Solving characteristic equation of orbital angular momentum modes in a ring fiber

Yixiao Zhu; Fan Zhang

doi:10.3788/COL201513.030501

Journals >Chinese Optics Letters >Volume 13 >Issue 3 >Page 030501 > Article

Chinese Optics Letters
Vol. 13, Issue 3, 030501 (2015)

Solving characteristic equation of orbital angular momentum modes in a ring fiber

Yixiao Zhu and Fan Zhang^*

Author Affiliations

State Key Laboratory of Advanced Optical Communication Systems and Networks, Peking University, Beijing 100871, China

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DOI: 10.3788/COL201513.030501 Cite this Article Set citation alerts

Yixiao Zhu, Fan Zhang. Solving characteristic equation of orbital angular momentum modes in a ring fiber[J]. Chinese Optics Letters, 2015, 13(3): 030501 Copy Citation Text

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Fig. 1. Cross sectional diagram of a ring fiber.

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Fig. 2. Electric field distribution on the cross section for several modes; (a) TE01; (b) TM01; (c) EH11; (d) HE31.

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Fig. 3. ERI difference between TE01 and HE21 as a function of the index difference and the wavelength.

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Fig. 4. Normalized propagation constant b for HE11 as a function of the normalized frequency V and the average radius of the ring.

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Fig. 5. Normalized propagation constant b of modes in a ring fiber as a function of the normalized frequency V with the average radius of the ring set as 3, 5, 7.5, and 10 μm.

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Mode	Simulation Result	Eq. (10) Solution	Relative Error
${HE}_{11}$	1.467350	1.467352	$1.4 \times 10^{- 6}$
${TE}_{01}$	1.466638	1.466641	$2.0 \times 10^{- 6}$
${HE}_{21}$	1.466159	1.466162	$2.0 \times 10^{- 6}$
${TM}_{01}$	1.465566	1.465566	$< 10^{- 6}$
${HE}_{31}$	1.462827	1.462831	$2.7 \times 10^{- 6}$
${EH}_{11}$	1.462714	1.462715	$6.8 \times 10^{- 7}$
${HE}_{41}$	1.457518	1.457526	$5.5 \times 10^{- 6}$
${EH}_{21}$	1.457473	1.457475	$1.4 \times 10^{- 6}$
${EH}_{31}$	1.450510	1.450517	$4.8 \times 10^{- 6}$

Table 1. Comparison between Simulation Results and the Solution of Eq. (10)

Yixiao Zhu, Fan Zhang. Solving characteristic equation of orbital angular momentum modes in a ring fiber[J]. Chinese Optics Letters, 2015, 13(3): 030501

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