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 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...

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We investigate numerically the properties of metallo-dielectric, one-dimensional, photonic band-gap structures. Our theory predicts that interference effects give rise to a new transparent metallic structure that permits the transmission of light over a tunable range of frequencies, for example, the ultraviolet, the visible, or the infrared wavelength range. The structure can be designed to block ultraviolet light, transmit in the visible range, and reflect all other electromagnetic waves of lower frequencies, from infrared to microwaves and beyond. The transparent metallic structure is composed of a stack of alternating layers of a metal and a dielectric material, such that the complex index of refraction alternates between a high and a low value. The structure remains transparent even if the total amount of metal is increased to hundreds of skin depths in net thickness.

We discuss the linear dispersive properties of finite one-dimensional photonic band-gap structures. We introduce the concept of a complex effective index for structures of finite length, derived from a generalized dispersion equation that identically satisfies the Kramers-Kronig relations. We then address the conditions necessary for optimal, phase-matched, resonant second harmonic generation. The combination of enhanced density of modes, field localization, and exact phase matching near the band edge conspire to yield conversion efficiencies orders of magnitude higher than quasi-phase-matched structures of similar lengths. We also discuss an unusual and interesting effect: counterpropagating waves can simultaneously travel with different phase velocities, pointing to the existence of two dispersion relations for structures of finite length.

It is shown, both theoretically and experimentally, that during laser pulse filamentation in air an intense ultrashort third-harmonic pulse is generated forming a two-colored filament. The third-harmonic pulse maintains both its peak intensity and energy over distances much longer than the characteristic coherence length. We argue that this is due to a nonlinear phase-locking mechanism between the two pulses in the filament and is independent of the initial material wave-vector mismatch. A rich spatiotemporal propagation dynamics of the third-harmonic pulse is predicted. Potential applications of this phenomenon to other parametric processes are discussed.

Using numerical methods, we study pulse propagation near the band edge of a one-dimensional photonic band gap material with a spatial gradiation in the linear refractive index, together with a nonlinear medium response. We find that such a structure can result in unidirectional pulse propagation. That is, the field will be transmitted for, say, a left-to-right direction of propagation, while for right-to-left nearly complete reflection occurs. This behavior constitutes the operational mechanism for a passive optical diode.

We present results of a theoretical investigation into a nonlinear thin-film multilayer device that exhibits passive anisotropic optical transmission—the analogue of the electronic diode. This optical diode is a nonlinear, asymmetric, distributed Bragg reflector. Material parameters for a nonlinear polymer (polydiacetylene 9-BCMU) and rutile are used in alternating layers to model a realistic device. The diode exhibits more than five times as much transmittance in one direction as in the opposite direction. It has a thickness of only 2 μm and is polarization insensitive.