The University of Dublin | Trinity College -- Ollscoil Átha Cliath | Coláiste na Tríonóide
Trinity's Access to Research Archive
Home :: Log In :: Submit :: Alerts ::

School of Engineering >
Electronic & Electrical Eng >
Electronic & Electrical Eng (Scholarly Publications) >

Please use this identifier to cite or link to this item:

Title: Calculation of the rise transient and relaxation time of the induced dipole Kerr effect
Author's Homepage:
Keywords: Electronic & Electrical Engineering
Issue Date: 1996
Publisher: American Physical Society
Citation: Déjardin, J.L., Blaise, P., Coffey, W.T., 'Calculation of the rise transient and relaxation time of the induced dipole Kerr effect' in Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 54, 1, (1996), pp 852 - 860
Series/Report no.: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Abstract: The exact calculation of the rise transient of the birefringence and the corresponding relaxation times by different theoretical methods is described, in particular the Kerr-effect response of an assembly of nonpolar but anisotropicaily polarizable molecules following the imposition of a constant electric field is studied by solving the Smoluchowski equation. This equation is transformed into a set of differential recurrence relations containing Legendre polynomials of even order only. By taking the Laplace transform of the birefringence function, it is shown that the singularity at s=0 (zero-frequency limit) may be removed so that the relaxation time for the rise process may be exactly expressed as a sum of products of Kummer functions and its first derivatives. The second approach is based on a matrix method where the spectrum of eigenvalues λ2j and their associated amplitudes A2j (extracted from the first components of eigenvectors) are calculated allowing one to express the relaxation time as ∑A2j(λ2j-1). Numerical values of this time are tabulated for a large range of g values (0<g<40), g being the parameter measuring the ratio of the orientational energy arising from the electrical polarizabilities to the thermal energy. It is thus demonstrated that the lowest eigenvalue (λ2) dominates almost completely the rise process. The effective relaxation time is also calculated exactly and expressed very simply as the ratio of two Kummer functions. Its evolution as a function of g leads to behavior similar to that of the relaxation time obtained either from the Kummer functions or from the eigenvalue method. It is characterized by a maximum situated around g = 2, which is interesting in view of experimental applications.
Description: PUBLISHED
Appears in Collections:Electronic & Electrical Eng (Scholarly Publications)

Files in This Item:

File Description SizeFormat
Calculation.pdfpublished (publisher copy) peer-review170.27 kBAdobe PDFView/Open

This item is protected by original copyright

Please note: There is a known bug in some browsers that causes an error when a user tries to view large pdf file within the browser window. If you receive the message "The file is damaged and could not be repaired", please try one of the solutions linked below based on the browser you are using.

Items in TARA are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0! DSpace Software Copyright © 2002-2010  Duraspace - Feedback