Abstract

Point-by-point (PbP) inscription of fiber Bragg gratings using femtosecond laser pulses is a versatile technique that is currently experiencing significant research interest for fiber laser and sensing applications. The recent demonstration of apodized gratings using this technique provides a new avenue of investigation into the nature of the refractive index perturbation induced by the PbP modifications, as apodized gratings are sensitive to variation in the average background index along the grating. In this work we compare experimental results for Gaussian- and sinc-apodized PbP gratings to a coupled-mode theory model, demonstrating that the refractive index perturbation induced by the PbP modifications has a negative contribution to the average background index which is small, despite the presence of strong reflective coupling. By employing Fourier analysis to a simplified model of an individual modification, we show that the presence of a densified shell around a central void can produce strong reflective coupling with near-zero change in the average background index. This result has important implications for the experimental implementation of apodized PbP gratings, which are of interest for a range of fiber laser and fiber sensing technologies.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  30. S. Juodkazis, H. Misawa, T. Hashimoto, E. G. Gamaly, and B. Luther-Davies, “Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids,” Appl. Phys. Lett.88, 201909 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  34. E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett.87, 171103 (2005).
    [CrossRef]
  35. S. Kanehira, J. Si, J. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett.5, 1591–1595 (2005).
    [CrossRef] [PubMed]
  36. X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys. A102, 39–44 (2011).
    [CrossRef]

2012 (5)

J. Thomas, C. Voigtländer, R. G. Becker, D. Richter, A. Tünnermann, and S. Nolte, “Femtosecond pulse written fiber gratings: A new avenue to integrated fiber technology,” Laser Photonics Rev.6, 709–723 (2012).
[CrossRef]

A. Stefani, M. Stecher, G. E. Town, and O. Bang, “Direct writing of fiber Bragg grating in microstructured polymer optical fiber,” IEEE Photonics Technol. Lett.24, 1148–1150 (2012).
[CrossRef]

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg gratings sensors,” Laser Photonics Rev.7, 83–108 (2012).
[CrossRef]

R. J. Williams, N. Jovanovic, G. D. Marshall, G. N. Smith, M. J. Steel, and M. J. Withford, “Optimizing the net reflectivity of point-by-point fiber Bragg gratings: The role of scattering loss,” Opt. Express20, 13451–13456 (2012).
[CrossRef] [PubMed]

J. U. Thomas, N. Jovanovic, R. G. Krämer, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings II: Complete vectorial analysis,” Opt. Express20, 21434–21449 (2012).
[CrossRef] [PubMed]

2011 (7)

J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra,” Opt. Express19, 325–341 (2011).
[CrossRef] [PubMed]

C. Koutsides, K. Kalli, D. J. Webb, and L. Zhang, “Characterizing femtosecond laser inscribed Bragg grating spectra,” Opt. Express19, 342–352 (2011).
[CrossRef] [PubMed]

J. Burgmeier, W. Schippers, N. Emde, P. Funken, and W. Schade, “Femtosecond laser-inscribed fiber Bragg gratings for strain monitoring in power cables of offshore wind turbines,” Appl. Opt.50, 1868–1872 (2011).
[CrossRef] [PubMed]

R. Goto, R. J. Williams, N. Jovanovic, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Linearly polarized fiber laser using a point-by-point Bragg grating in a single-polarization photonic bandgap fiber,” Opt. Lett.36, 1872–1874 (2011).
[CrossRef] [PubMed]

R. J. Williams, C. Voigtländer, G. D. Marshall, A. Tünnermann, S. Nolte, M. J. Steel, and M. J. Withford, “Point-by-point inscription of apodized fiber Bragg gratings,” Opt. Lett.36, 2988–2990 (2011).
[CrossRef] [PubMed]

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys. A102, 39–44 (2011).
[CrossRef]

C. Voigtländer, P. Zeil, J. Thomas, M. Ams, R. J. Williams, M. J. Withford, A. Tünnermann, and S. Nolte, “Fs laser induced apodised Bragg waveguides in fused silica,” Proc. SPIE7925, 79250Y (2011).
[CrossRef]

2010 (3)

2009 (1)

2008 (2)

M. L. Åslund, N. Jovanovic, N. Groothoff, J. Canning, G. D. Marshall, S. D. Jackson, A. Fuerbach, and M. J. Withford, “Optical loss mechanisms in femtosecond laser-written point-by-point fibre Bragg gratings,” Opt. Express16, 14248–14254 (2008).
[CrossRef] [PubMed]

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra-large effective-area, higher-order mode fibers: A new strategy for high-power lasers,” Laser Photonics Rev.2, 429–448 (2008).
[CrossRef]

