Stimulated Brillouin scattering enhancement in silicon inverse opal waveguides

Silicon is an ideal material for on-chip applications, however its poor acoustic properties limit its performance for important optoacoustic applications, particularly for stimulated Brillouin scattering (SBS). We theoretically show that silicon inverse opals exhibit a strongly improved acoustic performance that enhances the bulk SBS gain coefficient by more than two orders of magnitude. We also design a waveguide that incorporates silicon inverse opals and which has SBS gain values that are comparable with chalcogenide glass waveguides. This research opens new directions for opto-acoustic applications in on-chip material systems.

Metamaterial control of stimulated Brillouin scattering

Using full opto-acoustic numerical simulations, we demonstrate enhancement and suppression of the SBS gain in a metamaterial comprising a subwavelength cubic array of dielectric spheres suspended in a dielectric background material. We develop a general theoretical framework and present several numerical examples using technologically important materials. For As₂S₃ spheres in silicon, we achieve a gain enhancement of more than an order of magnitude compared to pure silicon and for GaAs spheres in silicon, full suppression is obtained. The gain for As₂S₃ glass can also be strongly suppressed by embedding silica spheres. The constituent terms of the gain coefficient are shown to depend in a complex way on the filling fraction. We find that electrostriction is the dominant effect behind the control of SBS in bulk media.

Paired modes of heterostructure cavities in photonic crystal waveguides with split band edges

We investigate the modes of double heterostructure cavities where the underlying photonic crystal waveguide has been dispersion engineered to have two band-edges inside the Brillouin zone. By deriving and using a perturbative method, we show that these structures possess two modes. For unapodized cavities, the relative detuning of the two modes can be controlled by changing the cavity length, and for particular lengths, a resonant-like effect makes the modes degenerate. For apodized cavities no such resonances exist and the modes are always non-degenerate.

Modes of shallow photonic crystal waveguides: semi-analytic treatment

We investigate the formation of photonic crystal waveguide (PCW) modes within the framework of perturbation theory. We derive a differential equation governing the envelope of PCW modes constructed from weak perturbations using an effective mass formulation based on the Luttinger-Kohn method from solid-state physics. The solution of this equation gives the frequency of the mode and its field. The differential equation lends itself to simple analytic approximations which reduce the problem to that of solving slab waveguide modes. By using this model, we demonstrate that the nature of the projected band structure and corresponding Bloch functions are central to the behaviour of PCW modes. With this understanding, we explain why the odd mode in a hexagonal PCW spans the entire Brillouin zone while the even mode is cut off.

High-Q cavities in multilayer photonic crystal slabs

We propose a novel concept for creating high-Q cavities in photonic crystal slabs (PCS). These cavities are formed by depositing a polymer layer on top of a photonic crystal membrane fabricated in a high index semiconductor slab. We show that such multilayer structures exhibit a mode-gap and can yield high-Q microcavities with quality factors of Q approximately 106. This allows the cavity to be created by polymer processing, following the much more demanding semiconductor processing that is used to generate a uniform PCS. Depending on the polymer used, these structures can be additionally tuned using photosensitivity or the electro-optic effect.

Tunable enhancement of a soliton spectrum using an acoustic long-period grating

We demonstrate a scheme for tunable shaping of a soliton spectrum. Specifically, we show a local enhancement of 6 dB in the pulse spectrum by propagating the pulse through a fiber containing micro-bends generated by a flexural acoustic wave - an acoustic long-period grating (LPG) - followed by nonlinear propagation through uniform fiber. The location of the enhancement peak can be tuned by external control of the acoustic frequency of the LPG. We discuss the potential application of this scheme to tunable supercontinuum sources.

Efficient slow light coupling into photonic crystals

We study light coupling between two photonic crystal wave-guides, one of which supports slow light. We show theoretically that a short photonic crystal waveguide between the two that need to be coupled, can lead to a vanishingly small reflectivity. The design relies on the analogy with a lambda/4 anti-reflection layer in thin-film optics.We find that some of the usual relationships between the Fresnel coefficients at an interface no longer hold.

Dispersion engineering of highly nonlinear As(2)S(3) waveguides for parametric gain and wavelength conversion

We numerically demonstrate the use of waveguide dispersion to shift the zero-dispersion wavelength of an As(2)S(3) waveguide to telecom wavelengths. The device implications for parametric gain and wavelength-conversion via four-wave mixing are investigated, giving an operating bandwidth of 550 nm. We also show that the photosensitivity of chalcogenide can be used for post-fabrication tuning of waveguide dispersion characteristics.

