Differential multipole method for microstructured optical fibers

S. Campbell; R. C. McPhedran; C. Martijn de Sterke; L. C. Botten

doi:10.1364/JOSAB.21.001919

Journal of the Optical Society of America B
Vol. 21,
Issue 11,
pp. 1919-1928
(2004)
•https://doi.org/10.1364/JOSAB.21.001919

Differential multipole method for microstructured optical fibers

S. Campbell, R. C. McPhedran, C. Martijn de Sterke, and L. C. Botten

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S. Campbell, R. C. McPhedran, C. Martijn de Sterke, and L. C. Botten, "Differential multipole method for microstructured optical fibers," J. Opt. Soc. Am. B 21, 1919-1928 (2004)

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Abstract

We describe the differential multipole method, an extended multipole method used to calculate the modes of microstructured optical fibers with noncircular inclusions. We use a multipole expansion centered on each inclusion and a differential method to calculate the scattering properties of the individual inclusions. Representative results for a fiber with one ring of elliptical inclusions are presented, and a direct comparison is made with an existing method. The new method is also applied to a microstructured optical fiber with seven rings of elliptical inclusions, which is found, in effect, to support a single polarization of the fundamental mode.

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Equations (63)

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$M_{max}$	$Re (n_{eff})$	$Im (n_{eff}) \times 10^{- 6}$	$W_{dot}$	$W_{dash}$
4	1.446419435	2.9437	$3.4 \times 10^{- 3}$	$5.5 \times 10^{- 3}$
5	1.446411348	1.4287	$2.0 \times 10^{- 3}$	$4.2 \times 10^{- 3}$
6	1.446397187	2.1808	$2.7 \times 10^{- 4}$	$1.7 \times 10^{- 3}$
7	1.446396099	2.4601	$1.2 \times 10^{- 4}$	$5.4 \times 10^{- 4}$
8	1.446397463	2.3382	$1.1 \times 10^{- 4}$	$3.5 \times 10^{- 4}$
9	1.446397587	2.3116	$4.7 \times 10^{- 2}$	$1.8 \times 10^{- 4}$

η	$Re (n_{eff})$	$Im (n_{eff})$
1
DMM	1.445395232	$3.1945 \times 10^{- 8}$
ABC	1.445397228	$3.2376 \times 10^{- 8}$
0.9
DMM	1.445672782	$1.1040 \times 10^{- 7}$
ABC	1.445672267	$1.1191 \times 10^{- 7}$
0.8
DMM	1.445929388	$3.5723 \times 10^{- 7}$
ABC	1.445929716	$3.7576 \times 10^{- 7}$
0.7
DMM	1.446169785	$9.8458 \times 10^{- 7}$
ABC	1.44617215	$1.1166 \times 10^{- 6}$
0.6
DMM	1.446397587	$2.3116 \times 10^{- 6}$
ABC	1.446404071	$2.9339 \times 10^{- 6}$

η	$Re (n_{eff})$	$Im (n_{eff})$
1
DMM	1.445395232	$3.1945 \times 10^{- 8}$
ABC	1.445397228	$3.2376 \times 10^{- 8}$
0.9
DMM	1.445677647	$1.3560 \times 10^{- 7}$
ABC	1.445676964	$1.3624 \times 10^{- 7}$
0.8
DMM	1.445941057	$4.6190 \times 10^{- 7}$
ABC	1.445941003	$4.8042 \times 10^{- 7}$
0.7
DMM	1.446189882	$1.2755 \times 10^{- 6}$
ABC	1.4461916	$1.4230 \times 10^{- 6}$
0.6
DMM	1.446427235	$2.9601 \times 10^{- 6}$
ABC	1.44643281	$3.6624 \times 10^{- 6}$

$M_{max}$	$Re (n_{eff})$	$Im (n_{eff}) \times 10^{- 6}$	$W_{dot}$	$W_{dash}$
4	1.446419435	2.9437	$3.4 \times 10^{- 3}$	$5.5 \times 10^{- 3}$
5	1.446411348	1.4287	$2.0 \times 10^{- 3}$	$4.2 \times 10^{- 3}$
6	1.446397187	2.1808	$2.7 \times 10^{- 4}$	$1.7 \times 10^{- 3}$
7	1.446396099	2.4601	$1.2 \times 10^{- 4}$	$5.4 \times 10^{- 4}$
8	1.446397463	2.3382	$1.1 \times 10^{- 4}$	$3.5 \times 10^{- 4}$
9	1.446397587	2.3116	$4.7 \times 10^{- 2}$	$1.8 \times 10^{- 4}$

η	$Re (n_{eff})$	$Im (n_{eff})$
1
DMM	1.445395232	$3.1945 \times 10^{- 8}$
ABC	1.445397228	$3.2376 \times 10^{- 8}$
0.9
DMM	1.445672782	$1.1040 \times 10^{- 7}$
ABC	1.445672267	$1.1191 \times 10^{- 7}$
0.8
DMM	1.445929388	$3.5723 \times 10^{- 7}$
ABC	1.445929716	$3.7576 \times 10^{- 7}$
0.7
DMM	1.446169785	$9.8458 \times 10^{- 7}$
ABC	1.44617215	$1.1166 \times 10^{- 6}$
0.6
DMM	1.446397587	$2.3116 \times 10^{- 6}$
ABC	1.446404071	$2.9339 \times 10^{- 6}$

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Equations (63)

Journal of the Optical Society of America B