Analogien zwischen außerordentlichen und ordentlichen Wellen nach nichtorthogonaler Koordinatentransformation und die parabolischen Näherungsgleichungen



Within the limits of Linear Optics we treat analogies between ordinary and extraordinary waves in uniaxial media which become conspicuous through a nonorthogonal transformation of coordinates. To any ordinary wave solution in unbounded uniaxial media we can construct a corresponding extraordinary wave solution by interchanging electrical and magnetical field components. Boundary conditions for instance for ideal conducting plane surfaces approximately preserve their original form, if the optical axis or the middle wave vector are normal to the surface. The parabolic approximative equations for slowly varying amplitudes are derived, the polarisation of these waves being considered as a slowly varying quantity. Further these approximative equations are expanded to include frequency dispersion. Through the specified transformation we can simplify problems with extraordinary waves.