Abstract

We report on the detailed investigation of the core to cladding mode coupling in femtosecond-written long period fiber gratings (LPFG). It is shown that the excitation of higher-order cladding modes with strong selectivity and high precision is possible. The coupling behavior of several gratings, as well as its dependence on the modified core cross-section, is determined theoretically and confirmed experimentally by its spectral response. The presented tool paves the way for a completely new class of tailored LPFGs for different fiber integrated devices.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. A. van Eijkelenborg, W. Padden, and J. A. Besley, “Mechanically induced long-period gratings in microstructured polymer fibre,” Opt. Commun. 236(1–3), 75–78 (2004).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  17. E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Transmission characteristics of long-period fiber gratings having arbitrary azimuthal/radial refractive index variations,” J. Lightwave Technol. 21(1), 218–227 (2003).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2018 (1)

2017 (1)

2016 (2)

2015 (1)

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” IEEE J. Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

2012 (1)

2011 (1)

2010 (2)

2007 (1)

2006 (2)

V. Grubsky and J. Feinberg, “Fabrication of Axially Symmetric Long-Period Gratings with a Carbon Dioxide Laser,” IEEE Photonics Technol. Lett. 18(21), 2296–2298 (2006).
[Crossref]

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, “Ultrafast processes for bulk modification of transparent materials,” MRS Bull. 31(8), 620–625 (2006).
[Crossref]

2005 (1)

2004 (1)

M. A. van Eijkelenborg, W. Padden, and J. A. Besley, “Mechanically induced long-period gratings in microstructured polymer fibre,” Opt. Commun. 236(1–3), 75–78 (2004).
[Crossref]

2003 (4)

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fibres,” Electron. Lett. 39(4), 349–350 (2003).
[Crossref]

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[Crossref]

B. L. Bachim and T. K. Gaylord, “Polarization-dependent loss and birefringence in long-period fiber gratings,” Appl. Opt. 42(34), 6816–6823 (2003).
[Crossref] [PubMed]

E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Transmission characteristics of long-period fiber gratings having arbitrary azimuthal/radial refractive index variations,” J. Lightwave Technol. 21(1), 218–227 (2003).
[Crossref]

2002 (1)

1999 (1)

1997 (2)

1996 (1)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

1979 (1)

H. Kogelnik, “Theory of dielectric waveguides,” Top. Appl. Phys. 7, 15–83 (1979).

1978 (1)

1971 (2)

Androz, G.

Anemogiannis, E.

Babin, S.

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” IEEE J. Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

Bachim, B. L.

Becker, R. G.

Bernier, M.

Besley, J. A.

M. A. van Eijkelenborg, W. Padden, and J. A. Besley, “Mechanically induced long-period gratings in microstructured polymer fibre,” Opt. Commun. 236(1–3), 75–78 (2004).
[Crossref]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Birks, T. A.

Bock, V.

M. Heck, V. Bock, R. G. Krämer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,”, Proc. SPIE LASE 10512–53, (2018).
[Crossref]

Boisvert, J.-S.

Chin, S. L.

Dostovalov, A. V.

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” IEEE J. Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

T. Erdogan, “Cladding-mode resonances in short- and long-period fiber grating filters,” J. Opt. Soc. Am. A 14(8), 1760–1773 (1997).
[Crossref]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Faucher, D.

Feinberg, J.

V. Grubsky and J. Feinberg, “Fabrication of Axially Symmetric Long-Period Gratings with a Carbon Dioxide Laser,” IEEE Photonics Technol. Lett. 18(21), 2296–2298 (2006).
[Crossref]

Fevrier, S.

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fibres,” Electron. Lett. 39(4), 349–350 (2003).
[Crossref]

Gaylord, T. K.

Gloge, D.

Glytsis, E. N.

Goebel, T. A.

M. Heck, V. Bock, R. G. Krämer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,”, Proc. SPIE LASE 10512–53, (2018).
[Crossref]

Grobnic, D.

Grubsky, V.

V. Grubsky and J. Feinberg, “Fabrication of Axially Symmetric Long-Period Gratings with a Carbon Dioxide Laser,” IEEE Photonics Technol. Lett. 18(21), 2296–2298 (2006).
[Crossref]

Heck, M.

M. Heck, S. Nolte, A. Tünnermann, R. Vallée, and M. Bernier, “Femtosecond-written long-period gratings in fluoride fibers,” Opt. Lett. 43(9), 1994–1997 (2018).
[Crossref] [PubMed]

M. Heck, V. Bock, R. G. Krämer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,”, Proc. SPIE LASE 10512–53, (2018).
[Crossref]

Hirao, K.

Humbert, G.

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fibres,” Electron. Lett. 39(4), 349–350 (2003).
[Crossref]

Iezzi, V. L.

Itoh, K.

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, “Ultrafast processes for bulk modification of transparent materials,” MRS Bull. 31(8), 620–625 (2006).
[Crossref]

James, S. W.

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[Crossref]

Jansen, F.

Jauregui, C.

Jovanovic, N.

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Kakarantzas, G.

Kashyap, R.

Kazansky, P. G.

Kogelnik, H.