Gap-edge Asymptotics of defect modes in 2D Photonic Crystals

We consider defect modes created in complete gaps of 2D photonic crystals by perturbing the dielectric constant in some region. We study their evolution from a band edge with increasing perturbation using an asymptotic method that approximates the Green function by its dominant component which is associated with the bulk mode at the band edge. From this, we derive a simple exponential law which links the frequency difference between the defect mode and the band edge to the relative change in the electric energy. We present numerical results which demonstrate the accuracy of the exponential law, for TE and TM polarizations, hexagonal and square arrays, and in each of the first and second band gaps.

Exact dynamic localization in curved AlGaAs optical waveguide arrays

We present experimental observations of exact dynamic localization of an optical beam in a periodically curved AlGaAs waveguide array. The dynamic localization of the beam is "exact" in that it is observed even when the photonic band of the array is not well described in the nearest-neighbor tight-binding approximation. We present the spatial evolution of the beam around the two-period plane in the structure, explicitly demonstrating the delocalization and subsequent relocalization of the beam. We also emonstrate the strong wavelength dependence of the beam relocalization for a four period structure.

Evidence of a mobility edge for photons in two dimensions

A scaling analysis of conductance for photons in two dimensions is carried out and, contrary to widely held belief, we find strong evidence of a mobility edge. Such behavior is compatible with the existence of an Anderson transition for electronic systems under symplectic symmetry, and indeed we show that the transfer matrix in the photonic system we have modelled has such a symmetry. We verify single parameter scaling of the conductance and demonstrate the transition from the metallic phase to localization. Key parameters, including the critical disorder, the conductance, and the critical exponent of the localization length are calculated, and it is shown that the value of the critical exponent is similar to that for electronic systems with symplectic symmetry.

Effects of disorder in two-dimensional photonic crystal waveguides

The effects of randomness on the guiding properties of waveguides embedded in disordered two-dimensional photonic crystals composed of a finite cluster of circular cylinders of infinite length are investigated for TM-polarized radiation. Different degrees of disorder in the radius, filling fraction, refractive index, and position are considered for both straight and 90 degrees bent guides. The crystals exhibit similar sensitivity to refractive index and radius disorder, with a degree of disorder from 15%-20% yielding little substantial change in the guiding properties. A smaller range of position disorder is also considered. For strong disorder in radius and refractive index, the guide effectively closes. These results were obtained by a Monte Carlo simulation method, and the performance of this method is analyzed. The method requires at least ten realizations in some cases for convergence to commence; substantially more realizations are required for moderate and strong disorder to achieve accurate results.

Ring structures in microstructured polymer optical fibres

Recent developments in polymer microstructured optical fibres allow for the realisation of microstructures in fibres that would be problematic to fabricate using glass-based capillary stacking. We present one class of such structures, where the holes lie on circular rings. A fibre of this type is fabricated and shown to be single moded for relatively long lengths of fibre, whereas shorter lengths are multimoded. An average index model for these fibres is developed. Comparison of its predictions to the calculated properties of the exact structure indicates that the ring structures emulate homogeneous rings of lower refractive index resulting in the ring structured fibres behaving approximately as cylindrically layered fibres.

Calculations of air-guided modes in photonic crystal fibers using the multipole method

We demonstrate that a combination of multipole and Bloch methods is well suited for calculating the modes of air core photonic crystal fibers. This includes determining the reflective properties of the cladding, which is a prerequisite for the modal calculations. We demonstrate that in the presence of absorption, the modal losses can be substantially smaller than in the corresponding bulk medium.

Confinement losses in microstructured optical fibers

We describe a multipole formulation that can be used for high-accuracy calculations of the full complex propagation constant of a microstructured optical fiber with a finite number of holes. We show how the imaginary part of the microstructure, which describes confinement losses not associated with absorption, varies with hole size, the number of rings of holes, and wavelength, and give the minimum number of rings of holes required for a specific loss for given parameters.

Microstructured polymer optical fibre

The first microstructured polymer optical fibre is described. Both experimental and theoretical evidence is presented to establish that the fibre is effectively single moded at optical wavelengths. Polymer-based microstructured optical fibres offer key advantages over both conventional polymer optical fibres and glass microstructured fibres. The low-cost manufacturability and the chemical flexibility of the polymers provide great potential for applications in data communication networks and for the development of a range of new polymer-based fibre-optic components.

