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.

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Available from: Bernhard J Hoenders, Dec 18, 2013
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    • "Beside the particular physics of the Sommerfeld-Brillouin precursors [1] [2] [3] [4] [5], the study of the short pulse propagation in optical media has been mainly developed until now in the context of femtosecond lasers [6] [7] [8]. At the present time, there is a renewal of the optics of ultra-short pulses with the advent of femto-, subfemto-and attosecond sources in the high energy domain of the electromagnetic spectrum: attopulses are delivered by high harmonic generation (HHG) sources in the X-UV range [9] [10] [11] [12], subfemto-and femtopulses are generated by x-ray free electron lasers (X-FEL) [13] or other new sources (Thomson scattering, …) in the x-ray domain [14] [15]. "
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    ABSTRACT: The time-dependence of the Bragg diffraction by one-dimensional photonic crystals and its influence on the short pulse reflection are studied in the framework of the coupled- wave theory. The indicial response of the photonic crystal is calculated and it appears that it presents a time-delay effect with a transient time conditioned by the extinction length. A numerical simulation is presented for a Bragg mirror in the x-ray domain and a pulse envelope modelled by a sine-squared shape. The potential consequences of the time-delay effect in time-dependent optics of short-pulses are emphasized.
    Preview · Article · Aug 2015 · Journal of optics
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    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.
    No preview · Article · Jan 2006 · Proceedings of SPIE - The International Society for Optical Engineering
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    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.
    Full-text · Article · Dec 2008 · Optics Communications
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