858 research outputs found
Surface EM waves on 1D Photonic Crystals
We study surface states of 1D photonic crystals using a semiclassical coupled
wave theory. Both TE and TM modes are treated. We derive analytic
approximations that clarify the systematics of the dispersion relations, and
the roles of the various parameters defining the crystal.Comment: 7 pages, 8 figure
Classical picture of post-exponential decay
Post-exponential decay of the probability density of a quantum particle
leaving a trap can be reproduced accurately, except for interference
oscillations at the transition to the post-exponential regime, by means of an
ensemble of classical particles emitted with constant probability per unit time
and the same half-life as the quantum system. The energy distribution of the
ensemble is chosen to be identical to the quantum distribution, and the
classical point source is located at the scattering length of the corresponding
quantum system. A 1D example is provided to illustrate the general argument
Biperiodic superlattices and the transparent state
Coquelin et al. studied biperiodic semiconductor superlattices, which consist
of alternating cell types, one with wide wells and the other narrow wells,
separated by equal strength barriers. If the wells were identical, it would be
a simply periodic system of half-cells. When asymmetry is introduced,
an allowed band splits at the Bragg point into two disjoint allowed bands. The
Bragg resonance turns into a transparent state located close to the band edge
of the lower(upper) band when the first(second) well is the wider. Analysis of
this system gives insight into how band splitting occurs. Further we consider
semi-periodic systems having half-cells. Surprisingly these have very
different transmission properties, with an envelope of maximum transmission
probability that crosses the envelope of minima at the transparent point.Comment: 12 pages, 10 figures Version 2: improved figures using colour, and
some small improvements in the text, in response to referee comments Version
3: incorporates changes which arose in proofs stag
Enhanced observability of quantum post-exponential decay using distant detectors
We study the elusive transition from exponential to post-exponential
(algebraic) decay of the probability density of a quantum particle emitted by
an exponentially decaying source, in one dimension. The main finding is that
the probability density at the transition time, and thus its observability,
increases with the distance of the detector from the source, up to a critical
distance beyond which exponential decay is no longer observed. Solvable models
provide explicit expressions for the dependence of the transition on resonance
and observational parameters, facilitating the choice of optimal conditions
Understanding quantum wires with circular bends
It is shown that propagation around a circular bend in a quantum wire is well approximated by a one¿dimensional problem with a square¿well potential replacing the bend. Simple analytic expressions are obtained for the transmission and bound states
- …