Parabolic fiber cutoffs: A comparison of theories

T. I. Lukowski; F. P. Kapron

doi:10.1364/JOSA.67.001185

Parabolic fiber cutoffs: A comparison of theories

T. I. Lukowski and F. P. Kapron

Journal of the Optical Society of America
Vol. 67,
Issue 9,
pp. 1185-1187
(1977)
•https://doi.org/10.1364/JOSA.67.001185

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T. I. Lukowski and F. P. Kapron, "Parabolic fiber cutoffs: A comparison of theories," J. Opt. Soc. Am. 67, 1185-1187 (1977)

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- Original Manuscript: May 3, 1977
- Published: September 1, 1977

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Abstract

The numerical values of cutoff for parabolic core uniform cladding fibers as obtained from various theories are found to disagree. Only one numerical method and an analytical result presented here correspond. The cutoffs are found to be well ordered and with periodic gaps, a situation not found in step-index guides. Finally, simple formulas yield the cutoff values and the total number of propagating bound modes.

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Equations (9)

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l, m	2(2m + l − l)	I	II	III	IV
0, 1	2	0	0	0
1, 1	4	3. 518	3. 517	3. 642	3. 400
0, 2	6	5. 068	5. 061	4. 693	5. 419
2, 1	6	5. 744	5. 747	6. 103	5. 419
1, 2	8	7. 451	7. 448	6. 994	7. 807
3, 1	8	7. 848	7. 850	8. 520	7. 263
0, 3	10	9. 158	9. 144	8. 592	9. 922
2, 2	10	9. 645	9. 644	9. 169	9. 922
4, 1	10	9. 904	9. 907	10. 96	9. 023
1, 3	12	11. 42	11. 42	10. 74	12. 24
3, 2	12	11. 76	11. 76	11. 31	11. 90
5, 1	12	11. 94	11. 94	13. 43	10. 73
0, 4	14	13. 20	13. 18	12. 46	14. 39
2, 3	14	13. 59	13. 59	12. 84	14. 39
4, 2	14	13. 83	13. 83	13. 45	13. 80
6, 1	14	13. 96	13. 96	15. 94	12. 41
1, 4	16	15. 41	15. 39	14. 55	16. 68
3, 3	16	15. 70	15. 70	14. 91	16. 43
5, 2	16	15. 88	15. 89	15. 60	15. 65
7, 1	16	15. 97	15. 98	18. 50	14. 05
0, 5	18	17. 22	17. 21	16. 32	18. 84
2, 4	18	17. 56	17. 56	16. 60	18. 84
4, 3	18	17. 78	17. 78	16. 97	18. 41
6, 2	18	17. 92	17. 92	17. 76	17. 45
8, 1	18	17. 98	⋯	⋯	15. 68
1, 5	20	19. 40	19. 37	18. 37	21. 12
3, 4	20	19. 66	19. 66	18. 64	20. 92
5, 3	20	19. 84	19. 85	19. 04	20. 33
7, 2	20	19. 94	19. 94	19. 94	19. 22
9, 1	20	19. 99	⋯	⋯	17. 29

l, m	υ(l, m)	l, m	υ(l, m)
0, 13	49. 3	1, 25	99. 4
2, 12	49. 5	3, 24	99. 5
4, 11	49. 6	5, 23	99. 6
6, 10	49. 7	7, 22	99. 6
8, 9	49. 8	9, 21	99. 7
10, 8	49. 9	11, 20	99. 8
12, 7	49. 9	13, 19	99. 8
14, 6	50. 0	15, 18	99. 9
⋮	⋮	17, 17	99. 9
⋮	⋮	19, 16	99. 9
24, 1	50. 0	21, 15	99. 9
		23, 14	100. 0
2(2m + l − 1) = 50		⋮	⋮
	g = 26	49, 1	100. 0
		2(2m + l − 1) = 100
			g = 51

l, m	2(2m + l − l)	I	II	III	IV
0, 1	2	0	0	0
1, 1	4	3. 518	3. 517	3. 642	3. 400
0, 2	6	5. 068	5. 061	4. 693	5. 419
2, 1	6	5. 744	5. 747	6. 103	5. 419
1, 2	8	7. 451	7. 448	6. 994	7. 807
3, 1	8	7. 848	7. 850	8. 520	7. 263
0, 3	10	9. 158	9. 144	8. 592	9. 922
2, 2	10	9. 645	9. 644	9. 169	9. 922
4, 1	10	9. 904	9. 907	10. 96	9. 023
1, 3	12	11. 42	11. 42	10. 74	12. 24
3, 2	12	11. 76	11. 76	11. 31	11. 90
5, 1	12	11. 94	11. 94	13. 43	10. 73
0, 4	14	13. 20	13. 18	12. 46	14. 39
2, 3	14	13. 59	13. 59	12. 84	14. 39
4, 2	14	13. 83	13. 83	13. 45	13. 80
6, 1	14	13. 96	13. 96	15. 94	12. 41
1, 4	16	15. 41	15. 39	14. 55	16. 68
3, 3	16	15. 70	15. 70	14. 91	16. 43
5, 2	16	15. 88	15. 89	15. 60	15. 65
7, 1	16	15. 97	15. 98	18. 50	14. 05
0, 5	18	17. 22	17. 21	16. 32	18. 84
2, 4	18	17. 56	17. 56	16. 60	18. 84
4, 3	18	17. 78	17. 78	16. 97	18. 41
6, 2	18	17. 92	17. 92	17. 76	17. 45
8, 1	18	17. 98	⋯	⋯	15. 68
1, 5	20	19. 40	19. 37	18. 37	21. 12
3, 4	20	19. 66	19. 66	18. 64	20. 92
5, 3	20	19. 84	19. 85	19. 04	20. 33
7, 2	20	19. 94	19. 94	19. 94	19. 22
9, 1	20	19. 99	⋯	⋯	17. 29

l, m	υ(l, m)	l, m	υ(l, m)
0, 13	49. 3	1, 25	99. 4
2, 12	49. 5	3, 24	99. 5
4, 11	49. 6	5, 23	99. 6
6, 10	49. 7	7, 22	99. 6
8, 9	49. 8	9, 21	99. 7
10, 8	49. 9	11, 20	99. 8
12, 7	49. 9	13, 19	99. 8
14, 6	50. 0	15, 18	99. 9
⋮	⋮	17, 17	99. 9
⋮	⋮	19, 16	99. 9
24, 1	50. 0	21, 15	99. 9
		23, 14	100. 0
2(2m + l − 1) = 50		⋮	⋮
	g = 26	49, 1	100. 0
		2(2m + l − 1) = 100
			g = 51

Abstract

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Equations (9)

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