Spinor solutions to Maxwell's equations in free space

1984 ◽  
Vol 62 (7) ◽  
pp. 674-682 ◽  
Author(s):  
P. Hillion ◽  
S. Quinnez
Keyword(s):  
Parabolic Equation ◽  
Light Beam ◽  
Free Space ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Hankel Transform ◽  
Cylindrical Symmetry ◽  
Paraxial Approximation ◽  
Gaussian Beams

Using the Hankel transform, we obtain, in their most general form, the spinor solutions of Maxwell's equations in free space for a light beam propagating along 0z with cylindrical symmetry around 0z. Then we compute a paraxial approximation of these solutions and we discuss the case of Gaussian beams. A comparison of the spinor solutions with the scalar ones supplied by the parabolic equation is also given.

On the integration of Maxwell’s equations, and charge and dipole fields

1964 ◽  
Vol 279 (1379) ◽  
pp. 562-571 ◽  
Keyword(s):  
Electromagnetic Fields ◽  
Free Space ◽  
Integral Identity ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Direct Integration ◽  
Magnetic Dipoles ◽  
Dimensional Integral

It is shown how the direct integration of Maxwell’s equations for free space may be accomplished by using a four-dimensional integral identity constructed for this purpose. The method is applied to the calculation of the electromagnetic fields of moving electric charges, and electric and magnetic dipoles.

scholarly journals The Dubious Authority of Maxwell’s Equations in Free Space

2021 ◽  
Author(s):  
Charles MacCluer
Keyword(s):  
Plane Wave ◽  
Free Space ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Uniform Plane

Because of the differential homogeneity of Maxwell's equations in free space, each solution can be additively perturbed in infinitely many ways into a physically unreasonable solution. Thus to be a solution holds no cachet. In particular, the traditional first example --- the uniform plane wave --- must be considered as only a metaphor.

scholarly journals The Dubious Authority of Maxwell’s Equations in Free Space

2021 ◽  
Author(s):  
Charles MacCluer
Keyword(s):  
Plane Wave ◽  
Free Space ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Uniform Plane

Because of the differential homogeneity of Maxwell's equations in free space, each solution can be additively perturbed in infinitely many ways into a physically unreasonable solution. Thus to be a solution holds no cachet. In particular, the traditional first example --- the uniform plane wave --- must be considered as only a metaphor.

Far-Field Properties of Vectorial Cosh-Squared-Gaussian Beams beyond the Paraxial Approximation

2011 ◽  
Vol 143-144 ◽  
pp. 204-210
Author(s):  
Mei Ping Jiang ◽  
Ning Ning Yu ◽  
Yi Jin ◽  
Xing Fang Jiang ◽  
Bin Tang
Keyword(s):  
Free Space ◽  
Numerical Calculations ◽  
Paraxial Approximation ◽  
Gaussian Beams ◽  
Far Field

The concept of vectorial nonparaxial cosh-squared-Gaussian (ChsG) beams is introduced and their free space propagation equations are derived analytically by using the vectorial Rayleigh-Sommerfeld diffraction integrals, and far-field expressions as well as paraxial propagation formula are obtained in free space. Numerical calculations and analysis show that, the f-parameter and decentered parameter plays an important role in determining the far-field properties of the vectorial nonparaxial ChsG beams.

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