Vectorial beam propagation method

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Abstract
The existing beam propagation method is based on the scalar Helmholtz wave equation and cannot adequately describe the vectorial properties of fields in optical structures. In particular, the coupling of the transverse and the longitudinal field components and the characteristics of the field line patterns imposed by the waveguide geometry are not considered. To take into account the vectorial field properties imposed by the structural geometry and the properties of the medium without this limitation, a vectorial beam propagation method based on the vectorial wave equation is developed. Considerations for computational efficiency are addressed. Representative examples are given to demonstrate the applicability of this method. The limitations and the possible extensions of the form are also discussed.

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