2007 (3)

2006 (3)

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation,” IEEE Photonics Technol. Lett.18, 2266–2268 (2006).
[CrossRef]

S. Juodkazis, H. Misawa, T. Hashimoto, E. G. Gamaly, and B. Luther-Davies, “Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids,” Appl. Phys. Lett.88, 201909 (2006).
[CrossRef]

T. Hashimoto, S. Juodkazis, and H. Misawa, “Void recording in silica,” Appl. Phys. A83, 337–340 (2006).
[CrossRef]

2005 (3)

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett.41, 176–178 (2005).
[CrossRef]

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett.87, 171103 (2005).
[CrossRef]

S. Kanehira, J. Si, J. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett.5, 1591–1595 (2005).
[CrossRef] [PubMed]

2004 (1)

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett.40, 1170–1172 (2004).
[CrossRef]

2000 (1)

1997 (2)

E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett.71, 882–884 (1997).
[CrossRef]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol.15, 1277–1294 (1997).
[CrossRef]

1995 (1)

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett.31, 1488–1490 (1995).
[CrossRef]

1994 (1)

1993 (2)

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fibre using single excimer pulse refractive index modification techniques,” Electron. Lett.29, 1668–1669 (1993).
[CrossRef]

V. Mizrahi and J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol.11, 1513–1517 (1993).
[CrossRef]

Albert, J.

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg gratings sensors,” Laser Photonics Rev.7, 83–108 (2012).
[CrossRef]

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fibre using single excimer pulse refractive index modification techniques,” Electron. Lett.29, 1668–1669 (1993).
[CrossRef]

Ams, M.

C. Voigtländer, P. Zeil, J. Thomas, M. Ams, R. J. Williams, M. J. Withford, A. Tünnermann, and S. Nolte, “Fs laser induced apodised Bragg waveguides in fused silica,” Proc. SPIE7925, 79250Y (2011).
[CrossRef]

Åslund, M. L.

Bang, O.

A. Stefani, M. Stecher, G. E. Town, and O. Bang, “Direct writing of fiber Bragg grating in microstructured polymer optical fiber,” IEEE Photonics Technol. Lett.24, 1148–1150 (2012).
[CrossRef]

Barcelos, S.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett.31, 1488–1490 (1995).
[CrossRef]

Becker, R. G.

J. Thomas, C. Voigtländer, R. G. Becker, D. Richter, A. Tünnermann, and S. Nolte, “Femtosecond pulse written fiber gratings: A new avenue to integrated fiber technology,” Laser Photonics Rev.6, 709–723 (2012).
[CrossRef]

J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra,” Opt. Express19, 325–341 (2011).
[CrossRef] [PubMed]

Bennion, I.

Y. Lai, K. Zhou, K. Sugden, and I. Bennion, “Point-by-point inscription of first-order fiber Bragg grating for C-band applications,” Opt. Express15, 18318–18325 (2007).
[CrossRef] [PubMed]

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation,” IEEE Photonics Technol. Lett.18, 2266–2268 (2006).
[CrossRef]

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett.41, 176–178 (2005).
[CrossRef]

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett.40, 1170–1172 (2004).
[CrossRef]

Berghmans, F.

Bian, H.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys. A102, 39–44 (2011).
[CrossRef]

Bilodeau, F.

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fibre using single excimer pulse refractive index modification techniques,” Electron. Lett.29, 1668–1669 (1993).
[CrossRef]

Burghoff, J.

E. Wikszak, J. Burghoff, M. Will, S. Nolte, A. Tünnermann, and T. Gabler, “Recording of fiber Bragg gratings with femtosecond pulses using a “point by point” technique,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2004), p. CThM7.

Burgmeier, J.

Canning, J.

Caucheteur, C.

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg gratings sensors,” Laser Photonics Rev.7, 83–108 (2012).
[CrossRef]

Chen, F.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys. A102, 39–44 (2011).
[CrossRef]

Cole, M. J.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett.31, 1488–1490 (1995).
[CrossRef]

de Sterke, C. M.

Dong, X.

Dubov, M.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation,” IEEE Photonics Technol. Lett.18, 2266–2268 (2006).
[CrossRef]

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett.40, 1170–1172 (2004).
[CrossRef]

Emde, N.

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol.15, 1277–1294 (1997).
[CrossRef]

Fang, Q.

Feced, R.

Fini, J. M.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra-large effective-area, higher-order mode fibers: A new strategy for high-power lasers,” Laser Photonics Rev.2, 429–448 (2008).
[CrossRef]

Fuerbach, A.

Fujita, K.

