volume | PIER Journals

2009-07-14

Analytical Computation of the Electromagnetic Field Produced by an Optical Fiber Helix

Ioannis D. Chremmos

Dr. Ioannis D. Chremmos

School of Electrical and Computer Engineering

National Technical University of Athens

Greece

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Progress In Electromagnetics Research B, Vol. 16, 189-207, 2009

doi:10.2528/PIERB09050503 | Google Scholar

Abstract

A completely analytical computation of the electromagnetic field produced by an optical fiber helix is presented for the first time. The analysis utilizes the transformation of radially traveling cylindrical waves between two skew cylindrical coordinates systems, that has been previously derived by the author, in order to express the waves radiated by each infinitesimal part of the helix in terms of cylindrical waves around the helix axis and be able to integrate the contributions analytically. Under certain realistic geometrical assumptions, an unperturbed propagation of a single fiber mode is assumed to account for the infinite fiber length, leading to elegant final series expressions in terms of mixed angular-axial Hartree space harmonics, which show clearly the effect of the helical geometry on the field distribution. Analytical formulas are obtained for the field inside and outside the helix cylinder and an interesting two-term decomposition of the outward radiated field is concluded.

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Ioannis D. Chremmos, "Analytical Computation of the Electromagnetic Field Produced by an Optical Fiber Helix," Progress In Electromagnetics Research B, Vol. 16, 189-207, 2009.
doi:10.2528/PIERB09050503

References

1. Chremmos, I. D. and N. K. Uzunoglu, "Transformation of radially traveling cylindrical waves between two skew cylindrical coordinate systems," J. Opt. Soc. Am. A, Vol. 23, 1884-1888, 2006.
doi:10.1364/JOSAA.23.001884 Google Scholar

2. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover, 1972.

3. Chremmos, I. D., N. K. Uzunoglu, and G. Kakarantzas, "Rigorous analysis of the coupling between two nonparallel optical fibers," IEEE J. Lightwave Technol., Vol. 24, 3779-3788, 2006.
doi:10.1109/JLT.2006.881852 Google Scholar

4. Tong, L. M., R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature, Vol. 426, 816-819, 2003.
doi:10.1038/nature02193 Google Scholar

5. Sumetsky, M., "Basic elements for microfiber photonics: Micro/nanofibers and microfiber coil resonators," J. Lightwave Technology, Vol. 26, 21-27, 2008.
doi:10.1109/JLT.2007.911898 Google Scholar

6. Xu, F. and G. Brambilla, "Manufacture of 3-D microfiber coil resonators," IEEE Photon. Technol. Lett., Vol. 19, 1481-1483, 2007.
doi:10.1109/LPT.2007.903762 Google Scholar

7. Sumetsky, M., "Optical fiber microcoil resonator," Opt. Express, Vol. 12, 2303-2316, 2004.
doi:10.1364/OPEX.12.002303 Google Scholar

8. Tai, C. T., Dyadic Green Functions in Electromagnetic Theory, IEEE Press, 1994.

9. Collin, R. E., Field Theory of Guided Waves, McGraw-Hill, 1960.