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**ABSTRACT:**In acoustic, ultrasonic or electromagnetic propagation, crossed media are often modelled by linear filters with complex gains in accordance with the Beer-Lambert law. This paper addresses the problem of propagation in media where polarization has to be taken into account. Because waves are now bi-dimensional, an unique filter is not sufficient to represent the effects of the medium. We propose a model which uses four linear invariant filters, which allows to take into account exchanges between components of the field. We call it bi-filter because it has two inputs and two outputs. Such a circuit can be fitted to light devices like polarizers, rotators and compensators and to propagation in free space. We give a generalization of the Beer-Lambert law which can be reduced to the usual one in some cases and which justifies the proposed model for propagation of electromagnic beams in continuous media. Comment: 26 pages, 2 figures08/2010; - [Show abstract] [Hide abstract]

**ABSTRACT:**We have modeled the path-length distribution in an integrating sphere used as a multipass optical cell for absorption measurements. The measured radiant flux as a function of analyte concentration is nonlinear as a result, deviating from that expected for a single path length. We have developed a full numerical model and introduce a new analytical relationship that describes this behavior for high reflectivity spheres. We have tested both models by measuring the optical absorption of methane at 1651 nm in a 50 mm diameter sphere, with good agreement with experimental data in the absorption range of 0-0.01 cm(-1). Our results compare well with previous work on the temporal response of integrating spheres.Applied Optics 10/2009; 48(30):5748-58. · 1.69 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Causality imposes restrictions on both the time-domain and frequency-domain responses of a system. The Kramers-Kronig (K-K) relations relate the real and imaginary parts of the frequency-domain response. In ultrasonics, K-K relations often are used to link attenuation and dispersion. We review both integral and differential forms of the frequency-domain K-K relations that are relevant to theoretical models and laboratory measurements. We consider two methods for implementing integral K-K relations for the case of finite-bandwidth data, namely, extrapolation of data and restriction of integration limits. For the latter approach, we discuss the accuracy of K-K predictions for specific classes of system behavior and how the truncation of the integrals affects this accuracy. We demonstrate the accurate prediction of attenuation and dispersion using several forms of the K-K relations relevant to experimental measurements of media with attenuation coefficients obeying a frequency power law and media consisting of resonant scatterers. We also review the time-causal relations that describe the time-domain consequences of causality in the wave equation. These relations can be thought of as time-domain analogs of the (frequency-domain) K-K relations. Causality-imposed relations, such as the K-K and time-causal relations, provide useful tools for the analysis of measurements and models of acoustic systems.IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 06/2005; · 1.82 Impact Factor

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