate on the top axis the complementary group velocity, vg (ω), of the waveguide’s guided mode.

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Fig. 3.
Fig. 3. Double-defect waveguide-cavity structure with the cavity created by two defect rods with the radius r def: (a) Electric field at the resonance reflection for r def=0.121a; (b) Transmission spectra for different values of r def: 0.119a (black), 0.120a (blue), 0.121a (red), 0.1213a (green).

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Fig. 4.
Fig. 4. (a) Quality factor Q vs. group velocity vg at resonance for the structure shown in Fig. 3; (b) Nonlinear bistable transmission in the same structure at the frequencies with 80% of linear light transmission vs. the incoming light power for different values of r def: 0.119a (black), 0.120a (blue), 0.121a (red), 0.1214a (green); (c) Switch-off bistability threshold Pth vs. the group velocity vg at resonance for the same structure.

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