Mode properties and dispersion for two optical fiber-index profiles by the propagating beam method

M. D. Feit; J. A. Fleck

doi:10.1364/AO.19.003140

Applied Optics
Vol. 19,
Issue 18,
pp. 3140-3150
(1980)
•https://doi.org/10.1364/AO.19.003140

Mode properties and dispersion for two optical fiber-index profiles by the propagating beam method

M. D. Feit and J. A. Fleck

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M. D. Feit and J. A. Fleck, "Mode properties and dispersion for two optical fiber-index profiles by the propagating beam method," Appl. Opt. 19, 3140-3150 (1980)

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Abstract

The propagating beam method generates solutions for the electric field in a graded-index optical fiber that emphasize beam characteristics rather than modal properties. Through Fourier analysis with respect to axial distance z, these solutions can be made to yield such mode properties as the propagation constants β_n, the mode group delays ∂β_n/∂ω, and the mode eigenfunctions. The propagating beam method has been applied to a detailed study of two index profiles with finite thickness cladding: an axisymmetric power-law (α = 1.85) profile both without and with an on-axis dip. In nine successive computer runs, eighty-five and eighty-four bound or guided modes were excited and characterized for the two respective profiles. The mode group delays near cutoff for both profiles show large deviation from those derived with the WKB method. In addition, sets of almost degenerate modes near cutoff show large differences in group delay. Modes with low azimuthal quantum number are strongly perturbed by the central dip. It is found that rms pulse dispersion is quite sensitive to the inclusion or exclusion of modes near cutoff, but that frequency response bandwidth is not. This leads to the conclusion that fiber bandwidth cannot be accurately inferred from rms pulse dispersion and may explain why broadband multimode fibers exist dispite strong perturbation of the modes near cutoff.

