Abstract

We investigate filter properties of chirped fiber Bragg grating (CFBG) (Fabry–Perot) F-P cavity through analyzing the coupled wave equation from one-dimensional Helmholtz equation. We derive an approximate formula of the reflectivity of a CFBG F-P cavity, simulate the central wavelength detuning, and calculate the central wavelength shift with the increase of ambient temperature. In the experiments, we measured the spectra of a diode laser with an FBG/CFBG F-P cavity at 0°C–110°C. The experimental results show that the CFBG F-P cavity can help a diode laser to obtain a less central wavelength shift and a narrower 3 dB reflection bandwidth, compared with the FBG F-P cavity at 0°C–110°C. The research results indicate that the CFBG F-P cavity is a potential wavelength stabilizer of uncooled diode laser.

© 2013 Optical Society of America

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  1. R. Gumenyuk, I. Vartiainen, H. Tuovinen, S. Kivistö, Y. Chamorovskiy, and O. G. Okhotnikov, “Dispersion compensation technologies for femtosecond fiber system,” Appl. Opt. 50, 797–801 (2011).
    [CrossRef]
  2. C. Ye, H. Fu, K. Zhu, and S. He, “All-optical approach to microwave frequency measurement with large spectral range and high accuracy,” IEEE Photon. Technol. Lett. 24, 614–616 (2012).
    [CrossRef]
  3. K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
    [CrossRef]
  4. Y. Huang, Y. Li, H. Wang, X. Yu, H. Zhang, W. Zhang, H. Zhu, S. Zhou, R. Sun, and Y. Zhang, “Wavelength stabilization of a 980 nm semiconductor laser module stabilized with high-power uncooled dual FBG,” Chin. Opt. Lett. 9, 031403 (2011).
  5. R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Academic, 2010).
  6. R. Gumenyuk, I. Vartiainen, H. Tuovinen, S. Kivistö, Y. Chamorovskiy, and O. G. Okhotnikov, “Dispersion compensation technologies for femtosecond fiber system,” Appl. Opt. 50, 797–801 (2011).
    [CrossRef]
  7. S. Kim, J. Bae, K. Lee, S. H. Kim, J. Jeong, and S. B. Lee, “Tunable dispersion slope compensator using two uniform fiber Bragg gratings mounted on S-shape plate,” Opt. Express 17, 4336–4341 (2009).
    [CrossRef]
  8. J. Thomas, C. Voigtländer, D. Schimpf, F. Stutzki, E. Wikszak, J. Limpert, S. Nolte, and A. Tünnermann, “Continuously chirped fiber Bragg gratings by femtosecond laser structuring,” Opt. Lett. 33, 1560–1562 (2008).
    [CrossRef]
  9. S. Wakabayashi, A. Baba, A. Itou, and J. Adachi, “Design and fabrication of an apodization profile in linearly chirped fiber Bragg gratings for wideband >35  nm and compact tunable dispersion compensator,” J. Opt. Soc. Am. B 25, 210–217 (2008).
    [CrossRef]
  10. P. Pérez-Millán, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Fabrication of chirped fiber Bragg gratings by simple combination of stretching movements,” Opt. Fiber Technol. 14, 49–53 (2008).
    [CrossRef]
  11. B. Dabarsyah, C. S. Goh, S. K. Khijwania, S. Y. Set, K. Katoh, and K. Kikuchi, “Adjustable group velocity dispersion and dispersion slope compensation devices with wavelength tunability based on enhanced thermal chirping of fiber Bragg gratings,” J. Lightwave Technol. 25, 2711–2718 (2007).
    [CrossRef]
  12. L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
    [CrossRef]
  13. D. Paladino, A. Iadicicco, S. Campopiano, A. Cutolo, and A. Cusano, “Not-lithographic fabrication of micro-structured fiber Bragg grating evanescent wave sensors,” Proc. SPIE 7003, 70031Z (2008).
    [CrossRef]
  14. M. Guy, F. Trépanier, A. Doyle, Y. Painchaud, and R. L. Lachance, “Novel applications of fiber Bragg grating components for next-generation WDM systems,” Ann. Télécommun. 58, 1275–1306 (2003).
  15. O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Group delay in Bragg grating with linear chirp,” Opt. Commun. 266, 512–520 (2006) .
    [CrossRef]

2012 (1)

C. Ye, H. Fu, K. Zhu, and S. He, “All-optical approach to microwave frequency measurement with large spectral range and high accuracy,” IEEE Photon. Technol. Lett. 24, 614–616 (2012).
[CrossRef]