Two-dimensional Green's function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length

Using the exact theory of multipole expansions, we construct the two-dimensional Green's function for photonic crystals, consisting of a finite number of circular cylinders of infinite length. From this Green's function, we compute the local density of states (LDOS), showing how the photonic crystal affects the radiation properties of an infinite fluorescent line source embedded in it. For frequencies within the photonic band gap of the infinite crystal, the LDOS decreases exponentially inside the crystal; within the bands, we find "hot" and "cold" spots. Our method can be extended to three dimensions as well as to treating disorder and represents an important and efficient tool for the design of photonic crystal devices.

Introduction

Progress in optics is intimately connected to the development of novel optical materials. This includes advances in synthesizing such materials as well as improvements in their theoretical understanding. Photonic Crystals represent a particularly lucid illustration of this principle: The advent of advanced microstructuring techniques has allowed the realization of two- and three-dimensional periodic arrays on sub-micron scales that provide Bragg-scattering for electromagnetic waves with frequencies in the near IR and the visible. Photonic band structure computations accurately predict crystal structures that posses complete photonic bandgaps and the minimal refractive index contrast that is needed to open them. The controlled fabrication, characterization and optimal design of cavities and waveguiding structures in photonic band gap materials represents another fascinating challenge for material scientists, spectroscopists and theorists alike. Finally, the incorporation of nonlinear and optically active materials into Photonic Crystal structures along with a detailed understanding of the optical properties of the resulting composite systems, may enhance the technological utility of Photonic Crystals over and above the conventional linear structures.

Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method

We present a formulation for wave propagation and scattering through stacked gratings comprising metallic and dielectric cylinders. By modeling a photonic crystal as a grating stack of this type, we thus formulate an efficient and accurate method for photonic crystal calculations that allows us to calculate reflection and transmission matrices. The stack may contain an arbitrary number of gratings, provided that each has a common period. The formulation uses a Green's function approach based on lattice sums to obtain the scattering matrices of each layer, and it couples these layers through recurrence relations. In a companion paper [J. Opt Soc. Am. A 17, 2177 (2000)] we discuss the numerical implementation of the method and give a comprehensive treatment of its conservation properties.

Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part II. Properties and implementation

A numerical implementation and generalized conservation properties of a formulation for calculating wave propagation through stacked gratings comprising metallic and dielectric cylinders are presented. The basic formulation of the method was given in a companion paper [J. Opt. Soc. Am. A. 17, 2165 (2000)]. Here, details of the numerical implementation of the method are discussed and are illustrated for the ensemble average of a strongly scattering structure with refractive index and radius disorder. Also presented are a comprehensive treatment of energy conservation and generalized phase relations, as well as reciprocity.

Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders

A method is developed to calculate electromagnetic properties of arrays of metallic and dielectric cylinders. It incorporates and exploits cylindrical boundary conditions and Rayleigh identities for efficient, high-accuracy calculation of scattering off individual layers that are stacked into arrays using scattering matrices. The method enables absorption, dispersion, and randomness to be incorporated efficiently, and reproduces known results with vastly improved speed and accuracy. It is used to demonstrate existence of states introduced into photonic band gaps of a dielectric array by disorder, and anomalous absorption behavior in arrays of aluminum cylinders.

Wavelength-encoding/temporal-spreading optical code division multiple-access system with in-fiber chirped moiré gratings

We propose an optical code division multiple-access (OCDMA) system that uses in-fiber chirped moiré gratings (CMG's) for encoding and decoding of broadband pulses. In reflection the wavelength-selective and dispersive nature of CMG's can be used to implement wavelength-encoding/temporal-spreading OCDMA. We give examples of codes designed around the constraints imposed by the encoding devices and present numerical simulations that demonstrate the proposed concept.

Theory of modulational instability in Bragg gratings with quadratic nonlinearity

Modulational instability in optical Bragg gratings with a quadratic nonlinearity is studied. The electric field in such structures consists of forward and backward propagating components at the fundamental frequency and its second harmonic. Analytic continuous wave (CW) solutions are obtained, and the intricate complexity of their stability, due to the large number of equations and number of free parameters, is revealed. The stability boundaries are rich in structures and often cannot be described by a simple relationship. In most cases, the CW solutions are unstable. However, stable regions are found in the nonlinear Schrödinger equation limit, and also when the grating strength for the second harmonic is stronger than that of the first harmonic. Stable CW solutions usually require a low intensity. The analysis is confirmed by directly simulating the governing equations. The stable regions found have possible applications in second-harmonic generation and dark solitons, while the unstable regions may be useful in the generation of ultrafast pulse trains at relatively low intensities.