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N	${β^{'}}_{n} ({cm}^{- 1})$	${\partial β^{'}}_{n} / \partial ω (nsec / km)$	β_n/k₀	∂β_n/∂ω(nsec/km)	μ	ν	2μ + ν
1	697.102	39.31095	1.5110540	39.15815	0	0	0
2	653.043	39.21984	1.5103577	39.06926	0	1	1
3	610.681	39.13235	1.5096880	38.98485	1	0	2
4	609.843	39.13049	1.5096748	38.98306	0	2	2
5	568.298	39.04473	1.5090176	38.90122	1	1	3
6	567.206	39.04234	1.5090004	38.89894	0	3	3
7	526.752	38.95885	1.5083602	38.82015	2	0	4
8	526.196	38.95783	1.5083514	38.81920	1	2	4
9	524.984	38.95522	1.5083322	38.81674	0	4	4
10	485.188	38.87295	1.5077022	38.73994	2	1	5
11	484.371	38.87124	1.5076893	38.73835	1	3	5
12	483.091	38.86832	1.5076690	38.73563	0	5	5
13	444.175	38.78808	1.5070527	38.66157	3	0	6
14	443.760	38.78737	1.5070461	38.66093	2	2	6
15	442.794	38.78528	1.5070308	38.65901	1	4	6
16	441.470	38.78220	1.5070098	38.65615	0	6	6
17	403.149	38.70335	1.5064026	38.58420	3	1	7
18	402.497	38.70207	1.5063923	38.58305	2	3	7
19	401.433	38.69971	1.5063755	38.58090	1	5	7
20	400.081	38.69653	1.5063540	38.57798	0	7	7
21	362.532	38.61920	1.5057588	38.50821	4	0	8
22	362.201	38.61879	1.5057536	38.50787	3	2	8
23	361.398	38.61711	1.5057408	38.50636	2	4	8
24	360.266	38.61454	1.5057229	38.50403	1	6	8
25	358.893	38.61129	1.5057011	38.50108	0	8	8
26	321.904	38.53521	1.5051145	38.43323	4	1	9
27	321.362	38.53432	1.5051060	38.43246	3	3	9
28	320.452	38.53243	1.5050915	38.43079	2	5	9
29	319.272	38.52973	1.5050728	38.42837	1	7	9
30	317.884	38.52589	1.5050508	38.42485	0	9	9
31	281.603	38.45113	1.5044752	38.35895	5	0	10
32	281.327	38.45108	1.5044708	38.35896	4	2	10
33	280.640	38.44994	1.5044599	38.35800	3	4	10
34	279.651	38.44795	1.5044442	38.35626	2	6	10
35	278.434	38.44521	1.5044249	38.35383	1	8	10
36	277.036	38.44067	1.5044027	38.34965	0	10	10
37	241.292	38.36585	1.5038354	38.28430	5	1	11
38	240.829	38.36573	1.5038280	38.28431	4	3	11
39	240.033	38.36493	1.5038154	38.28373	3	5	11
40	238.985	38.36333	1.5037988	38.28241	2	7	11
41	237.738	38.36085	1.5037790	38.28028	1	9	11
42	236.330	38.36009	1.5037566	38.27990	0	11	11
43	201.258	38.27343	1.5031997	38.20331	6	0	12
44	201.022	38.27449	1.5031960	38.20444	5	2	12
45	200.419	38.27616	1.5031864	38.20628	4	4	12
46	199.539	38.27756	1.5031724	38.20794	3	6	12
47	198.443	38.27779	1.5031550	38.20849	2	8	12
48	197.173	38.27610	1.5031348	38.20717	1	10	12
49	195.759	38.24588	1.5031124	38.17743	0	12	12
50	161.236	38.15659	1.5025640	38.09878	6	1	13
51	160.826	38.16291	1.5025574	38.10521	5	3	13
52	160.110	38.17268	1.5025461	38.11519	4	5	13
53	159.159	38.18238	1.5025310	38.12517	3	7	13
54	158.020	38.18888	1.5025129	38.13202	2	9	13
55	156.728	38.19374	1.5024923	38.13728	1	11	13
56	155.307	38.17692	1.5024698	38.12094	0	13	13
57	121.524	37.95079	1.5019329	37.90610	7	0	14
58	121.309	37.96229	1.5019294	37.91766	6	2	14
59	120.749	37.99178	1.5019206	37.94729	5	4	14
60	119.926	38.02996	1.5019075	37.98570	4	6	14
61	118.899	38.06568	1.5018911	38.02172	3	8	14
62	117.714	38.09059	1.5018723	38.04699	2	10	14
63	116.398	38.09244	1.5018514	38.04929	1	12	14
64	114.970	38.16460	1.5018287	38.12184	0	14	14
65	82.050	37.47447	1.5013053	37.44378	7	1	15
66	81.631	37.54118	1.5012986	37.51057	6	3	15
67	80.895	37.65427	1.5012869	37.62384	5	5	15
68	79.924	37.78187	1.5012715	37.75167	4	7	15
69	78.786	37.89295	1.5012534	37.86306	3	9	15
70	77.530	37.95501	1.5012334	37.92551	2	11	15
71	76.178	37.99670	1.5012119	37.96766	1	13	15
72	74.738	38.24039	1.5011890	38.21167	0	15	15
73	43.631	36.00074	1.5006942	35.98463	8	0	16
74	43.351	36.11671	1.5006898	36.10064	7	2	16
75	42.605	36.42847	1.5006779	36.41252	6	4	16
76	41.529	36.84249	1.5006608	36.82675	5	6	16
77	40.257	37.25250	1.5006406	37.23706	4	8	16
78	38.893	37.57846	1.5006189	37.56339	3	10	16
79	37.493	37.81588	1.5005966	37.80124	2	12	16
80	36.070	37.86429	1.5005740	37.85018	1	14	16
81	34.607	38.36996	1.5005507	38.35622	0	16	16
82	8.489	29.02364	1.5001351	29.02105	8	1	17
83	7.433	30.25405	1.5001183	30.25168	7	3	17
84	5.628	32.23884	1.5000896	32.23693	6	5	17
85	3.491	34.32493	1.5000556	34.32366	5	7	17

Abstract

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Applied Optics