Combining fractional time derivative loss models and the similarity transformation technique to turn lossless configurations into lossy ones

Details Combining fractional time derivative loss models and the similarity transformation technique to turn lossless configurations into lossy ones Combining fractional time derivative loss models and the similarity transformation technique to turn lossless configurations into lossy ones

Nov 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001spie.4491..183v&link_type=abstract

Proc. SPIE Vol. 4491, p. 183-192, Subsurface and Surface Sensing Technologies and Applications III, Cam Nguyen; Ed.

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A method is presented by which a complicated space-time domain electromagnetic wavefield in a lossless configuration may afterwards be transformed into the space-time domain field of a lossy configuration with a prescribed quality factor Q. The method is applicable to inhomogeneous and anisotropic media. Moreover, it may be employed to fields in 1D, 2D and 3D spatial configurations. The first step is the introduction of a specific loss model into the lossless Maxwell's equations. Two loss models will be presented. These are generalizations to the electromagnetic case of the elastodyanmic Scott-Blair stress-strain law and the elastodynamic Power Law, which yield a quality factor Q that is (nearly) constant over a long frequency range. Both loss models introduce fractional time derivatives in Maxwell's equations. The second step of the method relates the lossless and the lossy time domain Green's tensors by means of the similarity transformation technique. This approach has the benefit that an existing time domain wavefield for a lossless but otherwise intricate medium can be converted to the relevant lossy situation by a simple postprocessing step. Next, numerical results for both loss models will be shown. These will be compared with the results for a third loss model that is guaranteed to yield the correct arrival time. It is observed that the former two loss models cause deviations from the exact arrival time. However, these deviations are small except for high losses. As far as the shape of the time evolution of the fields is concerned, both loss models perform equally well, even in case of high losses.

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