Physics – Optics
Scientific paper
2008-06-15
Physics
Optics
20 pages and 3 figures
Scientific paper
A representation theory of finite electromagnetic beams in free space is formulated by introducing a mapping matrix that maps a 2-component Jones vector to a 3-component electric-field vector. It is shown that there exists one degree of freedom for the mapping matrix when the transversality condition is taken into account. This degree of freedom can be described by the azimuthal angle of a fixed unit vector with respect to the wave vector and is interpreted as mediating the interaction between the photon's momentum and spin. For a finite beam, the interaction angle can be represented by the angle that a fixed unit vector makes with the beam's propagation direction. The impact of the interaction angle on the properties of a beam is investigated in the first-order approximation under the paraxial condition. A transverse effect is found that a beam of elliptically-polarized angular spectrum is displaced from the center in the direction that is perpendicular to the plane formed by the fixed unit vector and the propagation direction. It is also shown with a beam of linearly-polarized angular spectrum that the transverse component is not uniformly polarized. The local polarization state is dependent on the interaction angle and is changing on propagation.
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