Minima and maxima of the local density of states for one-dimensional periodic systems

Issue		Europhys. Lett. Volume 46, Number 4, May 1999


Page(s)		419 - 424
Section		General
DOI		http://dx.doi.org/10.1209/epl/i1999-00278-2

DOI: 10.1209/epl/i1999-00278-2

Europhys. Lett, 46 (4), pp. 419-424 (1999)

Minima and maxima of the local density of states for one-dimensional periodic systems

A. Moroz

FOM-Instituut voor Atoom- en Molecuulfysica
Kruislaan 407, 1098 SJ Amsterdam, The Netherlands

(received 14 December 1998; accepted in final form 11 March 1999)

PACS. 03.40Kf - Waves and wave propagation: general mathematical aspects.
PACS. 42.70Qs - Photonic bandgap materials.

Abstract:

An analytic expression for the Green function of the one-dimensional periodic Helmholtz operator is used to analyze the behaviour of the local density of states (LDOS). We provide numerical evidence that in the n-th band the LDOS has at least n minima and maxima. Near the band edge $\omega_{\rm c}$ , the LDOS exhibits strong fluctuations, with its mimima approaching zero and the maxima diverging to infinity. For the lowest band, the ratio of the maximum to the minimum of the LDOS is shown to diverge as $(\omega_{\rm c}-\omega)^{-1}$ as $\omega$ approaches the band edge. Since, in the case of electromagnetic waves, the LDOS governs the spontaneous emission of light of embedded atoms and molecules, this may have profound implications for technology using photonic crystals.

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