S. Kanehira, J. Si, J. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett.5, 1591–1595 (2005).
[CrossRef] [PubMed]

Funken, P.

Gabler, T.

E. Wikszak, J. Burghoff, M. Will, S. Nolte, A. Tünnermann, and T. Gabler, “Recording of fiber Bragg gratings with femtosecond pulses using a “point by point” technique,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2004), p. CThM7.

Gamaly, E. G.

S. Juodkazis, H. Misawa, T. Hashimoto, E. G. Gamaly, and B. Luther-Davies, “Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids,” Appl. Phys. Lett.88, 201909 (2006).
[CrossRef]

Geernaert, T.

Ghalmi, S.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra-large effective-area, higher-order mode fibers: A new strategy for high-power lasers,” Laser Photonics Rev.2, 429–448 (2008).
[CrossRef]

Glezer, E. N.

E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett.71, 882–884 (1997).
[CrossRef]

Goto, R.

Groothoff, N.

Hashimoto, T.

T. Hashimoto, S. Juodkazis, and H. Misawa, “Void recording in silica,” Appl. Phys. A83, 337–340 (2006).
[CrossRef]

S. Juodkazis, H. Misawa, T. Hashimoto, E. G. Gamaly, and B. Luther-Davies, “Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids,” Appl. Phys. Lett.88, 201909 (2006).
[CrossRef]

Hill, K. O.

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fibre using single excimer pulse refractive index modification techniques,” Electron. Lett.29, 1668–1669 (1993).
[CrossRef]

Hirao, K.

S. Kanehira, J. Si, J. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett.5, 1591–1595 (2005).
[CrossRef] [PubMed]

Hou, X.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys. A102, 39–44 (2011).
[CrossRef]

Jackson, S. D.

Jin, L.

Johnson, D. C.

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fibre using single excimer pulse refractive index modification techniques,” Electron. Lett.29, 1668–1669 (1993).
[CrossRef]

Jovanovic, N.

R. J. Williams, N. Jovanovic, G. D. Marshall, G. N. Smith, M. J. Steel, and M. J. Withford, “Optimizing the net reflectivity of point-by-point fiber Bragg gratings: The role of scattering loss,” Opt. Express20, 13451–13456 (2012).
[CrossRef] [PubMed]

J. U. Thomas, N. Jovanovic, R. G. Krämer, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings II: Complete vectorial analysis,” Opt. Express20, 21434–21449 (2012).
[CrossRef] [PubMed]

R. Goto, R. J. Williams, N. Jovanovic, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Linearly polarized fiber laser using a point-by-point Bragg grating in a single-polarization photonic bandgap fiber,” Opt. Lett.36, 1872–1874 (2011).
[CrossRef] [PubMed]

J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra,” Opt. Express19, 325–341 (2011).
[CrossRef] [PubMed]

G. D. Marshall, R. J. Williams, N. Jovanovic, M. J. Steel, and M. J. Withford, “Point-by-point written fiber-Bragg gratings and their application in complex grating designs,” Opt. Express18, 19844–19859 (2010).
[CrossRef] [PubMed]

R. J. Williams, N. Jovanovic, G. D. Marshall, and M. J. Withford, “All-optical, actively Q-switched fiber laser,” Opt. Express18, 7714–7723 (2010).
[CrossRef] [PubMed]

N. Jovanovic, J. Thomas, R. J. Williams, M. J. Steel, G. D. Marshall, A. Fuerbach, S. Nolte, A. Tünnermann, and M. J. Withford, “Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers,” Opt. Express17, 6082–6095 (2009).
[CrossRef] [PubMed]

M. L. Åslund, N. Jovanovic, N. Groothoff, J. Canning, G. D. Marshall, S. D. Jackson, A. Fuerbach, and M. J. Withford, “Optical loss mechanisms in femtosecond laser-written point-by-point fibre Bragg gratings,” Opt. Express16, 14248–14254 (2008).
[CrossRef] [PubMed]

N. Jovanovic, A. Fuerbach, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Stable high-power continuous-wave Yb3+-doped silica fiber laser utilizing a point-by-point inscribed fiber Bragg grating,” Opt. Lett.32, 1486–1488 (2007).
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Kalli, K.

