Representation theory for vector electromagnetic beams

Abstract

A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a $3\times 2$ mapping matrix and a 2-component Jones-like vector. The mapping matrix has one degree of freedom that can be described by the azimuthal angle of a fixed unit vector with respect to the wave vector. This degree of freedom allows us to find out such a beam solution in which every plane-wave component is specified by the same fixed unit vector $\mathbf{I}$ and has the same normalized Jones-like vector. The angle ${\theta }_I$ between the fixed unit vector and the propagation axis acts as a parameter that describes the vectorial property of the beam. The impact of ${\theta }_I$ is investigated on a beam of angular-spectrum field scalar that is independent of the azimuthal angle. The field vector in position space is calculated 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 axis. The expression of the transverse displacement is obtained. Its paraxial approximation is also given.

16 pages. The final version appears in the Phys. Rev. A

References in corpus (5)

• Conservation of Angular Momentum, Transverse Shift, and Spin Hall Effect in Reflection and Refraction of Electromagnetic Wave Packet
• Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet
• Geometrical Aspects in Optical Wavepacket Dynamics
• Unified theory for Goos-Hänchen and Imbert-Fedorov effects
• Integral transformation solution of free-space cylindrical vector beams and prediction of modified-Bessel-Gaussian vector beams

Cited by in corpus (9)

• Internal flows and energy circulation in light beams
• Angular momentum of non-paraxial light beam: Dependence of orbital angular momentum on polarization
• Polarization-dependent transformation of a paraxial beam upon reflection and refraction: a real-space approach
• Improved theory for the polarization-dependent transverse shift of a paraxial light beam in free space
• Experimental evidence for new symmetry axis of electromagnetic beams
• Characterization of vector diffraction-free beams
• A full characterization of the polarization of vector light beams
• From Poynting vector to new degree of freedom of polarization
• New mechanism for polarization singularity of vector vortex beams