Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Elliptically polarized fields and responses


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.

This is a preview of subscription content, log in to check access.


  1. Helgesen, G., Pieranski, P., and Skjeltorp, A. T. (1990).Physical Review Letters,64, 1425.

  2. Kamke, E. (1943).Differentialgleichungen, (Akademische Verlagsgesellschaft Becker & Erler Kom.-GES, Leipzig), pp. 21, 119, 121, and 410.

  3. Wang, Z. X., and Guo, D. R. (1965).Special Functions, Academic Press, Beijing, pp. 680 and 705 [in Chinese] [English translation: World Scientific, London (1989)].

  4. Watson, G. N. (1944).Theory of Bessel Functions, 2nd ed., Cambridge University Press, Cambridge, p. 92.

  5. Whittaker, E. T., and Watson, G. N. (1927).A Course of Modern Analysis, 4th ed., Cambridge University Press, Cambridge, p. 404.

  6. Yang, Z. J., and Yao, J. (1990).International Journal of Theoretical Physics,29, 1111.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Yang, Z., Yao, J. & Helgesen, G. Elliptically polarized fields and responses. Int J Theor Phys 30, 531–536 (1991).

Download citation


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