The photonic analogue of the graded heterostructure: Analysis using the envelope approximation

摘要

We develop and deploy an envelope function formalism in order to study graded photonic crystals - periodic photonic media whose features vary continuously with position. We use the method to reduce the properties of the uniform crystals to the spectral position of their band edges and an effective mass-like term. These are employed within the Schrodinger-like equation derived herein to determine the behaviour of light inside a specific graded photonic crystal created using depth-dependent infiltration of an artificial opal. References: 14