The Sommerfeld precursor in photonic crystals

University of Groningen, Institute for Theoretical Physics and Materials Science Center, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands
Optics Communications (Impact Factor: 1.45). 06/2006; 262(2). DOI: 10.1016/j.optcom.2005.12.077
Source: OAI


We calculate the Sommerfeld precursor that results after transmission of a generic electromagnetic plane wave pulse with transverse electric polarization, through a one-dimensional rectangular N-layer photonic crystal with two slabs per layer. The shape of this precursor equals the shape of the precursor that would result from transmission through a homogeneous medium. However, amplitude and period of the precursor are now influenced by the spatial average of the plasma frequency squared instead of the plasma frequency squared for the homogeneous case.

Download full-text


Available from: Bernhard J Hoenders, Dec 18, 2013
28 Reads
  • [Show abstract] [Hide abstract]
    ABSTRACT: We derive the Sommerfeld precursor and present the first calculations for the Brillouin precursor that result from the transmission of a pulse through a photonic crystal. The photonic crystal is modelled by a one-dimensional N-layer medium and the pulse is a generic electromagnetic plane wave packet which is incident perpendicular onto the crystal. Each layer of the crystal consists of two slabs that may differ in their relative thickness and in their refractive indices. The resulting precursors are then compared to those that would arise after propagation through a reference homogeneous medium of the same length and the same optical length in order to isolate the effect of the slab contrast onto the shapes of the precursors. The Sommerfeld precursor is not influenced by this slab contrast; its wavefront invariantly propagates at the speed of light in vacuum and its amplitude and period only depend on the spatial average of the two squared plasma frequencies of the slabs which coincides with the plasma frequency squared of the reference medium. The Brillouin precursor does experience the slab contrast; its arrival time increases with increasing slab contrast.
    Proceedings of SPIE - The International Society for Optical Engineering 01/2006; 6182. DOI:10.1117/12.662680 · 0.20 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We have calculated the electromagnetic Brillouin precursor that arises in a one-dimensional photonic crystal that consists of two homogeneous slabs which each have a single electron resonance. This forerunner is compared with the Brillouin precursor that arises in a homogeneous double-electron resonance medium. In both types of medium, the precursor consists of the components of the applied pulse that have their frequencies below the lowest of the two electron resonances. In the inhomogeneous medium however, the slab contrast starts affecting the precursor field after a certain rise time of the precursor: its spectrum starts to peak at the geometric scattering resonances of the medium whereas minima appear at the Bragg-scattering frequencies.
    Optics Communications 12/2008; 281(23). DOI:10.1016/j.optcom.2008.07.064 · 1.45 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The large amount of light emitted from a light emitting diode (LED) being trapped inside the semiconductor structure is the consequence of the large value of the refractive index. The total internal reflection (light incident on a planar semiconductor/air interface is totally internally reflected if the angle of incidence exceeds the critical value determined by Snell’s law) is the major factor responsible for the small light extraction efficiency (other important contributions to the losses are the internal absorption and blocking of the light by contacts). The typical LED structure comprising a number of layers most of which have high refractive index could be considered as a multilayer waveguide that could support a large number of trapped guided modes. The paper reviews approaches to enhanced light extraction grouped into two sets depending on whether their application results in the change in the spontaneous emission (either the spontaneous emission rate or the angular distribution, or both): (1) molding of the flow of light emitted from the active region by the modification of the chip shape or the surface morphology to increase the light intensity; and (2) modification of spontaneous emission, for example, by placing of the light emitting region inside the optical cavity. Special attention is given to LEDs made from nitrides of elements of group III (InAlGaN) that cover a large part of visible and ultraviolet (UV) spectra and are considered as a major candidate for sources for the solid-state general illumination. An Appendix contains review of numerical models used to study the light extraction.
    Physics Reports 02/2011; 498(4):189-241. DOI:10.1016/j.physrep.2010.11.001 · 20.03 Impact Factor
Show more