Conversion relationships between several parameter groups of completely polarized electromagnetic waves

Abstract

It is known that polarization as the third characteristic of electromagnetic waves plays substantial roles which are comparable with the wave amplitude and phase, in describing the tempo and spatial properties of electromagnetic waves. Various parameter groups for characterizing the polarization state of electromagnetic waves with different initial states and boundary conditions have been proposed. However, a full-scale set of conversion relationships between these parameter groups with specific initial phases is not yet available. In this work, the initial phases as additional parameters for the orthogonal linear polarization and the polarization ellipse parameter groups and the digitized elliptical angle ' as a complementary parameter to the polarization ellipse parameter group are taken into account respectively. Consequently, a full-scale set of conversion relationships between these parameter groups has been rigorously derived out. The validity of these conversion relationships are confirmed by the numerical calculations in terms of mathematical completeness and one-to-one correspondence. These conversion relationships make the tedious computation of the wave polarization much simpler and straightforward, benefiting practical implementation of the polarization theory of electromagnetic waves.