Fabrication of rocking filters at 193 nm

We show that rocking filters can be fabricated in photosensitive elliptical-core fibers with 193-nm radiationfrom an excimer laser by the external point-by-point fabrication technique. We find that the writing efficiency at this wavelength is significantly larger than that at 240 nm. Furthermore, the growth dynamics of rocking filters fabricated with these two wavelengths are dissimilar, which may suggest different photosensitive mechanisms.

Nonlinear propagation in superstructure Bragg gratings

The existence of solitary waves in superstructure Bragg gratings is experimentally demonstrated, confirming theoretical predictions. We observe nonlinear compression as a result of a combination of the negative dispersion of the grating and the nonlinear phase shift associated with the pulse intensity. We also demonstrate that, in a superstructure Bragg grating, the dispersion is continuously tunable from normal to anomalous, which allows us to manipulate the shape of the transmitted pulse.

Second-harmonic generation in second-harmonic fiber Bragg gratings

We consider the production of second-harmonic light in gratings resonant with the generated field, through a Green's function approach. We recover some standard results and obtain new limits for the uniform grating case. With the extension to nonuniform gratings, we find the Green's function for the second harmonic in a grating with an arbitrary phase shift at some point. We then obtain closed form approximate expressions for the generated light for phase shifts close to π/2 and at the center of the grating. Finally, comparing the uniform and phase-shifted gratings with homogeneous materials, we discuss the enhancement in generated light and the bandwidth over which it occurs, and the consequences for second-harmonic generation in optical fiber Bragg gratings.

Bragg-assisted parametric amplification of short optical pulses

Parametric amplification of pulses in Bragg gratings is investigated numerically. Gain is observed for a much larger range of parameters than in uniform media. This is explained in terms of grating-assisted phase matching. In contrast to that for cw results, the input signal pulse need not be tuned to a particular frequency. Rather, through cross-phase modulation the signal self-locks to the correct frequency for growth.

Coupled-mode equations for periodic superstructure Bragg gratings

Periodic superstructure Bragg gratings are gratings in which the parameters vary periodically. Although one can determine their properties by using the standard coupled-mode equations for the electric field envelopes, it is shown that the analysis is simplified if one considers the super envelopes, i.e., the envelopes of the usual envelope functions. These super envelopes satisfy a set of (super) coupled-mode equations, which are formally identical to the standard coupled-mode equations for a uniform grating. This shows that, within certain frequency ranges, any superstructure Bragg grating acts approximately as a uniform grating.

Soliton propagation in twin-core fiber rocking filters

We investigate nonlinear pulse propagation in a twin-core fiber whose birefhingent axes have been periodically rocked at the beat length of the cores. We find that the four coupled-mode equations that describe this system can be reduced to a pair of coupled nonlinear Schrödinger equations under suitable conditions. Consequently we find two new types of compound soliton: one that propagates down both cores of the fiber simultaneously and another that couples completely between the cores of this structure without degradation. These solitons typically have a peak power of ~1 W and a length of ~10 ps.

Optical push broom

It is shown that the energy of a weak probe, copropagating with a strong pump pulse through a fiber grating, can be made to heap up on the pump's leading edge.

Electromagnetic Stark ladders in waveguide geometries

We argue that the planar optical waveguide is the geometry of choice for observing electromagnetic Stark ladders.

Polarization instability in a waveguide geometry

We show theoretically that polarization instability can be observed in planar optical waveguides. Such instability would lead to energy exchange between the spatial solitons associated with the TE(0) and TM(0) waveguide modes as well as to amplitude-modulation gain, which was recently observed in an optical-fiber geometry.

Self-localized light: launching of low-velocity solitons in corrugated nonlinear waveguides

We show that stationary gap solitons are just a limiting case of a wider set of (slowly) moving solitons associated with the photonic stop gap of a periodic nonlinear structure. We give an analytic description of these solitons and provide the prescription for launching such solitons in a realistic waveguide geometry.

Nonpolarizing beam splitter design

A three-step design procedure is developed for dielectric stacks which are required to be nonpolarizing for a given wavelength lambdar and angle of incidence theta 0,r, at which the reflectance Rr is prescribed. The method leads to solutions in which only three layer materials occur and can be applied for a wide range of values of theta0,r and Rr. The media can be chosen from the available coating materials. Furthermore, the procedure offers the possibility of optimizing with respect to the behavior of the reflectance in the neighborhood of lambdar and theta0,r. An example is elaborated, and its results are compared with an actually produced coating.