Theory of semiballistic wave propagation

Abstract

Theory of semiballistic wave propagationMosk, A.J.; Nieuwenhuizen, T.M.; Barnes, C.L. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Wave propagation through waveguides, quantum wires, or films with a modest amount of disorder is in the semiballistic regime when in the transversal direction͑s͒ almost no scattering occurs, while in the long direction͑s͒ there is so much scattering that the transport is diffusive. For such systems, randomness is modeled by an inhomogeneous density of pointlike scatterers. These are first considered in the second order Born approximation and then beyond that approximation. In the latter case, it is found that attractive point scatterers in a cavity always have geometric resonances, even for Schrödinger wave scattering. In the long sample limit, the transport equation is solved analytically. Various geometries are considered: waveguides, films, and tunneling geometries such as Fabry-Pérot interferometers and double-barrier quantum wells. The predictions are compared with new and existing numerical data and with experiment. The agreement is quite satisfactory. ͓S0163-1829͑96͒00923-X͔

Contribution of evanescent waves to the effective medium of disordered waveguides

“…The numerical and theoretical results of the present work demonstrate that even in the asymptotic region and far away from the threshold of the first evanescent mode, the evanescent modes could affect the statistical scattering properties of disordered waveguides. Equations (A5f), (20) together with (13), (16) and (17) summarize the main theoretical results of this Letter. They show that in the dense weak scattering limit, the mean free paths ℓ aa0 do not depend on the evanescent modes which provide a simple explanation of the numerical results and the success of the scaling approach to wave transport.…”

“…In contrast with previous approaches based on point or "delta"-scatterers [14,16], our approach (with slices having a finite thickness δ) converges for any number of evanescent modes and does not require any regularization scheme.…”

Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion

“…The so-called semiballistic regime occurs when in the transverse direction(s) there is almost no scattering, while in the long direction(s) there is so much scattering that the transport is diffusive. Various applications were noted by and discussed in detail by Mosk, Nieuwenhuizen, and Barnes (1996). The scattering was considered both in the second-order Born approximation and beyond that approximation.…”

Statistical properties of wave transport through surface-disordered waveguides

“…Then, in analogy with Ohm's law for electron wires, the waveguide 'resistance' can be described by an 'ohm-like' term proportional to L/W 0 plus a 'contact resistance' R c [60,62,64,84],…”

“…Classical size effects arise when the thickness of the film approaches the bulk mean free path, and have largely been interpreted according to the theories of Fuchs [55] and Sondheimer [56]. Most of the extensions of the classical Boltzmann-like approaches to wave-like transport through waveguides or quasi-one-dimensional (Q1D) disordered systems have been focused on the consequences of inhomogeneities and defects randomly distributed over the whole sample (bulk disorder) [57][58][59][60][61][62][63][64][65].…”