844 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
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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
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
Correcting the Record Regarding theRestatement of Property’s Slayer Rulein the Brooklyn Law Review’sSymposium Issue on Restatements
In 2014, the Brooklyn Law Review published a symposium issue on Restatements of the Law. The organizer of the symposium, Professor Anita Bernstein, did not afford an opportunity for Restatement reporters to comment on the articles. The organizer did invite the Director of the American Law Institute, Lance Liebman, to contribute an essay commenting on the symposium as a whole. Liebman’s essay—unintentionally no doubt—misstated the position that we took in formulating the slayer rule for the Restatement (Third) of Property: Wills and Other Donative Transfers. Liebman’s misstatement—that we recommended that the Institute adopt a rule allowing a murderer to inherit from his or her victim—needs to be corrected
Reforming the Law of Gratuitous Transfers: The New Uniform Probate Code
In the mid-1980s the Uniform Law Commission undertook a landmark revision of the American law of gratuitous transfers. These reforms culminated in a drastically revised Uniform Probate Code ( UPC ). The revisions inspired the Albany Law Review to organize this symposium issue for the purpose of examining the 1990 UPC. In this introductory paper, we point to the main themes of the reform movement, discuss some of the traits and constraints of the uniform law process, and comment on some of the suggestions and insights that appear in the symposium articles
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