C. Martijn de Sterke

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.

Symmetry and degeneracy in microstructured optical fibers

The symmetry of an optical waveguide determines its modal degeneracies. A fiber with rotational symmetry of order higher than 2 has modes that either are nondegenerate and support the complete fiber symmetry or are twofold degenerate pairs of lower symmetry. The latter case applies to the fundamental modes of perfect microstructured optical fibers, guaranteeing that such fibers are not birefringent. We explore two numerical methods and demonstrate their agreement with these symmetry constraints.

Modal cutoff in microstructured optical fibers

We analyze the nature of modal cutoff in microstructured optical fibers of finite cross section. In doing so, we reconcile the striking endlessly single-mode behavior with the fact that in such fibers all propagation constants are complex. We show that the second mode undergoes a strong change of behavior that is reflected in the losses, effective area, and multipolar structure. We establish the parameter subspace in which the fibers are single mode and an accurate value for the limit of the endlessly single-mode regime.

Propagation through nonuniform grating structures

We consider linear propagation through shallow, nonuniform gratings, such as those written in the core of photosensitive optical fibers. Though, of course, the coupled-mode equations for such gratings are well known, they are often derived heuristically. Here we present a rigorous derivation and include effects that are second order in the grating parameters. While the resulting coupled-mode equations can easily be solved numerically, such a calculation often does not give direct insight into the qualitative nature of the response. Here we present a new way of looking at nonuniform gratings that immediately does yield such insight and, as well, provides a convenient starting point for approximate treatments such as WKB analysis. Our approach, which is completely within the context of coupled-mode theory, makes use of an effective-medium description, in which one replaces the (in general, nonuniform) grating by a medium with a frequency-dependent refractive index distribution but without a grating.

III – Gap Solitons

This chapter describes the gap solitons. Gap solitons are electromagnetic field structures that can exist in a nonlinear optical medium if there is also a periodic variation in the linear optical properties over a length scale on the order of the wavelength of light. The chapter outlines coupled-mode theory, leading to the nonlinear coupled-mode equations and describes the three sets of solutions to the coupled-mode equations, including stationary solutions, solitary-wave solutions, and soliton solutions. The chapter investigates the relationship between these solitons and the solitary-wave solutions and also the relationship with regular fiber solitons. The numerical solutions show that periodic nonlinear media exhibit self-pulsations that become chaotic at high intensities. The issues involved in trying to generate gap solitons are discussed and experimental schemes to detect gap solitons in the laboratory are outlined in the chapter.

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.

Diamond based photonic crystal microcavities.

Diamond based technologies offer a material platform for the implementation of qubits for quantum computing. The photonic crystal architecture provides the route for a scalable and controllable implementation of high quality factor (Q) nanocavities, operating in the strong coupling regime for cavity quantum electrodynamics. Here we compute the photonic band structures and quality factors of microcavities in photonic crystal slabs in diamond, and compare the results with those of the more commonly-used silicon platform. We find that, in spite of the lower index contrast, diamond based photonic crystal microcavities can exhibit quality factors of Q=3.0x10(4), sufficient for proof of principle demonstrations in the quantum regime.

Bragg solitons in the nonlinear Schrödinger limit: experiment and theory

We present a detailed experimental and theoretical study of nonlinear pulse propagation in an apodized fiber Bragg grating. In particular, we consider the generation and the propagation of Bragg solitons with a frequency content just outside the grating’s photonic bandgap, where, thanks to the apodization, the transmissivity of the grating is high and the strong grating dispersion dominates. We demonstrate the efficient launching of Bragg solitons with velocities as low as 50% of that in untreated fiber. The experimental results agree well with numerical simulations obtained by solving the full nonlinear coupled-mode equations that govern the experimental geometry. We also show that, for most parameters, the experimental results are in very good agreement with a nonlinear-Schrodinger-equation model. Thus many of the results known for the nonlinear Schrodinger equation can be brought to bear on our results.

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 Greens 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.

Microstructured optical fibers: where’s the edge?

We establish that Microstructured Optical Fibers (MOFs) have a fundamental mode cutoff, marking the transition between modal confinement and non-confinement, and give insight into the nature of this transition through two asymptotic models that provide a mapping to conventional fibers. A small parameter space region where neither of these asymptotic models holds exists for the fundamental mode but not for the second mode; we show that designs exploiting unique MOF characteristics tend to concentrate in this preferred region.