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Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings

Yuri O. Barmenkov, Dobryna Zalvidea, Salvador Torres-Peiró, Jose L. Cruz, and Miguel V. Andrés

Open Access Open Access

Abstract

In this paper, we describe the properties of Fabry-Perot fiber cavity formed by two fiber Bragg gratings in terms of the grating effective length. We show that the grating effective length is determined by the group delay of the grating, which depends on its diffraction efficiency and physical length. We present a simple analytical formula for calculation of the effective length of the uniform fiber Bragg grating and the frequency separation between consecutive resonances of a Fabry-Perot cavity. Experimental results on the cavity transmission spectra for different values of the gratings’ reflectivity support the presented theory.

©2006 Optical Society of America

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Figures (5)
Fig. 1.
Fig. 1. Fabry-Perot fiber cavity formed by two FBGs (FBG1 and FBG2). L 1,2 are the physical lengths of FBGs and L 0 is the distance between them.

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Fig. 2.
Fig. 2. Relative effective length Leff /L of a uniform 4-cm fiber Bragg grating versus its diffraction efficiency for λ 0=1530 nm. The labels near the curves correspond to detuning from the peak wavelength.

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Fig. 3.
Fig. 3. Group delay calculated for uniform 4-cm fiber Bragg grating versus detuning from the grating peak wavelength (1530 nm). The labels near the curves correspond to the diffraction efficiency values.

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Fig. 4.
Fig. 4. (a) Theoretical and (b) experimental transmittance spectra of the Fabry-Perot fiber cavity formed by two equal uniform 4-cm FBGs separated by 5 cm. Gratings are centered at 1531.08 nm. The diffraction efficiency values are labeled near the corresponding curves.

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Fig. 5.
Fig. 5. Comparison between theoretical (solid line) and experimental (stars) mode-spacing values.

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Equations (8)

Equations on this page are rendered with MathJax. Learn more.

T = ( 1 − R 1 ) ( 1 − R 2 ) ( 1 − R 1 R 2 ) 2 + 4 R 1 R 2 sin 2 ( β L 0 + φ 1 + φ 2 2 ) ,
Δ λ = λ 2 2 n g ( L 0 + L eff 1 + L eff 2 ) ,
L eff = v g τ 1,2 2 ,
ρ = − κ sinh ⁡ ( εL ) ξ sinh ⁡ ( εL ) + iε ⁡ cosh ( εL ) ,
τ = − λ 2 2 π c d φ d λ ,
φ = − atan ( ε ξ cotanh ( εL ) ) .
L eff = λ 0 2 π n 1 tanh ( π n 1 λ 0 L ) .
L eff = L R 2 atanh ( R ) .
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