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

T-shaped silicon waveguide coupled with a micro-ring resonator-based Fano resonance modulator

Fano resonance has an asymmetric and sharp resonance peak near the resonance wavelength, enhancing optical modulation performance. Here, a Fano resonant silicon optical modulator with a micro-ring resonator (MRR) coupled with a T-shaped waveguide is designed. Compared with an MRR modulator, a Fano resonance-based modulator has a smaller wavelength range of changes in optical intensity (from 0 a.u. to 1 a.u.). Under the condition of achieving the same light intensity change, Fano resonance only needs to shift the wavelength by 0.07 times compared with MRR. By optimizing the doping section and the Fano resonance line shape, the modulation depth of the Fano modulator is 12.44 dB, and an insertion loss of 0.41 dB is obtained. Moreover, it improves the modulation linearity. This modulator provides a new idea, to the best of our knowledge, for the single-cavity Fano resonance modulator.

Optical bistability, amplification, and transparency in a one-dimensional photonic crystal with a nonlinear central layer

In this paper, we investigate optical properties of a multilayer one-dimensional photonic crystal, where the central layer is doped with one of different kinds of three-level atomic systems, e.g., Vee, Λ, upper coupling ladder, and lower coupling ladder. Then, the control of optical bistability properties of the photonic crystal, by Rabi frequency of the coupling field, spontaneously generated coherence, and probe detuning, is studied. We discuss the advantages and disadvantages of different systems' optical properties. It is shown that the investigated photonic crystals have a bistability property as well as full transparency. Also, the photonic crystals show some amplification in transmission and even reflection of the probe field.

Coupled-mode-theory framework for nonlinear resonators comprising graphene

A general framework combining perturbation theory and coupled-mode theory is developed for analyzing nonlinear resonant structures comprising dispersive bulk and sheet materials. To allow for conductive sheet materials, a nonlinear current term is introduced in the formulation in addition to the more common nonlinear polarization. The framework is applied to model bistability in a graphene-based traveling-wave resonator system exhibiting third-order nonlinearity. We show that the complex conductivity of graphene disturbs the equality of electric and magnetic energies on resonance (a condition typically taken for granted), due to the reactive power associated with the imaginary part of graphene's surface conductivity. Furthermore, we demonstrate that the dispersive nature of conductive materials must always be taken into account, since it significantly impacts the nonlinear response. This is explained in terms of the energy stored in the surface current, which is zeroed-out when linear dispersion is neglected. The results obtained with the proposed framework are compared with full-wave nonlinear finite-element simulations with excellent agreement. Very low characteristic power for bistability is obtained, indicating the potential of graphene for nonlinear applications.

Self-organization of frozen light in near-zero-index media with cubic nonlinearity

Optical beams are generally unbound in bulk media, and propagate with a velocity approximately amounting to the speed of light in free-space. Guidance and full spatial confinement of light are usually achieved by means of waveguides, mirrors, resonators, and photonic crystals. Here we theoretically demonstrate that nonlinear self-organization can be exploited to freeze optical beams in bulk near-zero-index media, thus enabling three-dimensional self-trapping of still light without the need of optical resonators. Light is stopped to a standstill owing to the divergent wavelength and the vanishing group velocity, effectively rendering, through nonlinearity, a positive-epsilon trapping cavity carved in an otherwise slightly-negative-epsilon medium. By numerically solving Maxwell’s equations, we find a soliton-like family of still azimuthal doughnuts, which we further study through an adiabatic perturbative theory that describes soliton evaporation in lossy media or condensation in actively pumped materials. Our results suggest applications in optical data processing and storage, quantum optical memories, and soliton-based lasers without cavities. Additionally, near-zero-index conditions can also be found in the interplanetary medium and in the atmosphere, where we provide a complementary explanation to the rare phenomenon of ball-lightning.

Deterministic phase engineering for optical Fano resonances with arbitrary lineshape and frequencies

We present an approach of deterministic phase engineering that can enable the rational design of optical Fano resonances with arbitrarily pre-specified lineshapes. Unlike all the approaches previously used to design optical Fano resonances, which fall short of designing the resonances with arbitrary lineshapes because of the lack of information for the optical phases involved, we develop our approach by capitalizing on unambiguous knowledge for the phase of optical modes. Optical Fano resonances arise from the interference of photons interacting with two optical modes with substantially different quality factors. We find that the phase difference of the two modes involved in optical Fano resonances is determined by the eigenfrequency difference of the modes. This allows us to deterministically engineer the phase by tuning the eigenfrequency, which may be very straightforward. We use dielectric grating structures as an example to illustrate the notion of deterministic engineering for the design of optical Fano resonances with arbitrarily pre-specified symmetry, linewidth, and wavelengths.

Symmetry breaking in binary chains with nonlinear sites

We consider a system of two or four nonlinear sites coupled with binary chain waveguides. When a monochromatic wave is injected into the first (symmetric) propagation channel, the presence of cubic nonlinearity can lead to symmetry breaking, giving rise to emission of antisymmetric wave into the second (antisymmetric) propagation channel of the waveguides. We found that in the case of nonlinear plaquette, there is a domain in the parameter space where neither symmetry-preserving nor symmetry-breaking stable stationary solutions exit. As a result, injection of a monochromatic symmetric wave gives rise to emission of nonsymmetric satellite waves with energies differing from the energy of the incident wave. Thus, the response exhibits nonmonochromatic behavior.

