844 research outputs found

    Exact mode volume and Purcell factor of open optical systems

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    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

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    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

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    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

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    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

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    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

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    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

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    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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