Simple Model of Spontaneous Emission in 1D Photonic Crystal

2007

The subject of this paper is the derivation of expressions describing envelopes of electromagnetic fields inside a 1D photonic crystal. The presented approach is based on an effective resonator model, which treats each layer of the photonic crystal as a resonant cavity. The model is analytic and allows one to derive parameters characterizing the photonic crystal and express electric and magnetic fields as their function. It is general enough to take into account defects of the crystal or even be used for an aperiodic structure. In the end of the paper, a few results are provided for the case of a source of radiation inside a photonic crystal along with a short discussion.PACS numbers: 42.70.Qs MotivationIt has been in the late 1980s when photonic crystals have been recognized as a distinct group of materials with unique optical properties [1,2]. Their properties are associated with an optical band structure resembling the band structure of semiconductors in electronics, and therefore photonic crystals are sometimes called "semiconductors of light". Because semiconductors have played a very important role in science and technology, becoming the fundamentals of contemporary electronics, this similarity is the cause of great interest and expectations regarding photonic crystals. Indeed, photonic crystals have been used to build many optical devices -one can mention optical waveguides [3,4], filters [5], optical switches [6], LEDs with increased efficiency [7], distributed Bragg reflector (DBR) and distributed feedback (DFB) lasers [8].It is important to understand the physics of photonic crystals to develop new devices and improve already existing ones. In this paper, there is presented an effective resonator model of a 1D photonic crystal, which allows one to exam-

Section: Reflection and Transmission Coefficientsmentioning

confidence: 99%

Analytic Expressions for Electromagnetic Field Envelopes in a 1D Photonic Crystal

2007

“…In this system, coordinates x and y are the same as in the global coordinate system, and the coordinate z (j) runs from 0 to L (j) z in the same direction as the z axis of the global coordinate system. The exception is the region j = −N L , in which z (−N L ) runs from −∞ to 0. ρ (k) is the so-called mode spectrum (see [5]), a function of wave vector k and polarization , calculated for the layer containing the source of radiation. For the presented calculations, the following properties of mode spectrum of the considered structure are important: it does not depend on the sign of any component of k, in particular…”

Section: Adopted Notationmentioning

confidence: 99%

“…This model is a tool, which has been proposed for modeling photonic crystals [5]. It is based on a simple concept and has a clear physical interpretation.…”

Section: Introductionmentioning

confidence: 99%

Orthonormalization of Radiation Modes in Effective Resonator Model of Dielectric Multilayer Structure

2007

“…In the previous papers [1][2][3][4] the model has been proposed and its physical background and interpretation [1,2,5], as well as orthonormalization of modes [3,4] have been described. However, there remain a few aspects of the model, which require a rigorous treatment or explanation.…”

Section: Introductionmentioning

confidence: 99%

Some Mathematical Properties of Effective Resonator Model of 1D Dielectric Multilayer Structure

2009