2011 (3)

2009 (1)

2008 (5)

J. Thomas, C. Voigtländer, D. Schimpf, F. Stutzki, E. Wikszak, J. Limpert, S. Nolte, and A. Tünnermann, “Continuously chirped fiber Bragg gratings by femtosecond laser structuring,” Opt. Lett. 33, 1560–1562 (2008).
[CrossRef]

S. Wakabayashi, A. Baba, A. Itou, and J. Adachi, “Design and fabrication of an apodization profile in linearly chirped fiber Bragg gratings for wideband >35  nm and compact tunable dispersion compensator,” J. Opt. Soc. Am. B 25, 210–217 (2008).
[CrossRef]

P. Pérez-Millán, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Fabrication of chirped fiber Bragg gratings by simple combination of stretching movements,” Opt. Fiber Technol. 14, 49–53 (2008).
[CrossRef]

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

D. Paladino, A. Iadicicco, S. Campopiano, A. Cutolo, and A. Cusano, “Not-lithographic fabrication of micro-structured fiber Bragg grating evanescent wave sensors,” Proc. SPIE 7003, 70031Z (2008).
[CrossRef]

2007 (1)

2006 (2)

L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
[CrossRef]

O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Group delay in Bragg grating with linear chirp,” Opt. Commun. 266, 512–520 (2006) .
[CrossRef]

2003 (1)

M. Guy, F. Trépanier, A. Doyle, Y. Painchaud, and R. L. Lachance, “Novel applications of fiber Bragg grating components for next-generation WDM systems,” Ann. Télécommun. 58, 1275–1306 (2003).

Adachi, J.

Andrés, M. V.

P. Pérez-Millán, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Fabrication of chirped fiber Bragg gratings by simple combination of stretching movements,” Opt. Fiber Technol. 14, 49–53 (2008).
[CrossRef]

Baba, A.

Bae, J.

Baik, S.

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

Belai, O. V.

O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Group delay in Bragg grating with linear chirp,” Opt. Commun. 266, 512–520 (2006) .
[CrossRef]

Campopiano, S.

D. Paladino, A. Iadicicco, S. Campopiano, A. Cutolo, and A. Cusano, “Not-lithographic fabrication of micro-structured fiber Bragg grating evanescent wave sensors,” Proc. SPIE 7003, 70031Z (2008).
[CrossRef]

Chamorovskiy, Y.

Choi, K.

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

Cruz, J. L.

P. Pérez-Millán, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Fabrication of chirped fiber Bragg gratings by simple combination of stretching movements,” Opt. Fiber Technol. 14, 49–53 (2008).
[CrossRef]

Cusano, A.

D. Paladino, A. Iadicicco, S. Campopiano, A. Cutolo, and A. Cusano, “Not-lithographic fabrication of micro-structured fiber Bragg grating evanescent wave sensors,” Proc. SPIE 7003, 70031Z (2008).
[CrossRef]

Cutolo, A.

D. Paladino, A. Iadicicco, S. Campopiano, A. Cutolo, and A. Cusano, “Not-lithographic fabrication of micro-structured fiber Bragg grating evanescent wave sensors,” Proc. SPIE 7003, 70031Z (2008).
[CrossRef]

Dabarsyah, B.

Doyle, A.

M. Guy, F. Trépanier, A. Doyle, Y. Painchaud, and R. L. Lachance, “Novel applications of fiber Bragg grating components for next-generation WDM systems,” Ann. Télécommun. 58, 1275–1306 (2003).

Feng, K. M.

L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
[CrossRef]

Fu, H.

C. Ye, H. Fu, K. Zhu, and S. He, “All-optical approach to microwave frequency measurement with large spectral range and high accuracy,” IEEE Photon. Technol. Lett. 24, 614–616 (2012).
[CrossRef]

Goh, C. S.

Gumenyuk, R.

Guy, M.

M. Guy, F. Trépanier, A. Doyle, Y. Painchaud, and R. L. Lachance, “Novel applications of fiber Bragg grating components for next-generation WDM systems,” Ann. Télécommun. 58, 1275–1306 (2003).

He, S.

C. Ye, H. Fu, K. Zhu, and S. He, “All-optical approach to microwave frequency measurement with large spectral range and high accuracy,” IEEE Photon. Technol. Lett. 24, 614–616 (2012).
[CrossRef]

Huang, Y.

Iadicicco, A.