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E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett.87, 171103 (2005).
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S. Kanehira, J. Si, J. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett.5, 1591–1595 (2005).
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A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation,” IEEE Photonics Technol. Lett.18, 2266–2268 (2006).
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S. Juodkazis, H. Misawa, T. Hashimoto, E. G. Gamaly, and B. Luther-Davies, “Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids,” Appl. Phys. Lett.88, 201909 (2006).
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R. Goto, R. J. Williams, N. Jovanovic, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Linearly polarized fiber laser using a point-by-point Bragg grating in a single-polarization photonic bandgap fiber,” Opt. Lett.36, 1872–1874 (2011).
[CrossRef] [PubMed]

J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra,” Opt. Express19, 325–341 (2011).
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R. J. Williams, C. Voigtländer, G. D. Marshall, A. Tünnermann, S. Nolte, M. J. Steel, and M. J. Withford, “Point-by-point inscription of apodized fiber Bragg gratings,” Opt. Lett.36, 2988–2990 (2011).
[CrossRef] [PubMed]

G. D. Marshall, R. J. Williams, N. Jovanovic, M. J. Steel, and M. J. Withford, “Point-by-point written fiber-Bragg gratings and their application in complex grating designs,” Opt. Express18, 19844–19859 (2010).
[CrossRef] [PubMed]

R. J. Williams, N. Jovanovic, G. D. Marshall, and M. J. Withford, “All-optical, actively Q-switched fiber laser,” Opt. Express18, 7714–7723 (2010).
[CrossRef] [PubMed]

N. Jovanovic, J. Thomas, R. J. Williams, M. J. Steel, G. D. Marshall, A. Fuerbach, S. Nolte, A. Tünnermann, and M. J. Withford, “Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers,” Opt. Express17, 6082–6095 (2009).
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M. L. Åslund, N. Jovanovic, N. Groothoff, J. Canning, G. D. Marshall, S. D. Jackson, A. Fuerbach, and M. J. Withford, “Optical loss mechanisms in femtosecond laser-written point-by-point fibre Bragg gratings,” Opt. Express16, 14248–14254 (2008).
[CrossRef] [PubMed]

N. Jovanovic, A. Fuerbach, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Stable high-power continuous-wave Yb3+-doped silica fiber laser utilizing a point-by-point inscribed fiber Bragg grating,” Opt. Lett.32, 1486–1488 (2007).
[CrossRef] [PubMed]

Martinez, A.

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Photoinduced modifications in fiber gratings inscribed directly by infrared femtosecond irradiation,” IEEE Photonics Technol. Lett.18, 2266–2268 (2006).
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A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett.41, 176–178 (2005).
[CrossRef]

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett.40, 1170–1172 (2004).
[CrossRef]

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E. N. Glezer and E. Mazur, “Ultrafast-laser driven micro-explosions in transparent materials,” Appl. Phys. Lett.71, 882–884 (1997).
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S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra-large effective-area, higher-order mode fibers: A new strategy for high-power lasers,” Laser Photonics Rev.2, 429–448 (2008).
[CrossRef]

Misawa, H.

S. Juodkazis, H. Misawa, T. Hashimoto, E. G. Gamaly, and B. Luther-Davies, “Laser-induced microexplosion confined in a bulk of silica: Formation of nanovoids,” Appl. Phys. Lett.88, 201909 (2006).
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T. Hashimoto, S. Juodkazis, and H. Misawa, “Void recording in silica,” Appl. Phys. A83, 337–340 (2006).
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V. Mizrahi and J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol.11, 1513–1517 (1993).
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Nasilowski, T.

Nicholson, J. W.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra-large effective-area, higher-order mode fibers: A new strategy for high-power lasers,” Laser Photonics Rev.2, 429–448 (2008).
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J. U. Thomas, N. Jovanovic, R. G. Krämer, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings II: Complete vectorial analysis,” Opt. Express20, 21434–21449 (2012).
[CrossRef] [PubMed]

J. Thomas, C. Voigtländer, R. G. Becker, D. Richter, A. Tünnermann, and S. Nolte, “Femtosecond pulse written fiber gratings: A new avenue to integrated fiber technology,” Laser Photonics Rev.6, 709–723 (2012).
[CrossRef]

R. J. Williams, C. Voigtländer, G. D. Marshall, A. Tünnermann, S. Nolte, M. J. Steel, and M. J. Withford, “Point-by-point inscription of apodized fiber Bragg gratings,” Opt. Lett.36, 2988–2990 (2011).
[CrossRef] [PubMed]

J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra,” Opt. Express19, 325–341 (2011).
[CrossRef] [PubMed]

C. Voigtländer, P. Zeil, J. Thomas, M. Ams, R. J. Williams, M. J. Withford, A. Tünnermann, and S. Nolte, “Fs laser induced apodised Bragg waveguides in fused silica,” Proc. SPIE7925, 79250Y (2011).
[CrossRef]

N. Jovanovic, J. Thomas, R. J. Williams, M. J. Steel, G. D. Marshall, A. Fuerbach, S. Nolte, A. Tünnermann, and M. J. Withford, “Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers,” Opt. Express17, 6082–6095 (2009).
[CrossRef] [PubMed]

E. Wikszak, J. Burghoff, M. Will, S. Nolte, A. Tünnermann, and T. Gabler, “Recording of fiber Bragg gratings with femtosecond pulses using a “point by point” technique,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2004), p. CThM7.

