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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Fano-resonance mirrors with photonic crystal waveguides

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

Published Jan 25, 2006• 0 citations
Publisher

Abstract

In this work, We have generalized the discrete Fano-Anderson model to a nonlinear regime, where we assume that a discrete state possesses Kerr-type nonlinearity. In PC waveguides, it can be achieved by the filling of the removed rod with some nonlinear material. We show that the presence of nonlinearity leads to a shift of the position of the Fano resonance. By tuning the incoming light intensity, it is possible to observed Fano resonance for almost any frequency, which makes robust in the nonlinear regime. For large nonlinear frequency shift, the transmission bistability may occur

DOI
10.1109/cleoe.2005.1568378

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In this work, We have generalized the discrete Fano-Anderson model to a nonlinear regime, where we assume that a discrete state possesses Kerr-type nonlinearity. In PC waveguides, it can be achieved by the filling of the removed rod with some nonlinear material. We show that the presence of nonlinearity leads to a shift of the position of the Fano resonance. By tuning the incoming light intensity, it is possible to observed Fano resonance for almost any frequency, which makes robust in the nonlinear regime. For large nonlinear frequency shift, the transmission bistability may occur
We analyze the resonant linear and nonlinear transmission through a photonic crystal waveguide side-coupled to a Kerr-nonlinear photonic crystal resonator. First, we extend the standard coupled-mode theory analysis to photonic crystal structures and obtain explicit analytical expressions for the bistability thresholds and transmission coefficients which provide the basis for a detailed understanding of the possibilities associated with these structures. Next, we discuss limitations of standard coupled-mode theory and present an alternative analytical approach based on the effective discrete equations derived using a Green's function method. We find that the discrete nature of the photonic crystal waveguides allows a geometry-driven enhancement of nonlinear effects by shifting the resonator location relative to the waveguide, thus providing an additional control of resonant waveguide transmission and Fano resonances. We further demonstrate that this enhancement may result in the lowering of the bistability threshold and switching power of nonlinear devices by several orders of magnitude. Finally, we show that employing such enhancements is of paramount importance for the design of all-optical devices based on slow-light photonic crystal waveguides.
The reflectivity of a single-channel waveguide mode upon resonantly coupling to a Kerr-active nonlinear resonant cavity is calculated analytically, including the effects of two-photon absorption. The resonant reflectivity takes the form of a Fano resonance because the solution includes linear reflections from perturbations downstream of the localized cavity. Instead of using a Hamiltonian formulation of the scattering problem, an intuitive set of basis states is used to expand the Green's function of the electric field wave equation. All resulting overlap functions describing the linear coupling between guided and localized states, and the nonlinear renormalization of the material's refractive index, are in terms of well-defined physical quantities. Although derived in the context of photonic crystal-based waveguides and cavities, the treatment is valid for any low-loss waveguide-resonator geometry that satisfies specific weak coupling criteria. For a cavity consisting of Al0.18Ga0.82As, hosting a localized mode at 1.55 microm with a Q of 4000 and a mode volume of 0.055 microm(3), we predict the onset of bistable reflection at incident powers of approximately 40 mW. The downstream reflections lead to hysteresis loops in the reflectivity that are topologically distinct from conventional Lorentzian-derived loops characteristic of isolated Fabry-Perot cavities. We provide a stability argument that reveals the unstable branches of these unique hysteresis loops, and we illustrate some of the rich bistable behaviors that can be engineered with such downstream sources.
The authors observe experimentally optical bistability enhanced through Fano interferences in high-Q localized silicon photonic crystal resonances (Q∼30000 and modal volume ∼0.98 cubic wavelengths). This phenomenon is analyzed through nonlinear coupled-mode formalism, including the interplay of χ(3) effects such as two-photon absorption and related free-carrier dynamics, and optical Kerr as well as thermal effects and linear losses. Experimental and theoretical results demonstrate Fano resonance based bistable states with switching thresholds of 185μW and 4.5fJ internally stored cavity energy (∼540fJ consumed energy) in silicon for scalable optical buffering and logic.
We propose an optical approach to realizing Fano-type spectra of quadrature squeezing in a double-cavity-waveguide structure based on photonic crystals (PhCs). In this scheme, a partially transmitting element (PTE) in the waveguide creates the transmission and reflection light, which interferes with the outflow from the intracavity field and subsequently gives rise to Fano-type interference. Meanwhile, a degenerate parametric amplifier (DPA) embedded into the cavity is expected to yield quantum squeezed states in the interference process. After verifying the existence of the Fano resonance, we report that increasing the nonlinear gain of the DPA not only amplifies the transmitted intensity of the output field, but also improves its quadrature squeezing degree. More importantly, we illustrate that, when maintaining the high performance of quadrature squeezing, the linewidths and frequencies of the asymmetrical spectra can be modulated by adjusting the double-cavity coupling strength. This combination of Fano-type spectra and quadrature squeezing is beneficial for optimizing optical communications and signal processing with a low noise level.
We consider nonlinear Mach-Zehnder-Fano interferometer in which supports the nonlinear Fano resonances. Based on the introduced figure of merit, we demonstrate that the nonlinear Mach-Zehnder-Fano interferometer could enhance the nonlinear response up to two orders of magnitude and produce the nearly perfect dynamical bistable response compared to standard Fano resonance geometry. The enhanced resonance excitation in the nonlinear Fano defect and the step-function like linear transmission suggest that the Mach-Zehnder-Fano interferometer could be a suitable candidate involving in nonlinear manipulation of the Fano resonance. We confirm the significant enhancement of the nonlinear sensitivity both in stationary and dynamic manners. We further suggest a nonlinear photonic crystal circuit as one of the possibilities to realize our results.
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.