Proposal and analysis of two-cavity Fabry-Perot structures based on fiber Bragg gratings

Ou Xu; Shaohua Lu; Suchun Feng; Shuisheng Jian

doi:10.1364/JOSAA.26.000639

Journal of the Optical Society of America A
Vol. 26,
Issue 3,
pp. 639-649
(2009)
•https://doi.org/10.1364/JOSAA.26.000639

Proposal and analysis of two-cavity Fabry–Perot structures based on fiber Bragg gratings

Ou Xu, Shaohua Lu, Suchun Feng, and Shuisheng Jian

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Ou Xu, Shaohua Lu, Suchun Feng, and Shuisheng Jian, "Proposal and analysis of two-cavity Fabry-Perot structures based on fiber Bragg gratings," J. Opt. Soc. Am. A 26, 639-649 (2009)

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Table of Contents Category
- Fiber Optics and Optical Communications
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About this Article
History
- Original Manuscript: July 29, 2008
- Revised Manuscript: December 22, 2008
- Manuscript Accepted: December 26, 2008
- Published: February 24, 2009

Abstract

An all-fiber two-cavity Fabry–Perot (FP) configuration based on fiber Bragg gratings (FBGs) is proposed. The characteristics of transmission spectra for the two-cavity FP structure are theoretically analyzed and comprehensively modeled. The explicit expression of the transmission coefficient for the structures is derived. The general conditions for the lengths of two cavities and reflectivities of FBGs are presented to produce the single resonant transmission peak at the central wavelength in the FBG stop band. Based on the theoretical analysis, the transmission spectra of symmetric and asymmetric two-cavity FP structures are simulated, and the simulation results are discussed and explained qualitatively. The design guidelines of the device, including the choices of cavity lengths, grating lengths, and index modulation depths, are concluded. The results show that when the increasing of the cavity length of a single-cavity FP structure results in multiple resonant peaks in the stop band, the two-cavity FP structures of the same length can inhibit the secondary resonant peaks and keep the main peak without degrading the performance through appropriately designing the cavity lengths and FBGs. Finally, the fabrication error tolerances of the structures, including inaccurate cavity lengths and reflectivities of FBGs, are calculated and discussed.

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	$L 1$ , $L 2 ∕ mm$	$Δ λ_{\max} ∕ pm$	FWHM/pm	$T_{\max}$
$s = 3$ (a)	10.048543, 10.048543	0	3.8	1
	10.0486, 10.0485	$- 3.4$	3.8	0.90119
	10.0484, 10.0485	$- 4.3$	3.8	0.90129
$s = 9$ (b)	10.048543	0	2.4	1
	10.0486, 10.0485	$- 3.7$	2.5	0.77286
	10.0484, 10.0485	$- 4.6$	2.4	0.77295

	$Δ n_{1} (\times 10^{- 5})$	$Δ n_{2} (\times 10^{- 5})$	$Δ n_{3} (\times 10^{- 5})$	$Δ λ_{\max} ∕ pm$	FWHM/pm	$T_{\max}$
Ideal	4	36 (12)	4	0	2.4 (3.8)	1
(a)	4	37 (12.3)	4	0.4	2.3 (3.6)	0.99383 (0.99634)
	4	35 (11.7)	4	$- 0.4$	2.6 (4)	0.9995 (0.99966)
(b)	4.1	36 (12)	4.1	0.3	2.4 (3.8)	0.99995 (0.99988)
	3.9	36 (12)	3.9	$- 0.4$	2.4 (3.8)	0.9946 (0.99618)
	4.1	36 (12)	3.9	0.4	2.4 (3.8)	0.87182 (0.95384)
(c)	4.1	37 (12.3)	3.9	0.8 (0.6)	2.3 (3.6)	0.84426 (0.94271)
	4.1	35 (11.7)	3.9	0 (0.2)	2.6 (4)	0.89378 (0.96268)
(d)	4.1	37 (12.3)	3.9	$- 3.4$ $(- 3.2)$	2.2 (3.6)	0.85678 (0.94722)
$L = 10.0485 mm$	4.1	35 (11.7)	3.9	$- 4$ $(- 3.6)$	2.7 (4)	0.90221 (0.96439)

	$L 1$ , $L 2 ∕ mm$	$Δ λ_{\max} ∕ pm$	FWHM/pm	$T_{\max}$
$q \approx 3$ (a)	10.048009, 30.145629	0	2	1
	10.0480, 30.1456	$- 1.4$	2	0.98384
	10.0479, 30.1457	$- 0.6$	1.9	0.89728
$q \approx 7$ (b)	5.024405, 35.169233	0	2	1
	5.0244, 35.1692	$- 1.4$	1.9	0.99247
	5.0243, 35.1693	$- 0.7$	1.6	0.9344

	$Δ n_{1} (\times 10^{- 5})$	$Δ n_{2} (\times 10^{- 5})$	$Δ n_{3} (\times 10^{- 5})$	$Δ λ_{\max} ∕ pm$	FWHM/pm	$T_{\max}$
Ideal	4	16	4	0	2	1
(a)	4	16.4	4	0.1	1.9 (1.8)	0.98739 (0.98991)
	4	15.6	4	0	2.2	0.99924 (0.99965)
(b)	4.1	16	4.1	$- 0.1$ (0)	2	0.99872 (0.9992)
	3.9	16	3.9	$- 0.1$ (0)	2	0.99339 (0.99818)
	4.1	16	3.9	$- 0.3$	2.1 (2)	0.96218 (0.98931)
(c)	4.1	16.4	3.9	$- 0.1$	1.9 (1.8)	0.89704 (0.92648)
	4.1	15.6	3.9	$- 0.6 (- 0.4)$	$2.3$	0.99731 (0.99727)
(d)	4.1	16.4	3.9	$- 1.3$	1.6 (1.2)	0.78637 (0.81934)
(Imperfect L)	4.1	15.6	3.9	$- 1.8 (- 1.7)$	$2.2$	0.95163 (0.99008)

	$L 1$ , $L 2 ∕ mm$	$Δ λ_{\max} ∕ pm$	FWHM/pm	$T_{\max}$
$s = 3$ (a)	10.048543, 10.048543	0	3.8	1
	10.0486, 10.0485	$- 3.4$	3.8	0.90119
	10.0484, 10.0485	$- 4.3$	3.8	0.90129
$s = 9$ (b)	10.048543	0	2.4	1
	10.0486, 10.0485	$- 3.7$	2.5	0.77286
	10.0484, 10.0485	$- 4.6$	2.4	0.77295

Abstract

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Figures (12)

Tables (4)

Equations (11)

Journal of the Optical Society of America A