D. Paladino, A. Iadicicco, S. Campopiano, A. Cutolo, and A. Cusano, “Not-lithographic fabrication of micro-structured fiber Bragg grating evanescent wave sensors,” Proc. SPIE 7003, 70031Z (2008).
[CrossRef]

Im, K.

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

Itou, A.

Jeong, J.

Kashyap, R.

R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Academic, 2010).

Katoh, K.

Khijwania, S. K.

Khosravani, R.

L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
[CrossRef]

Kikuchi, K.

Kim, G.

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

Kim, J.

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

Kim, S.

Kim, S. H.

Kim, Y.

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

Kivistö, S.

Lachance, R. L.

M. Guy, F. Trépanier, A. Doyle, Y. Painchaud, and R. L. Lachance, “Novel applications of fiber Bragg grating components for next-generation WDM systems,” Ann. Télécommun. 58, 1275–1306 (2003).

Lee, K.

S. Kim, J. Bae, K. Lee, S. H. Kim, J. Jeong, and S. B. Lee, “Tunable dispersion slope compensator using two uniform fiber Bragg gratings mounted on S-shape plate,” Opt. Express 17, 4336–4341 (2009).
[CrossRef]

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

Lee, S. B.

Li, Y.

Limpert, J.

Luo, T.

L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
[CrossRef]

Nolte, S.

Okhotnikov, O. G.

Painchaud, Y.

M. Guy, F. Trépanier, A. Doyle, Y. Painchaud, and R. L. Lachance, “Novel applications of fiber Bragg grating components for next-generation WDM systems,” Ann. Télécommun. 58, 1275–1306 (2003).

Paladino, D.

D. Paladino, A. Iadicicco, S. Campopiano, A. Cutolo, and A. Cusano, “Not-lithographic fabrication of micro-structured fiber Bragg grating evanescent wave sensors,” Proc. SPIE 7003, 70031Z (2008).
[CrossRef]

Pérez-Millán, P.

P. Pérez-Millán, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Fabrication of chirped fiber Bragg gratings by simple combination of stretching movements,” Opt. Fiber Technol. 14, 49–53 (2008).
[CrossRef]

Podivilov, E. V.

O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Group delay in Bragg grating with linear chirp,” Opt. Commun. 266, 512–520 (2006) .
[CrossRef]

Schimpf, D.

Set, S. Y.

Shapiro, D. A.

O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Group delay in Bragg grating with linear chirp,” Opt. Commun. 266, 512–520 (2006) .
[CrossRef]

Son, J.

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

Stutzki, F.

Sun, R.

Thomas, J.

Torres-Peiró, S.

P. Pérez-Millán, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Fabrication of chirped fiber Bragg gratings by simple combination of stretching movements,” Opt. Fiber Technol. 14, 49–53 (2008).
[CrossRef]

Trépanier, F.

M. Guy, F. Trépanier, A. Doyle, Y. Painchaud, and R. L. Lachance, “Novel applications of fiber Bragg grating components for next-generation WDM systems,” Ann. Télécommun. 58, 1275–1306 (2003).

Tünnermann, A.

Tuovinen, H.

Vartiainen, I.

Voigtländer, C.

Wakabayashi, S.

Wang, H.

Wikszak, E.

Willner, A. E.

L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
[CrossRef]

Xie, Y.

L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
[CrossRef]

Yan, L. S.

L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
[CrossRef]

Ye, C.

C. Ye, H. Fu, K. Zhu, and S. He, “All-optical approach to microwave frequency measurement with large spectral range and high accuracy,” IEEE Photon. Technol. Lett. 24, 614–616 (2012).
[CrossRef]

Youn, J.

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

Yu, Q.

L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
[CrossRef]

Yu, X.

Zhang, H.

Zhang, W.

Zhang, Y.

Zhou, S.

Zhu, H.

Zhu, K.

C. Ye, H. Fu, K. Zhu, and S. He, “All-optical approach to microwave frequency measurement with large spectral range and high accuracy,” IEEE Photon. Technol. Lett. 24, 614–616 (2012).
[CrossRef]

Ann. Télécommun. (1)

M. Guy, F. Trépanier, A. Doyle, Y. Painchaud, and R. L. Lachance, “Novel applications of fiber Bragg grating components for next-generation WDM systems,” Ann. Télécommun. 58, 1275–1306 (2003).

