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2021-09-07
Time-Harmonic Electromagnetic Fields with E||b Represented by Superposing Two Counter-Propagating Beltrami Fields
By
Progress In Electromagnetics Research M, Vol. 104, 171-183, 2021
Abstract
In this paper, we present a general solution for time-harmonic electromagnetic fields with its electric and magnetic fields parallel to each other (E || B fields) in source-free vacuum and demonstrate that every time-harmonic E || B field is composed of the superposition of two counter-propagating Beltrami fields. We show that every E || B field can be categorized into one of two cases depending on the time dependence of the function that describes the proportionality between the electric and magnetic fields. After presenting the mathematical definition of a Beltrami field in electromagnetism and its handedness, we perform a detailed analysis of time-harmonic E || B fields for each case. For the first case, we find the general solution for the E || B fields using the angular-spectrum method and prove that every first-case E || B field can be generated by superposing two oppositely traveling Beltrami fields with the same handedness. For the second case, we deduce the general solution for the E || B fields by employing complex analysis and demonstrate that every time-harmonic E || B field is composed of two counter-propagating planar Beltrami fields with opposite handedness.
Citation
Ryo Mochizuki Naoki Shinohara Atsushi Sanada , "Time-Harmonic Electromagnetic Fields with E||b Represented by Superposing Two Counter-Propagating Beltrami Fields," Progress In Electromagnetics Research M, Vol. 104, 171-183, 2021.
doi:10.2528/PIERM21071603
http://www.jpier.org/PIERM/pier.php?paper=21071603
References

1. Drazin, P. G. and N. Riley, Steady Flows Bounded by Plane Boundaries, Ser. London Mathematical Society Lecture Note Series, 11-44, Cambridge University Press, 2006.

2. Dombre, T., U. Frisch, J. M. Greene, M. Hénon, A. Mehr, and A. M. Soward, "Chaotic streamlines in the ABC flows," Journal of Fluid Mechanics, Vol. 167, 353-391, 1986.
doi:10.1017/S0022112086002859

3. Silberstein, L., "Elektromagnetische grundgleichungen in bivektorieller behandlung," Annalen der Physik, Vol. 327, No. 3, 579-586, 1907, [Online], available: https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.19073270313.
doi:10.1002/andp.19073270313

4. Woltjer, L., "A theorem on force-free magnetic fields," Proc. Natl. Acad. Sci. U.S.A., Vol. 44, No. 6, 489-491, 1958, [Online], available: https://www.pnas.org/content/44/6/489.
doi:10.1073/pnas.44.6.489

5. Lakhtakia, A., Beltrami Fields in Chiral Media, World Scientific, 1994, [Online], available: https://www.worldscientific.com/doi/abs/10.1142/2031.
doi:10.1142/2031

6. Weiglhofer, W. S. and A. Lakhtakia, "Time-dependent Beltrami fields in free space: Dyadic green functions and radiation potentials," Phys. Rev. E, Vol. 49, 5722-5725, Jun. 1994, [Online], available: https://link.aps.org/doi/10.1103/PhysRevE.49.5722.
doi:10.1103/PhysRevE.49.5722

7. Lakhtakia, A., "Time-dependent Beltrami fields in material continua: The Beltrami-Maxwell postulates," International Journal of Infrared and Millimeter Waves, Vol. 15, No. 2, 369-394, Feb. 1994, [Online], available: https://doi.org/10.1007/BF02096247.
doi:10.1007/BF02096247

8. Chu, C. and T. Ohkawa, "Transverse electromagnetic waves with E||B," Phys. Rev. Lett., Vol. 48, 837-838, Mar. 1982, [Online], available: https://link.aps.org/doi/10.1103/PhysRevLett.48.837.
doi:10.1103/PhysRevLett.48.837

9. Lee, K. K., "Comments on ``transverse electromagnetic waves with E||B''," Phys. Rev. Lett., Vol. 50, 138, Jan. 1983, [Online], available: https://link.aps.org/doi/10.1103/PhysRevLett.50.138..
doi:10.1103/PhysRevLett.50.138

10. Chu, C., "Chu responds," Phys. Rev. Lett., Vol. 50, 139, Jan. 1983, [Online], available: https://link.aps.org/doi/10.1103/PhysRevLett.50.139.
doi:10.1103/PhysRevLett.50.139

