990 research outputs found
Exact mode volume and Purcell factor of open optical systems
The Purcell factor quantifies the change of the radiative decay of a dipole
in an electromagnetic environment relative to free space. Designing this factor
is at the heart of photonics technology, striving to develop ever smaller or
less lossy optical resonators. The Purcell factor can be expressed using the
electromagnetic eigenmodes of the resonators, introducing the notion of a mode
volume for each mode. This approach allows to use an analytic treatment,
consisting only of sums over eigenmode resonances, a so-called spectral
representation. We show in the present work that the expressions for the mode
volumes known and used in literature are only approximately valid for modes of
high quality factor, while in general they are incorrect. We rectify this
issue, introducing the exact normalization of modes. We present an analytic
theory of the Purcell effect based on the exact mode normalization and
resulting effective mode volume. We use a homogeneous dielectric sphere in
vacuum, which is analytically solvable, to exemplify these findings.Comment: Letter: 5 pages, 2 figures. Supplementary material: 16 pages, 10
figure
Realistic heterointerfaces model for excitonic states in growth-interrupted quantum wells
We present a model for the disorder of the heterointerfaces in GaAs quantum
wells including long-range components like monolayer island formation induced
by the surface diffusion during the epitaxial growth process. Taking into
account both interfaces, a disorder potential for the exciton motion in the
quantum well plane is derived. The excitonic optical properties are calculated
using either a time-propagation of the excitonic polarization with a
phenomenological dephasing, or a full exciton eigenstate model including
microscopic radiative decay and phonon scattering rates. While the results of
the two methods are generally similar, the eigenstate model does predict a
distribution of dephasing rates and a somewhat modified spectral response.
Comparing the results with measured absorption and resonant Rayleigh scattering
in GaAs/AlAs quantum wells subjected to growth interrupts, their specific
disorder parameters like correlation lengths and interface flatness are
determined. We find that the long-range disorder in the two heterointerfaces is
highly correlated, having rather similar average in-plane correlation lengths
of about 60 and 90 nm. The distribution of dephasing rates observed in the
experiment is in agreement with the results of the eigenstate model. Finally,
we simulate highly spatially resolved optical experiments resolving individual
exciton states in the deduced interface structure.Comment: To appear in Physical Review
Resonant state expansion applied to planar open optical systems
The resonant state expansion (RSE), a novel perturbation theory of
Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and
Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar,
effectively one-dimensional optical systems, such as layered dielectric slabs
and Bragg reflector microcavities. It is demonstrated that the RSE converges
with a power law in the basis size. Algorithms for error estimation and their
reduction by extrapolation are presented and evaluated. Complex
eigenfrequencies, electro-magnetic fields, and the Green's function of a
selection of optical systems are calculated, as well as the observable
transmission spectra. In particular we find that for a Bragg-mirror
microcavity, which has sharp resonances in the spectrum, the transmission
calculated using the resonant state expansion reproduces the result of the
transfer/scattering matrix method
Resonant state expansion applied to two-dimensional open optical systems
The resonant state expansion (RSE), a rigorous perturbative method in
electrodynamics, is applied to two-dimensional open optical systems. The
analytically solvable homogeneous dielectric cylinder is used as unperturbed
system, and its Green's function is shown to contain a cut in the complex
frequency plane, which is included in the RSE basis. The complex
eigenfrequencies of modes are calculated using the RSE for a selection of
perturbations which mix unperturbed modes of different orbital momentum, such
as half-cylinder, thin-film and thin-wire perturbation, demonstrating the
accuracy and convergency of the method. The resonant states for the thin-wire
perturbation are shown to reproduce an approximative analytical solution
Stochastic properties of systems controlled by autocatalytic reactions II
We analyzed the stochastic behavior of systems controlled by autocatalytic
reaction A+X -> X+X, X+X -> A+X, X -> B provided that the distribution of
reacting particles in the system volume is uniform, i.e. the point model of
reaction kinetics introduced in arXiv:cond-mat/0404402 can be applied. Assuming
the number of substrate particles A to be kept constant by a suitable
reservoir, we derived the forward Kolmogorov equation for the probability of
finding n=0,1,... autocatalytic particles X in the system at a given time
moment. We have shown that the stochastic model results in an equation for the
mean value of autocatalytic particles X which differs strongly from the kinetic
rate equation. It has been found that not only the law of the mass action is
violated but also the bifurcation point is disappeared in the well-known
diagram of X particle- vs. A particle-concentration. Therefore, speculations
about the role of autocatalytic reactions in processes of the "natural
selection" can be hardly supported.Comment: 17 pages, 6 figure
Resonant state expansion applied to planar waveguides
The resonant state expansion, a recently developed method in electrodynamics,
is generalized here to planar open optical systems with non-normal incidence of
light. The method is illustrated and verified on exactly solvable examples,
such as a dielectric slab and a Bragg reflector microcavity, for which explicit
analytic formulas are developed. This comparison demonstrates the accuracy and
convergence of the method. Interestingly, the spectral analysis of a dielectric
slab in terms of resonant states reveals an influence of waveguide modes in the
transmission. These modes, which on resonance do not couple to external light,
surprisingly do couple to external light for off-resonant excitation
Binding energy and dephasing of biexcitons in In0.18Ga0.82As/GaAs single quantum wells
Biexciton binding energies and biexciton dephasing in In0.18Ga0.82As/GaAs single quantum wells have been measured by time-integrated and spectrally resolved four-wave mixing. The biexciton binding energy increases from 1.5 to 2.6 meV for well widths increasing from 1 to 4 nm. The ratio between exciton and biexciton binding energy changes from 0.23 to 0.3 with increasing inhomogeneous broadening, corresponding to increasing well width. From the temperature dependence of the exciton and biexciton four-wave mixing signal decay, we have deduced the acoustic-phonon scattering of the exciton-biexciton transition. It is found to be comparable to that of the exciton transition, indicating that the deformation potential interactions for the exciton and the exciton-biexciton transitions are comparable
Resonant-state expansion of dispersive open optical systems: Creating gold from sand
A resonant-state expansion (RSE) for open optical systems with a general frequency dispersion of the permittivity is presented. The RSE of dispersive systems converts Maxwell's wave equation into a linear matrix eigenvalue problem in the basis of unperturbed resonant states, in this way numerically exactly determining all relevant eigenmodes of the optical system. The dispersive RSE is verified by application to the analytically solvable system of a sphere in vacuum, with a dispersion of the permittivity described by the Drude and Drude-Lorentz models. We calculate the optical modes converting the sphere material from gold to nondispersive sand and back to gold, and evaluate the accuracy using exact solutions
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