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Elliptically polarized fields and responses

Abstract

An ellipticaliy polarized field applied to a physical system and related responses are very common in physics. Due to the loss of symmetry, the response problems are very difficult to solve, and are usually described by nonlinear and unseparable equations. By introducing a time transformationτ=(1/ω)tan−1(r tanωt), wherer is the ratio between the two components, one may reset the symmetry of the field. The equation

$$\frac{{d\theta }}{{dt}} = \frac{{\omega r}}{{\cos ^2 \omega t + r^2 \sin ^2 \omega t}} - \omega _{\text{c}} (\cos ^2 \omega t + r^2 \sin ^2 \omega t)\sin {\text{2}}\theta $$

describing the relative angular motion of a magnetic dipole pair in an elliptical magnetic field has been solved with this transformation.

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References

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Yang, Z., Yao, J. & Helgesen, G. Elliptically polarized fields and responses. Int J Theor Phys 30, 531–536 (1991). https://doi.org/10.1007/BF00672898

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Keywords

  • Magnetic Field
  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Physical System