Abstract

The intuition that nonlinearity can alter qualitatively the response of a Bragg grating or distributed-feedback structure dates back to the seventies.¹ In these thirty years, however, our ability to describe and engineer periodic dielectrics has seen an incredible growth. Well-assessed examples range from structures which exhibit linear periodic properties (fiber, semiconductor, or Lithium Niobate Bragg gratings, 2D and 3D bandgap materials, microstructured fibers, etc.), to techniques such as quasi-phase-matching which exploit the periodic properties of the nonlinearity. We will review the recent progress made to analyze and describe the nonlinear behavior of these structures. The emphasis will be posed on the role of localized soliton-like structures. These constitute indeed the key to understand the fascinating behavior of different types of structures sharing the main characteristics of being both periodic and nonlinear. First, we will focus on 1D photonic band-gap (PBG) structures with linear periodic properties, e.g. Bragg gratings, which are known to support gap-solitons in Kerr media, first observed in fiber gratings.² In this context, it is emerging a full description of gap-soliton properties which account for observed experimental features and will serve as a guideline for the next generation of experiments, ultimately aimed at tracking the evolution of short pulses along PBG materials.³ Equally important is the fact that nonlinearities allow for the coupling of different (higher-orders) bandgaps of the same physical structure, a possibility which is prevented at low intensity. Quadratic nonlinearities responsible for second-harmonic generation are best suited for this purpose, and will lead to multicolor gap-solitons with peculiar properties.⁴ Fig. 1 shows the excitation of such entity by induced nonlinear (partial) transparency at a grating interface. We propose a unified view of gap- soliton properties and their relation with the input-output characteristic of lD-PBGs. Second, we will show that the concept of PBG itself must be generalized to account for structures which are transparent at low intensity, but strongly reflective at high intensity, namely photonic crystals of pure nonlinear origin. The best example of this type of grating is given by backward second-harmonic generation (for the same concept in 2D, see Ref. [5]), made possible by the advances of QPM techniques. In spite of the absence of any linear damping mechanism, localized solutions exist also for this kind of structures.⁶ Although, we can call them nonlinear gap-solitons, their origin is completely different from a gap-soliton in a linear PBG. In fact the former stem from the compensation of two competing intrinsic nonlinear effects, rather than the mutual compensation of nonlinearity and grating dispersion occuring in a Bragg grating. Finally and importantly, we will discuss device-oriented applications of these concepts. In particular controlling and engineering these localized structures encompass full tailoring of light pulse velocity (slowing down to zero in the lab frame, or even entities with superluminal velocities) for delay lines and other applications, multistability, strong limiting action (frustrated bistability), time-of- flight controlled frequency-conversion, cavityless lasing, and noise-suppression or regeneration schemes.

© 2002 Optical Society of America