Lie Groups in Electromagnetic Wave Propagation and Scattering

The theory of Lie algebras and their classification based on Dynkin diagrams is reviewed and application of the theory to vector wave scattering and propagation is outlined. The main applications arise through the matrix exponential function and associated matrix representations for the underlying groups. By projecting experimental measurements onto the eigenvectors of these basis elements, clear physical significance may be attached to the propagation operators. A new method for dealing with partially coherent propagators is outlined and an example for backscatter from a cloud of dipoles is used to illustrate the technique.

[1]  E. Kennaugh.  Polarization properties of radar reflections , 1952 .

[2]  A. Schroth,et al.  A polarimetric covariance matrix concept for random radar targets , 1991 .

[3]  P. Wacker.  Unified theory of near-field analysis and measurement: Scattering and inverse scattering , 1981 .

[4]  C. Papas.  Theory of electromagnetic wave propagation , 1965 .

[5]  S. Coleman,et al.  Aspects of Symmetry , 1985 .

[6]  H. Zebker,et al.  The unpolarized component in polarimetric radar observations of forested areas , 1990 .

[7]  S. Cloude.  Group theory and polarisation algebra , 1986 .

[8]  S. Coleman.  Aspects of symmetry: Selected Erice lectures: Contents , 1985 .

[9]  S. Cloude.  Measurement and Analysis in Radar Polarimetry , 1992 .

[10]  Ad Lagendijk,et al.  Polarisation effects in weak localisation of light , 1988 .

[12]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[13]  E. Fry,et al.  Measurement of polarized light interactions via the Mueller matrix. , 1980, Applied optics.

[14]  S. R. Cloude.  Optimisation methods in radar polarimetry , 1991 .

[15]  A. Ludwig.  The definition of cross polarization , 1973 .

[16]  J. Kong.  Electromagnetic Wave Theory , 1986 .

[17]  R. Clark Jones,et al.  A New Calculus for the Treatment of Optical Systems. VII. Properties of the N-Matrices , 1948 .

[18]  Alexander B. Kostinski,et al.  On foundations of radar polarimetry , 1986 .

[19]  Rasheed M. A. Azzam,et al.  Propagation of partially polarized light through anisotropic media with or without depolarization: A differential 4 × 4 matrix calculus , 1978 .

[20]  R. Chipman.  Polarization analysis of optical systems , 1989 .

[21]  S. Cloude.  Uniqueness of Target Decomposition Theorems in Radar Polarimetry , 1992 .

[22]  W. Scott,et al.  Group Theory. , 1964 .

[23]  E. K. Miller,et al.  A selective survey of computational electromagnetics , 1988 .

[24]  Jan Drewes Achenbach,et al.  Acoustic and Electromagnetic Waves , 1986 .

[25]  C. Brosseau,et al.  Analysis of experimental data for Mueller polarization matrices , 1990 .

[26]  M. El-Arini,et al.  Polarization dependence in electromagnetic inverse problems , 1981 .