Appl. Opt. (2)

Chin. Opt. Lett. (1)

IEEE Photon. Technol. Lett. (2)

C. Ye, H. Fu, K. Zhu, and S. He, “All-optical approach to microwave frequency measurement with large spectral range and high accuracy,” IEEE Photon. Technol. Lett. 24, 614–616 (2012).
[CrossRef]

K. Choi, J. Son, G. Kim, K. Lee, J. Youn, S. Baik, K. Im, J. Kim, and Y. Kim, “Enhancement of FBG multiplexing capability using a spectral tag method,” IEEE Photon. Technol. Lett. 20, 2013–2015 (2008).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

O. V. Belai, E. V. Podivilov, and D. A. Shapiro, “Group delay in Bragg grating with linear chirp,” Opt. Commun. 266, 512–520 (2006) .
[CrossRef]

Opt. Express (1)

Opt. Fiber Technol. (2)

P. Pérez-Millán, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Fabrication of chirped fiber Bragg gratings by simple combination of stretching movements,” Opt. Fiber Technol. 14, 49–53 (2008).
[CrossRef]

L. S. Yan, T. Luo, Q. Yu, Y. Xie, K. M. Feng, R. Khosravani, and A. E. Willner, “Investigation of performance variations due to the amplitude of group-delay ripple in chirped fiber Bragg gratings,” Opt. Fiber Technol. 12, 238–242 (2006).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

D. Paladino, A. Iadicicco, S. Campopiano, A. Cutolo, and A. Cusano, “Not-lithographic fabrication of micro-structured fiber Bragg grating evanescent wave sensors,” Proc. SPIE 7003, 70031Z (2008).
[CrossRef]

Other (1)

R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Academic, 2010).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic diagram of a diode laser with a CFBG F-P cavity.

Fig. 2.
Fig. 2.

Schematic diagram of the CFBG F-P cavity composed of a pair of symmetrical CFBGs.

Fig. 3.
Fig. 3.

Reflectivity of uniform FBG F-P cavity and symmetrical CFBG F-P cavity at L=1mm, h=0.1mm. Other CFBG parameters are α=5mm1, k0=5×103mm1, and β=7×104.

Fig. 4.
Fig. 4.

Wavelength detuning of 3 dB reflection bandwidth of uniform FBG F-P cavity and symmetrical CFBG F-P cavity, respectively, at h=0.1mm. Other CFBG parameters are α=5mm1, k0=5×103mm1, and β=7×104.

Fig. 5.
Fig. 5.

Numerical relation between the central wavelength reflectivity and L from 0 to 3.2 mm, h=0.1mm. Other CFBG parameters are α=5mm1, k0=5×103mm1, and β=7×104.

Fig. 6.
Fig. 6.

Relation between the central wavelength detuning and the ambient temperature change (ΔT) at L=1mm, h=0.1mm, α=5mm1, k0=5×103mm1, and β=7×104.

Fig. 7.
Fig. 7.

Relation between the central wavelength detuning and the ambient temperature change (ΔT) of the CFBG F-P cavity at h=0.1mm, L=2, 3, and 4 mm. The other parameters are α=5mm1, k0=5×103mm1, and β=7×104.

Fig. 8.
Fig. 8.

Measured central wavelength of the two CFBG F-P cavities with increasing ambient temperature from 0°C to 110°C. The light source is a broadband light source.

Fig. 9.
Fig. 9.

Measured output spectra of the experimental diode laser at 0°C, 50°C, and 110°C, respectively.

Fig. 10.
Fig. 10.

Measured central wavelength of the diode laser with the external CFBG/FBG F-P cavity. The ambient temperature is from 0°C to 110°C.

Equations (6)

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

{aiα(zz0)ak02β2a=0b+iα(zz0)bk02β2b=0.
R=|b(0)a(0)|2=|t12ei2kh1r1r2ei2kh|2=|t2ei2kh1r2ei2kh|2=|β2k02[ρU1(L)+U2(L)]2β2k02[ρU1(0)+U2(0)]2ei2kh+[U1*(0)+β2k02ρU2*(0)]eiαz02|2,
{U1=F(iβ2k02/2α;1/2;iα(zz0)2/2)U2=(zz0)F(1/2iβ2k02/2α;3/2;iα(zz0)2/2).
ρ=F(iβ2k02/2α;1/2;iα(Lz0)2/2)β2k02(Lz0)F(1/2+iβ2k02/2α;3/2;iα(Lz0)2/2).
Δλ=ξnΛΔT.
λi=ξΛ(iΔz)n(T)dT=ξΛ(iΔz)[n(1+kTΔT)+nTΔT].

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