Sergei F. Mingaleev

All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures.

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 Greens 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.

Tunable photonic crystal circuits: concepts and designs based on single-pore infiltration.

We demonstrate that the infiltration of individual pores of certain two-dimensional photonic crystals with liquid crystals and (or) polymers provides an efficient platform for the realization of integrated photonic crystal circuitry. As an illustration of this principle, we present designs for monomode photonic crystal wave-guides and certain functional elements, such as waveguide bends, beam splitters, and waveguide intersections. These devices exhibit very low reflection over broad frequency ranges. In addition, we discuss the inherent tunability of these devices that originates in the tunability of the infiltrated material.

The Wannier function approach to photonic crystal circuits

We introduce a novel approach to the accurate and efficient calculation of the optical properties of defect structures embedded in photonic crystals (PCs). This approach is based on an expansion of the electromagnetic field into optimally adapted photonic Wannier functions, which leads to effective lattice models of the PC structures. Calculations for eigenmode frequencies of simple and complex cavities as well as the dispersion relations for straight waveguides agree extremely well with the results from numerically exact supercell calculations. Similarly, calculations of the transmission through various waveguiding structures agree very well with the results of corresponding finite-difference time domain simulations. Besides being substantially more efficient than standard simulation tools, the Wannier function approach offers considerable insight into the nature of defect modes in PCs. With this approach, design studies and accurate simulation of optical anisotropic and non-linear defects as well as detailed investigations of disorder effects in higher-dimensional PCs become accessible.

Nonlinear Fano resonance and bistable wave transmission

We consider a discrete model that describes a linear chain of particles coupled to a single-site defect with instantaneous Kerr nonlinearity. We show that this model can be regarded as a nonlinear generalization of the familiar Fano-Anderson model and it can generate amplitude-dependent bistable resonant transmission or reflection. We identify these effects as the nonlinear Fano resonance and study its properties for continuous waves and pulses.

Coupled-resonator-induced reflection in photonic-crystal waveguide structures

We study the resonant transmission of light in a coupled-resonator optical waveguide interacting with two nearly identical side cavities. We reveal and describe a novel effect of the coupled-resonator-induced reflection (CRIR) characterized by a very high and easily tunable quality factor of the reflection line, for the case of the inter-site coupling between the cavities and the waveguide. This effect differs sharply from the coupled-resonator-induced transparency (CRIT)--an all-optical analogue of the electromagnetically-induced transparency--which has recently been studied theoretically and experimentally for the structures based on micro-ring resonators and photonic crystal cavities. Both CRIR and CRIT effects have the same physical origin which can be attributed to the Fano-Feshbach resonances in the systems exhibiting more than one resonance. We discuss the applicability of the novel CRIR effect to the control of the slow-light propagation and low-threshold all-optical switching.

Nonlinear Photonic Crystals Toward All-Optical Technologies

Photonic crystals, an analog of semiconductors for light waves, are composite periodic dielectric materials that provide novel and unique ways to control many aspects of electromagnetic radiation. Harnessing the nonlinear properties of photonic crystals and photonic-crystal waveguides offers an opportunity to create the all-optical analogs of diodes and transistors that will one day enable the first all-optical computer to be built.

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

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.

Wannier basis design and optimization of a photonic crystal waveguide crossing

We employ a novel platform for the realization of tunable photonic crystal (PC) circuits together with a Wannier basis modeling and optimization scheme in order to design a broad-band waveguide crossing. The superior performance characteristics of our design include a high bandwidth (2% of the center frequency) as well as low values for crosstalk (-40 dB) and reflection (-30 dB). In addition, we demonstrate the robustness of the device performance against fabrication disorder. Our novel design paradigm will enable efficient and ultracompact PC-based device designs with complex functionalities.

Scattering matrix approach to large-scale photonic crystal circuits.

We propose a scattering matrix approach to the modeling of large-scale photonic crystal circuits and show that the transmission properties of complex circuits can be accurately calculated on the basis of scattering matrices of individual photonic crystal devices and waveguides that connect them. In addition, we show that functional devices such as waveguide bends generally exhibit a discontinuous frequency dependence in the phases associated with their complex reflection and transmission coefficients and emphasize its importance for the adequate modeling of photonic crystal circuits.

Arbitrary angle waveguiding applications of two-dimensional curvilinear-lattice photonic crystals

We introduce a fresh class of photonic band-gap materials, curvilinear-lattice photonic crystals, whose distinctive feature is that their individual scatterers are arranged in a curvilinear lattice. We show that adhering to some restrictions in the acceptable lattice transformations, one can achieve omnidirectional photonic band gaps for an entire subclass of such structures. We demonstrate, designing an efficient arbitrary-angle waveguide bend, that curvilinear-lattice photonic crystals can be employed for creation of original types of nanophotonic devices.