Modal characteristic equation and dispersion curves for an elliptical step-index fiber with a conducting helical winding on the core-cladding boundary - an analytical study
A special type of elliptical step-index fiber with a conducting helical winding on the core-cladding boundary is proposed and investigated theoretically. Using elliptic cylindrical coordinates, boundary conditions are derived and longitudinal field components for the even and odd modes are obtained....
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| Published in: | Journal of lightwave technology Vol. 20; no. 8; pp. 1416 - 1424 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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New York, NY
IEEE
01-08-2002
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | A special type of elliptical step-index fiber with a conducting helical winding on the core-cladding boundary is proposed and investigated theoretically. Using elliptic cylindrical coordinates, boundary conditions are derived and longitudinal field components for the even and odd modes are obtained. The characteristic equation for the waveguide to be studied is determined by solving the fourth-order determinantal equation, which also contains complex quantities. In order to study the fundamental mode, the modal index /spl nu/ is put as /spl nu/=1. The equations obtained involve modified Mathieu functions of the first order and their derivatives. Applying approximations, cutoff conditions are obtained. Numerical computations are made. Dispersion curves are obtained for different pitch angles of the helical winding. |
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| AbstractList | A special type of elliptical step-index fiber with a conducting helical winding on the core-cladding boundary is proposed and investigated theoretically. Using elliptic cylindrical coordinates, boundary conditions are derived and longitudinal field components for the even and odd modes are obtained. The characteristic equation for the waveguide to be studied is determined by solving the fourth-order determinantal equation, which also contains complex quantities. In order to study the fundamental mode, the modal index /nu/ is put as /nu/=1. The equations obtained involve modified Mathieu functions of the first order and their derivatives. Applying approximations, cutoff conditions are obtained. Numerical computations are made. Dispersion curves are obtained for different pitch angles of the helical winding. A special type of elliptical step-index fiber with a conducting helical winding on the core-cladding boundary is proposed and investigated theoretically. Using elliptic cylindrical coordinates, boundary conditions are derived and longitudinal field components for the even and odd modes are obtained. The characteristic equation for the waveguide to be studied is determined by solving the fourth-order determinantal equation, which also contains complex quantities. In order to study the fundamental mode, the modal index *n is put as *n = 1. The equations obtained involve modified Mathieu functions of the first order and their derivatives. Applying approximations, cutoff conditions are obtained. Numerical computations are made. Dispersion curves are obtained for different pitch angles of the helical winding. A special type of elliptical step-index fiber with a conducting helical winding on the core-cladding boundary is proposed and investigated theoretically. Using elliptic cylindrical coordinates, boundary conditions are derived and longitudinal field components for the even and odd modes are obtained. The characteristic equation for the waveguide to be studied is determined by solving the fourth-order determinantal equation, which also contains complex quantities. In order to study the fundamental mode, the modal index /spl nu/ is put as /spl nu/=1. The equations obtained involve modified Mathieu functions of the first order and their derivatives. Applying approximations, cutoff conditions are obtained. Numerical computations are made. Dispersion curves are obtained for different pitch angles of the helical winding. |
| Author | Kumar, D. Singh, O.N. |
| Author_xml | – sequence: 1 givenname: D. surname: Kumar fullname: Kumar, D. organization: Dept. of Appl. Phys., Banaras Hindu Univ., Varanasi, India – sequence: 2 givenname: O.N. surname: Singh fullname: Singh, O.N. organization: Dept. of Appl. Phys., Banaras Hindu Univ., Varanasi, India |
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| Cites_doi | 10.1063/1.1931144 10.1364/JOSAB.12.001273 10.1002/ecja.4410680513 10.1029/RS016i004p00541 10.1364/OL.16.000135 10.1364/OL.17.001658 10.1364/OL.12.000729 10.1109/22.31075 10.1007/BF00620076 10.1109/TMTT.1982.1131284 10.1049/el:19790275 10.1364/OL.14.000817 10.1109/22.362983 10.1109/22.754887 10.1109/TMTT.1985.1133181 10.1049/el:19790401 10.1049/el:19800193 10.1002/ecja.4410690913 |
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| Keywords | Modal analysis Electromagnetic wave propagation Dispersion relation Characteristic equation Helical structure Boundary condition Elliptical waveguide helical structures in electromagnetic (EM) fields Optical fiber |
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| SubjectTerms | Applied sciences Boundary conditions Circuit properties Communication system control Electric, optical and optoelectronic circuits Electromagnetic scattering Electromagnetic waveguides Electronics Equations Exact sciences and technology Integrated optics. Optical fibers and wave guides Optical and optoelectronic circuits Optical fiber dispersion Optical fiber polarization Optical fibers Optical propagation Optical waveguides |
| Title | Modal characteristic equation and dispersion curves for an elliptical step-index fiber with a conducting helical winding on the core-cladding boundary - an analytical study |
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