Obara, M.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett.87, 171103 (2005).
[CrossRef]

Poladian, L.

Qiu, J.

S. Kanehira, J. Si, J. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett.5, 1591–1595 (2005).
[CrossRef] [PubMed]

Ramachandran, S.

S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra-large effective-area, higher-order mode fibers: A new strategy for high-power lasers,” Laser Photonics Rev.2, 429–448 (2008).
[CrossRef]

Richter, D.

J. Thomas, C. Voigtländer, R. G. Becker, D. Richter, A. Tünnermann, and S. Nolte, “Femtosecond pulse written fiber gratings: A new avenue to integrated fiber technology,” Laser Photonics Rev.6, 709–723 (2012).
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X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys. A102, 39–44 (2011).
[CrossRef]

S. Kanehira, J. Si, J. Qiu, K. Fujita, and K. Hirao, “Periodic nanovoid structures via femtosecond laser irradiation,” Nano Lett.5, 1591–1595 (2005).
[CrossRef] [PubMed]

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[CrossRef]

V. Mizrahi and J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol.11, 1513–1517 (1993).
[CrossRef]

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Stecher, M.

A. Stefani, M. Stecher, G. E. Town, and O. Bang, “Direct writing of fiber Bragg grating in microstructured polymer optical fiber,” IEEE Photonics Technol. Lett.24, 1148–1150 (2012).
[CrossRef]

Steel, M. J.

J. U. Thomas, N. Jovanovic, R. G. Krämer, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings II: Complete vectorial analysis,” Opt. Express20, 21434–21449 (2012).
[CrossRef] [PubMed]

R. J. Williams, N. Jovanovic, G. D. Marshall, G. N. Smith, M. J. Steel, and M. J. Withford, “Optimizing the net reflectivity of point-by-point fiber Bragg gratings: The role of scattering loss,” Opt. Express20, 13451–13456 (2012).
[CrossRef] [PubMed]

J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra,” Opt. Express19, 325–341 (2011).
[CrossRef] [PubMed]

R. J. Williams, C. Voigtländer, G. D. Marshall, A. Tünnermann, S. Nolte, M. J. Steel, and M. J. Withford, “Point-by-point inscription of apodized fiber Bragg gratings,” Opt. Lett.36, 2988–2990 (2011).
[CrossRef] [PubMed]

G. D. Marshall, R. J. Williams, N. Jovanovic, M. J. Steel, and M. J. Withford, “Point-by-point written fiber-Bragg gratings and their application in complex grating designs,” Opt. Express18, 19844–19859 (2010).
[CrossRef] [PubMed]

N. Jovanovic, J. Thomas, R. J. Williams, M. J. Steel, G. D. Marshall, A. Fuerbach, S. Nolte, A. Tünnermann, and M. J. Withford, “Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers,” Opt. Express17, 6082–6095 (2009).
[CrossRef] [PubMed]

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A. Stefani, M. Stecher, G. E. Town, and O. Bang, “Direct writing of fiber Bragg grating in microstructured polymer optical fiber,” IEEE Photonics Technol. Lett.24, 1148–1150 (2012).
[CrossRef]

Sugden, K.

Thienpont, H.

Thomas, J.

J. Thomas, C. Voigtländer, R. G. Becker, D. Richter, A. Tünnermann, and S. Nolte, “Femtosecond pulse written fiber gratings: A new avenue to integrated fiber technology,” Laser Photonics Rev.6, 709–723 (2012).
[CrossRef]

J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra,” Opt. Express19, 325–341 (2011).
[CrossRef] [PubMed]

C. Voigtländer, P. Zeil, J. Thomas, M. Ams, R. J. Williams, M. J. Withford, A. Tünnermann, and S. Nolte, “Fs laser induced apodised Bragg waveguides in fused silica,” Proc. SPIE7925, 79250Y (2011).
[CrossRef]

N. Jovanovic, J. Thomas, R. J. Williams, M. J. Steel, G. D. Marshall, A. Fuerbach, S. Nolte, A. Tünnermann, and M. J. Withford, “Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers,” Opt. Express17, 6082–6095 (2009).
[CrossRef] [PubMed]

Thomas, J. U.

Toratani, E.

E. Toratani, M. Kamata, and M. Obara, “Self-fabrication of void array in fused silica by femtosecond laser processing,” Appl. Phys. Lett.87, 171103 (2005).
[CrossRef]

Town, G. E.

