We derive an exact expression for the electromagnetic mode density, and hence the group velocity, for a finite, N-period, one-dimensional, photonic band-gap structure. We begin by deriving a general formula for the mode density in terms of the complex transmission coefficient of an arbitrary index profile. Then we develop a specific formula that gives the N-period mode density in terms of the complex transmission coefficient of the unit cell. The special cases of mode-density enhancement and suppression at the photonic band edge and also at midgap, respectively, are derived. The specific example of a quarter-wave stack is analyzed, and applications to three-dimensional structures, spontaneous emission control, delay lines, band-edge lasers, and superluminal tunneling times are discussed.

Near the band edge of a one-dimensional photonic band gap structure the photon group velocity approaches zero. This effect implies an exceedingly long optical path length in the structure. If an active medium is present, the optical path length increase near the photonic band edge can lead to a better than fourfold enhancement of gain. This new effect has important applications to vertical-cavity surface-emitting lasers.

We present a theoretical approach to the study of second- and third-harmonic generation from metallic structures and nanocavities filled with a nonlinear material in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We study the effects of incident TE- and TM-polarized fields and show that a simple reexamination of the basic equations reveals additional, exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures

We numerically investigate nonlinear propagation of ultrashort pulses in a one-dimensional photonic band gap structure. We find that, near the band edge, nonlinear effects cause a dynamical shift in the location of the band gap. We demonstrate that this nonlinear mechanism can induce intensity-dependent pulse transmission and rejections. In addition, pulse reshaping and pulse generation is observed. This phenomenon has important new applications in both optical limiting and optical switching. PACS numbers: 42.25.Bs, 42.25.Hz, 42.70.Nq, 42.79.Sz If a multilayer stack of dielectric material is arranged in such a way that alternating layers have a high index of refraction, say n2, and a low, say n&, and the thickness of each layer also alternates and is such that a = A/4n& and b = A/4nq, where A is the free-space wavelength, then this dielectric stack forms a reflective dielectric coating [1]. Such a structure is usually referred to as a distributed Bragg reflector, and it is depicted in Fig. 1. A range of wavelengths centered at A will be reAected, that is, propagation of those wavelengths is not allowed inside the structure. This is an example of the phenomenon from which the name "photonic band gap" (PBG) is derived in analogy with electronic band gaps of semiconductorAlthough this is a well-known phenomenon, we are interested in using the language of photonic band gap theory to study the nonlinear dynamics of a pulse that impinges on such a structure, with its carrier frequency near the gap edge. Theoretical investigations regarding pulse propagation inside a similar structure have been previously carried out to examine a band edge, distributed feedback enhancement of gain in a photonic band edge laser (PBEL) [3]. The example we investigated yielded nearly a factor of 4 enhancement of gain, primarily due to band edge effects. Near the band edge of a one-dimensional PBG structure, the group velocity approaches zero [4]. As I I a 1 h a result, a photon sees an increased effective path length due to the many multiple reflections it undergoes, a phenomenon sometimes referred to as photon localization. A pulse at the band edge tends to form a standing wave, whose antinodal intensities have amplitudes several times over the free-space intensity. Other band edge effects, such as anomalous index of refraction effects, have also been studied [4].In this Letter, we study the results of including a g3 nonlinearity in a one-dimensional PBG structure. Previous studies of nonlinear effects include the investigation of steady state optical bistability and band gap solitary waves [5,6]. We concentrate on the nonlinear dynamics of ultrashort pulses which are only 100 optical cycles long (about 300 fs for A = 1 p, m). The model we have developed to examine pulse propagation is simple and applicable to a wide range of problems. With the advent of commercially available Kerr lens mode-locked lasers, the understanding of femtosecond pulse propagation is increasingly important to a diverse range of investigators.Aside from the opt...