Coupled-resonator-induced transparency in photonic crystal waveguide resonator systems

We present an optical coupling system, which consists of waveguide, cavity and waveguide resonator, to investigate coupled-resonator-induced transparency effect. The transmission properties are analyzed theoretically by using coupled-mode theory in time domain. We also numerically demonstrate the effect by simulating the propagation of electromagnetic waves in photonic crystals by finite-difference time-domain method.

Transfer of micro and nano-photonic silicon nanomembrane waveguide devices on flexible substrates

This paper demonstrates transfer of optical devices without extra un-patterned silicon onto low-cost, flexible plastic substrates using single-crystal silicon nanomembranes. Employing this transfer technique, stacking two layers of silicon nanomembranes with photonic crystal waveguide in the first layer and multi mode interference couplers in the second layer is shown, respectively. This technique is promising to realize high density integration of multilayer hybrid structures on flexible substrates.

Transmission through a Kerr barrier in photonic crystal waveguides: dispersion effects

The transmission of guided modes through a barrier of Kerr nonlinear optical media contained within a photonic crystal waveguide of linear dielectric media is studied in order to determine the effects of the dispersion of the incident waveguide modes on their barrier transmission coefficients. In McGurn (2008 Phys. Rev. B 77 115105) the conditions under which resonances exist in the guided mode transmission through the barrier were investigated for an incident waveguide mode having a single fixed frequency and a wavevector near the edge of the Brillouin zone. The transmission coefficient maxima were determined as functions of two parameters characterizing the Kerr nonlinearity of the barrier media and shown to exhibit a complex pattern in the two parameter space of the Kerr parameters, associated with various kinds of modes excited within the barrier. In the present paper the focus is on how the pattern of transmission resonance maxima in the two parameter Kerr parameter space is affected by varying the wavevector and frequency of the guided modes incident on the barrier. In addition, the effects of the barrier size on the pattern are determined. The focus of the paper is on affirming the classification scheme proposed in our previous papers upon the introduction of dispersive effects. The dynamical equations of our model are quite general, so it is expected that this scheme will be useful in studying the nonlinear dynamics of other nonlinear physical models which may or may not be based on photonic crystal waveguides.

Modulation instability in nonlinear coupled resonator optical waveguides and photonic crystal waveguides

Modulation instability (MI) in a coupled resonator optical waveguide (CROW) and photonic-crystal waveguide (PCW) with nonlinear Kerr media was studied by using the tight-binding theory. By considering the coupling between the defects, we obtained a discrete nonlinear evolution equation and termed it the extended discrete nonlinear Schrödinger (EDNLS) equation. By solving this equation for CROWs and PCWs, we obtained the MI region and the MI gains, G(p,q), for different wavevectors of the incident plane wave (p) and perturbation (q) analytically. In CROWs, the MI region, in which solitons can be formed, can only occur for pa being located either before or after pi/2, where a is the separation of the cavities. The location of the MI region is determined by the number of the separation rods between defects and the sign of the Kerr coefficient. However, in the PCWs, pa in the MI region can exceed the pi/2. For those wavevectors close to pi/2, the MI profile, G(q), can possess two gain maxima at fixed pa. It is quite different from the results of the nonlinear CROWs and optical fibers. By numerically solving the EDNLS equation using the 4th order Runge-Kutta method to observe exponential growth of small perturbation in the MI region, we found it is consistent with our analytic solutions.

Nonlinear Fano-Feshbach resonances

We study the wave scattering in an one-dimensional discrete system with two side-coupled defects. Each of the defects exhibits the Fano resonance as a resonant suppression of transmission, i.e., resonant reflection. We demonstrate that the interaction between two Fano resonances may give rise to a birth of a very narrow resonance. This effect may be understood in terms of the overlapping resonances, as suggested by Feshbach [Ann. Phys. 5, 357 (1958)]. We consider two cases, when the defects are coupled either locally or nonlocally to the discrete array. In the latter case, a sharp asymmetric resonance appears with a large quality factor. We demonstrate that by introducing a nonlinearity at side-coupled defects a closed loop in the nonlinear transmission coefficient may appear, which results in bistable response.

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.

Light scattering by a finite obstacle and fano resonances

The conditions for observing Fano resonances at elastic light scattering by a single finite-size obstacle are discussed. General arguments are illustrated by consideration of the scattering by a small (relative to the incident light wavelength) spherical obstacle based upon the exact Mie solution of the diffraction problem. The most attention is paid to recently discovered anomalous scattering. An exactly solvable one-dimentional discrete model with nonlocal coupling for simulating diffraction in wave scattering in systems with reduced spatial dimensionality is also introduced and analyzed. Deep connections between the resonances in the continuous and discrete systems are revealed.

Trapping gap solitons in a resonant photonic crystal of finite length

The finite-length effect of a resonant nonlinear photonic crystal on the propagation dynamics of gap solitons is theoretically studied. This effect results in a dissipation and deceleration of the moving gap solitons such that the propagation dynamics is essentially different from that on an infinite domain. Due to this effect, two slow counterpropagating solitons can collide into a nonmoving breatherlike bound state, even under many realistic excitation circumstances.

Localized modes and bistable scattering in nonlinear network junctions

We study the properties of junctions created by the crossing of N identical branches of linear discrete networks. We reveal that for N>2 such a junction creates a topological defect and supports two types of spatially localized modes. We analyze the wave scattering by the junction defect and demonstrate nonzero reflection for any set of parameters. If the junction is nonlinear, it is possible to achieve the maximum transmission for any frequency by tuning the intensity of the scattering wave. In addition, near the maximum transmission the system shows the bistable behavior.