11. Zaghloul, H., K. Volk, and H. A. Buckmaster, "Comment on ``transverse electromagnetic waves with E||B''," Phys. Rev. Lett., Vol. 58, 423, Jan. 1987, [Online], available: https://link.aps.org/doi/10.1103/PhysRevLett.58.423.
doi:10.1103/PhysRevLett.58.423

12. Chu, C. and T. Ohkawa, "Chu and ohkawa respond," Phys. Rev. Lett., Vol. 58, 424, Jan. 1987, [Online], available: https://link.aps.org/doi/10.1103/PhysRevLett.58.424.
doi:10.1103/PhysRevLett.58.424

13. Zaghloul, H. and H. A. Buckmaster, "Transverse electromagnetic standing waves with E||B," American Journal of Physics, Vol. 56, No. 9, 801-806, 1988, [Online], available: https://doi.org/10.1119/1.15489.
doi:10.1119/1.15489

14. Shimoda, K., T. Kawai, and K. Uehara, "Electromagnetic plane waves with parallel electric and magnetic fields E||H in free space," American Journal of Physics, Vol. 58, No. 4, 394-396, 1990, [Online], available: https://doi.org/10.1119/1.16482.
doi:10.1119/1.16482

15. Uehara, K., T. Kawai, and K. Shimoda, "Non-transverse electromagnetic waves with parallel electric and magnetic fields," Journal of the Physical Society of Japan, Vol. 58, No. 10, 3570-3575, 1989, [Online], available: https://doi.org/10.1143/JPSJ.58.3570.
doi:10.1143/JPSJ.58.3570

16. Nishiyama, T., "General plane or spherical electromagnetic waves with electric and magnetic fields parallel to each other," Wave Motion, Vol. 54, 58-65, 2015, [Online], available: http://www.sciencedirect.com/science/article/pii/S016521251400167X.
doi:10.1016/j.wavemoti.2014.11.011

17. Evtuhov, V. and A. E. Siegman, "A ``twisted-mode'' technique for obtaining axially uniform energy density in a laser cavity," Appl. Opt., Vol. 4, No. 1, 142-143, 1965.
doi:10.1364/AO.4.000142

18. Draegert, D., "Efficient single-longitudinal-mode Nd:YAG laser," IEEE J. Quantum Electron., Vol. 8, No. 2, 235-239, Feb. 1972.
doi:10.1109/JQE.1972.1076921

19. De Jong, D. J. and D. Andreou, "An Nd: YAG laser whose active medium experiences no hole burning effects," Opt. Commun., Vol. 22, No. 2, 138-142, 1977.
doi:10.1016/0030-4018(77)90005-0

20. Polynkin, P., A. Polynkin, M. Mansuripur, J. Moloney, and N. Peyghambarian, "Single frequency laser oscillator with watts-level output power at 1.5 μm by use of a twisted-mode technique," Opt. Lett., Vol. 30, No. 20, 2745-2747, Oct. 2005, [Online], available: http://ol.osa.org/abstract.cfm?URI=ol-30-20-2745.
doi:10.1364/OL.30.002745

21. Zhang, Y., C. Gao, M. Gao, Z. Lin, and R. Wang, "A diode pumped tunable single-frequency tm:YAG laser using twisted-mode technique," Laser Physics Letters, Vol. 7, No. 1, 17-20, Jan. 2010, [Online], available: https://doi.org/10.1002/lapl.200910098.
doi:10.1002/lapl.200910098

22. Raab, E. L., M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, "Trapping of neutral sodium atoms with radiation pressure," Phys. Rev. Lett., Vol. 59, 2631-2634, Dec. 1987, [Online], available: https://link.aps.org/doi/10.1103/PhysRevLett.59.2631.
doi:10.1103/PhysRevLett.59.2631

23. Clemmow, P. C., Plane Wave Representation, 11-38, Wiley-IEEE Press, 1997.

24. Zel'dovich, B. Y., N. F. Pilipetsky, and V. V. Shkunov, Introduction to Optical Phase Conjugation, 1-24, Springer Berlin Heidelberg, 1985, [Online], available: https://doi.org/10.1007/978-3-540-38959-0_1.