A. Stefani, M. Stecher, G. E. Town, and O. Bang, “Direct writing of fiber Bragg grating in microstructured polymer optical fiber,” IEEE Photonics Technol. Lett.24, 1148–1150 (2012).
[CrossRef]

Tünnermann, A.

J. U. Thomas, N. Jovanovic, R. G. Krämer, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings II: Complete vectorial analysis,” Opt. Express20, 21434–21449 (2012).
[CrossRef] [PubMed]

J. Thomas, C. Voigtländer, R. G. Becker, D. Richter, A. Tünnermann, and S. Nolte, “Femtosecond pulse written fiber gratings: A new avenue to integrated fiber technology,” Laser Photonics Rev.6, 709–723 (2012).
[CrossRef]

R. J. Williams, C. Voigtländer, G. D. Marshall, A. Tünnermann, S. Nolte, M. J. Steel, and M. J. Withford, “Point-by-point inscription of apodized fiber Bragg gratings,” Opt. Lett.36, 2988–2990 (2011).
[CrossRef] [PubMed]

J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra,” Opt. Express19, 325–341 (2011).
[CrossRef] [PubMed]

C. Voigtländer, P. Zeil, J. Thomas, M. Ams, R. J. Williams, M. J. Withford, A. Tünnermann, and S. Nolte, “Fs laser induced apodised Bragg waveguides in fused silica,” Proc. SPIE7925, 79250Y (2011).
[CrossRef]

N. Jovanovic, J. Thomas, R. J. Williams, M. J. Steel, G. D. Marshall, A. Fuerbach, S. Nolte, A. Tünnermann, and M. J. Withford, “Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers,” Opt. Express17, 6082–6095 (2009).
[CrossRef] [PubMed]

E. Wikszak, J. Burghoff, M. Will, S. Nolte, A. Tünnermann, and T. Gabler, “Recording of fiber Bragg gratings with femtosecond pulses using a “point by point” technique,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2004), p. CThM7.

Urbanczyk, W.

Voigtländer, C.

J. Thomas, C. Voigtländer, R. G. Becker, D. Richter, A. Tünnermann, and S. Nolte, “Femtosecond pulse written fiber gratings: A new avenue to integrated fiber technology,” Laser Photonics Rev.6, 709–723 (2012).
[CrossRef]

R. J. Williams, C. Voigtländer, G. D. Marshall, A. Tünnermann, S. Nolte, M. J. Steel, and M. J. Withford, “Point-by-point inscription of apodized fiber Bragg gratings,” Opt. Lett.36, 2988–2990 (2011).
[CrossRef] [PubMed]

C. Voigtländer, P. Zeil, J. Thomas, M. Ams, R. J. Williams, M. J. Withford, A. Tünnermann, and S. Nolte, “Fs laser induced apodised Bragg waveguides in fused silica,” Proc. SPIE7925, 79250Y (2011).
[CrossRef]

Wang, X.

X. Wang, F. Chen, Q. Yang, H. Liu, H. Bian, J. Si, and X. Hou, “Fabrication of quasi-periodic micro-voids in fused silica by single femtosecond laser pulse,” Appl. Phys. A102, 39–44 (2011).
[CrossRef]

Wang, Z.

Webb, D. J.

Wikszak, E.

E. Wikszak, J. Burghoff, M. Will, S. Nolte, A. Tünnermann, and T. Gabler, “Recording of fiber Bragg gratings with femtosecond pulses using a “point by point” technique,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2004), p. CThM7.

Will, M.

E. Wikszak, J. Burghoff, M. Will, S. Nolte, A. Tünnermann, and T. Gabler, “Recording of fiber Bragg gratings with femtosecond pulses using a “point by point” technique,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2004), p. CThM7.

Williams, R. J.

R. J. Williams, N. Jovanovic, G. D. Marshall, G. N. Smith, M. J. Steel, and M. J. Withford, “Optimizing the net reflectivity of point-by-point fiber Bragg gratings: The role of scattering loss,” Opt. Express20, 13451–13456 (2012).
[CrossRef] [PubMed]

R. Goto, R. J. Williams, N. Jovanovic, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Linearly polarized fiber laser using a point-by-point Bragg grating in a single-polarization photonic bandgap fiber,” Opt. Lett.36, 1872–1874 (2011).
[CrossRef] [PubMed]

C. Voigtländer, P. Zeil, J. Thomas, M. Ams, R. J. Williams, M. J. Withford, A. Tünnermann, and S. Nolte, “Fs laser induced apodised Bragg waveguides in fused silica,” Proc. SPIE7925, 79250Y (2011).
[CrossRef]

