Kramers-Kronig relations in optical data inversion

Physical review. B, Condensed matter (Impact Factor: 3.66). 11/1991; 44(15):8301-8303. DOI: 10.1103/PhysRevB.44.8301
Source: PubMed


Some remarks are made on the use of Kramers-Kronig relations in optical data inversion. It is shown that symmetry relations imposed on the optical constant should be taken into account when modeling the tails of the absorption and extinction curves.

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Available from: Erik Vartiainen, Nov 05, 2014
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    • "The Gaussian oscillator model may be a good approximation for amorphous and glassy materials, where atomic bond lengths and angles are normally distributed around the average values [58] [59]. Therefore it may be used for modeling of the optical functions of molecular resists or copolymers as well as for the dielectric functions of disordered materials in the infrared range to account for the phonon contribution in absorption . "
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    Thin Solid Films 08/2015; 589:844-851. DOI:10.1016/j.tsf.2015.07.035 · 1.76 Impact Factor
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    • "This may raise issue of computational costs and/or experimental set-up. The extrapolations in K-K analysis can be a serious source of errors [30] [31]. "
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    ABSTRACT: We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.
    Journal of Statistical Physics 05/2008; 131(3):543-558. DOI:10.1007/s10955-008-9498-y · 1.20 Impact Factor
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    ABSTRACT: Thesis (Ph. D.)--University of Texas at Austin, 2007. Includes bibliographical references. Vita. Requires PDF file reader.
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