| Issue |
Europhys. Lett.
Volume 46, Number 4, May II 1999
|
|
|---|---|---|
| Page(s) | 419 - 424 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i1999-00278-2 | |
| Published online | 01 September 2002 | |
Minima and maxima of the local density of states for one-dimensional periodic systems
FOM-Instituut voor Atoom- en Molecuulfysica Kruislaan 407,
1098 SJ Amsterdam, The Netherlands
Received:
14
December
1998
Accepted:
11
March
1999
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 
, 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
as ω 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.
PACS: 03.40.Kf – Waves and wave propagation: general mathematical aspects / 42.70.Qs – Photonic bandgap materials
© EDP Sciences, 1999
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