R. J. Williams, C. Voigtländer, G. D. Marshall, A. Tünnermann, S. Nolte, M. J. Steel, and M. J. Withford, “Point-by-point inscription of apodized fiber Bragg gratings,” Opt. Lett.36, 2988–2990 (2011).
[CrossRef] [PubMed]

G. D. Marshall, R. J. Williams, N. Jovanovic, M. J. Steel, and M. J. Withford, “Point-by-point written fiber-Bragg gratings and their application in complex grating designs,” Opt. Express18, 19844–19859 (2010).
[CrossRef] [PubMed]

R. J. Williams, N. Jovanovic, G. D. Marshall, and M. J. Withford, “All-optical, actively Q-switched fiber laser,” Opt. Express18, 7714–7723 (2010).
[CrossRef] [PubMed]

N. Jovanovic, J. Thomas, R. J. Williams, M. J. Steel, G. D. Marshall, A. Fuerbach, S. Nolte, A. Tünnermann, and M. J. Withford, “Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers,” Opt. Express17, 6082–6095 (2009).
[CrossRef] [PubMed]

Withford, M. J.

R. J. Williams, N. Jovanovic, G. D. Marshall, G. N. Smith, M. J. Steel, and M. J. Withford, “Optimizing the net reflectivity of point-by-point fiber Bragg gratings: The role of scattering loss,” Opt. Express20, 13451–13456 (2012).
[CrossRef] [PubMed]

J. U. Thomas, N. Jovanovic, R. G. Krämer, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings II: Complete vectorial analysis,” Opt. Express20, 21434–21449 (2012).
[CrossRef] [PubMed]

C. Voigtländer, P. Zeil, J. Thomas, M. Ams, R. J. Williams, M. J. Withford, A. Tünnermann, and S. Nolte, “Fs laser induced apodised Bragg waveguides in fused silica,” Proc. SPIE7925, 79250Y (2011).
[CrossRef]

R. Goto, R. J. Williams, N. Jovanovic, G. D. Marshall, M. J. Withford, and S. D. Jackson, “Linearly polarized fiber laser using a point-by-point Bragg grating in a single-polarization photonic bandgap fiber,” Opt. Lett.36, 1872–1874 (2011).
[CrossRef] [PubMed]

R. J. Williams, C. Voigtländer, G. D. Marshall, A. Tünnermann, S. Nolte, M. J. Steel, and M. J. Withford, “Point-by-point inscription of apodized fiber Bragg gratings,” Opt. Lett.36, 2988–2990 (2011).
[CrossRef] [PubMed]

J. Thomas, N. Jovanovic, R. G. Becker, G. D. Marshall, M. J. Withford, A. Tünnermann, S. Nolte, and M. J. Steel, “Cladding mode coupling in highly localized fiber Bragg gratings: Modal properties and transmission spectra,” Opt. Express19, 325–341 (2011).
[CrossRef] [PubMed]

G. D. Marshall, R. J. Williams, N. Jovanovic, M. J. Steel, and M. J. Withford, “Point-by-point written fiber-Bragg gratings and their application in complex grating designs,” Opt. Express18, 19844–19859 (2010).
[CrossRef] [PubMed]

R. J. Williams, N. Jovanovic, G. D. Marshall, and M. J. Withford, “All-optical, actively Q-switched fiber laser,” Opt. Express18, 7714–7723 (2010).
[CrossRef] [PubMed]

N. Jovanovic, J. Thomas, R. J. Williams, M. J. Steel, G. D. Marshall, A. Fuerbach, S. Nolte, A. Tünnermann, and M. J. Withford, “Polarization-dependent effects in point-by-point fiber Bragg gratings enable simple, linearly polarized fiber lasers,” Opt. Express17, 6082–6095 (2009).
[CrossRef] [PubMed]

M. L. Åslund, N. Jovanovic, N. Groothoff, J. Canning, G. D. Marshall, S. D. Jackson, A. Fuerbach, and M. J. Withford, “Optical loss mechanisms in femtosecond laser-written point-by-point fibre Bragg gratings,” Opt. Express16, 14248–14254 (2008).
[CrossRef] [PubMed]

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Proc. SPIE (1)

C. Voigtländer, P. Zeil, J. Thomas, M. Ams, R. J. Williams, M. J. Withford, A. Tünnermann, and S. Nolte, “Fs laser induced apodised Bragg waveguides in fused silica,” Proc. SPIE7925, 79250Y (2011).
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Figures (9)

Fig. 1
Fig. 1

(a) Illustration of the refractive index profile of a Gaussian-apodized grating with exaggerated period. (b) Band-diagram representation of such a Gaussian-apodized grating showing a Fabry-Pérot cavity on the short-wavelength side of the main stop-band, and the relative magnitudes of the detuning and coupling constants, σ and κ. (c) Modelled reflection spectra of a Gaussian-apodized grating with positive index modifications, exhibiting strong transmission notches on the short-wavelength side of the main reflection peak.

Fig. 2
Fig. 2

Illustration of the Gaussian apodization technique [19].

Fig. 3
Fig. 3

Illustration of the sinc apodization technique.

Fig. 4
Fig. 4

Transmission and reflection spectrum of a Gaussian-apodized PbP grating compared with modelled grating spectra with: (a) σ(z) = −2|κ(z)|, (b) σ(z) = −0.5|κ(z)| and (c) σ(z) = 0. The measured transmission and reflection spectra are the solid black and red curves, respectively; the modelled transmission and reflection spectra are the dotted blue and green curves, respectively.

Fig. 5
Fig. 5

Differential-interference-contrast (DIC) micrographs of the extremities of the Gaussian-apodized grating. The top images are viewed from the direction of the inscribing beam; the bottom images are viewed from the orthogonal direction.

Fig. 6
Fig. 6

Transmission and reflection spectrum of a sinc-apodized PbP grating compared with modelled grating spectra with: (a) σ(z) = −2|κ(z)|, (b) σ(z) = −0.5|κ(z)| and (c) σ(z) = 0. The measured transmission and reflection spectra are the solid black and red curves, respectively; the modelled transmission and reflection spectra are the dotted blue and green curves, respectively.

Fig. 7
Fig. 7

Optical micrographs of a cross-sectioned PbP FBG: (a) side view; (b) top view. The fiber can be seen protruding at an angle from between two glass coverslips (see (a)). The polished end-face of the fiber features in the centre of image (b), and is elliptical due to the angle of the fiber with respect to the polishing axis.

Fig. 8
Fig. 8

Scanning electron micrographs of cross-sectioned PbP gratings inscribed with: (a) 120 nJ pulses; (b) 200 nJ pulses; and (c) 350 nJ pulses. The dark round dots in each image are the voids. In both images the grating periods are arranged approximately top to bottom, as indicated. The horizontally-running striations are an artefact of the cross-sectional polishing process.

Fig. 9
Fig. 9

Local detuning σ (blue), coupling strength κ (red) and the ratio σ/κ (black) as a function of void width wv for second order gratings with λB = 1541 nm. In each case the shell width ws = Λ. In (a) the void ellipticity ηv = 1 and the shell height hs = 4 μm. For (b), ηv = 3 and hs = 8 μm. The dashed lines at σ/κ = 0 and −1 are a guide to the eye.

Equations (16)

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i d A + d z = [ δ + σ ( z ) i α ( z ) A + + κ ( z ) A i d A d z = [ δ + σ ( z ) i α ( z ) ] A + κ ( z ) A + ,
δ = 2 π n eff ( 1 λ 1 λ B ) ,
σ ( z ) = 2 π λ ( n ¯ ( z ) n 0 ) ,
| κ ( z ) | = κ 0 exp [ ( 4 x ( z ) w ) 2 ] ,
α ( z ) = α 0 | κ ( z ) / κ 0 | ,
T off-res = exp [ 2 0 L α ( z ) d z ] ,
σ ( z ) = σ 0 | κ ( z ) / κ 0 |
x ( z ) = w 4 ln | sinc ( 2 π N 0 z / L ) | ,
ε ( x , y , z ) = ε bg ( x , y ) + δ ε ( x , y , z ) ,
δ ε ( x , y , z ) = j δ ε j ( x , y , Z ) e i 2 j π z / Λ ,
ε ( x , y , z ) = ( n 0 ( x , y ) + Δ n ( x , y ) [ 1 + cos 2 π z Λ ] ) 2
δ ε j ( x , y , Z ) = 1 Λ Λ / 2 Λ / 2 ε ( x , y , z , Z ) e i 2 π j z / Λ d z ,
± i β A + z + i ω c 2 γ bg A + t + ω 2 2 c 2 γ 0 A ± + ω 2 4 c 2 γ m A = 0 ,
γ bg = d x d y | f ( x , y ) | 2 ε bg ( x , y ) γ 0 ( Z ) = d x d y | f ( x , y ) | 2 δ ε 0 ( x , y , Z ) γ m ( Z ) = d x d y | f ( x , y ) | 2 δ ε m ( x , y , Z ) ,
σ ( Z ) = ω 2 γ 0 ( Z ) 2 β c 2 ,
κ m ( Z ) = ω 2 γ m ( Z ) 4 β c 2 .

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