H. Kogelnik, “Theory of dielectric waveguides,” Top. Appl. Phys. 7, 15–83 (1979).

Kondo, Y.

Krämer, R. G.

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. Express 20(19), 21434–21449 (2012).
[Crossref] [PubMed]

M. Heck, V. Bock, R. G. Krämer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,”, Proc. SPIE LASE 10512–53, (2018).
[Crossref]

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Liem, A.

M. Heck, V. Bock, R. G. Krämer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,”, Proc. SPIE LASE 10512–53, (2018).
[Crossref]

Limpert, J.

Liu, Y.

Loranger, S.

Malki, A.

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fibres,” Electron. Lett. 39(4), 349–350 (2003).
[Crossref]

Marshall, G. D.

Matzdorf, C.

M. Heck, V. Bock, R. G. Krämer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,”, Proc. SPIE LASE 10512–53, (2018).
[Crossref]

Mihailov, S.

Mitsuyu, T.

Nodop, D.

Nolte, S.

Nouchi, K.

Padden, W.

M. A. van Eijkelenborg, W. Padden, and J. A. Besley, “Mechanically induced long-period gratings in microstructured polymer fibre,” Opt. Commun. 236(1–3), 75–78 (2004).
[Crossref]

Pagnoux, D.

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fibres,” Electron. Lett. 39(4), 349–350 (2003).
[Crossref]

Richter, D.

M. Heck, V. Bock, R. G. Krämer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,”, Proc. SPIE LASE 10512–53, (2018).
[Crossref]

Roy, P.

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fibres,” Electron. Lett. 39(4), 349–350 (2003).
[Crossref]

Russell, P. St. J.

Saliminia, A.

Schaffer, C. B.

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, “Ultrafast processes for bulk modification of transparent materials,” MRS Bull. 31(8), 620–625 (2006).
[Crossref]

Schreiber, T.

M. Heck, V. Bock, R. G. Krämer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,”, Proc. SPIE LASE 10512–53, (2018).
[Crossref]

Sheng, Y.

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Smelser, C.

Snyder, A.

Steel, M. J.

Tatam, R. P.

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[Crossref]

Thomas, J.

Thomas, J. U.

Tünnermann, A.

Vallée, R.

van Eijkelenborg, M. A.

M. A. van Eijkelenborg, W. Padden, and J. A. Besley, “Mechanically induced long-period gratings in microstructured polymer fibre,” Opt. Commun. 236(1–3), 75–78 (2004).
[Crossref]

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

Wang, T.

Watanabe, M.

Watanabe, W.

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, “Ultrafast processes for bulk modification of transparent materials,” MRS Bull. 31(8), 620–625 (2006).
[Crossref]

Wen, J.

Williams, R. J.

Withford, M. J.

Wolf, A.

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” IEEE J. Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

Young, W.

Zhang, C.

Zhang, L.

Zhao, Y.

Appl. Opt. (3)

Electron. Lett. (1)

G. Humbert, A. Malki, S. Fevrier, P. Roy, and D. Pagnoux, “Electric arc-induced long-period gratings in Ge-free air-silica microstructure fibres,” Electron. Lett. 39(4), 349–350 (2003).
[Crossref]

IEEE J. Quantum Electron. (1)

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” IEEE J. Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (1)

V. Grubsky and J. Feinberg, “Fabrication of Axially Symmetric Long-Period Gratings with a Carbon Dioxide Laser,” IEEE Photonics Technol. Lett. 18(21), 2296–2298 (2006).
[Crossref]

J. Lightwave Technol. (3)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14(1), 58–65 (1996).
[Crossref]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997).
[Crossref]

E. Anemogiannis, E. N. Glytsis, and T. K. Gaylord, “Transmission characteristics of long-period fiber gratings having arbitrary azimuthal/radial refractive index variations,” J. Lightwave Technol. 21(1), 218–227 (2003).
[Crossref]

J. Opt. Soc. Am. (1)

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

Meas. Sci. Technol. (1)

S. W. James and R. P. Tatam, “Optical fibre long-period grating sensors: characteristics and application,” Meas. Sci. Technol. 14(5), R49–R61 (2003).
[Crossref]

MRS Bull. (1)

K. Itoh, W. Watanabe, S. Nolte, and C. B. Schaffer, “Ultrafast processes for bulk modification of transparent materials,” MRS Bull. 31(8), 620–625 (2006).
[Crossref]

Opt. Commun. (1)

M. A. van Eijkelenborg, W. Padden, and J. A. Besley, “Mechanically induced long-period gratings in microstructured polymer fibre,” Opt. Commun. 236(1–3), 75–78 (2004).
[Crossref]

Opt. Express (5)

Opt. Lett. (7)

Top. Appl. Phys. (1)

H. Kogelnik, “Theory of dielectric waveguides,” Top. Appl. Phys. 7, 15–83 (1979).

Other (2)

B. E. A. Saleh, M. C. Teich, and J. W. Goodman, Fundamentals of photonics, pp. 272–309 (Wiley, 1991).

M. Heck, V. Bock, R. G. Krämer, D. Richter, T. A. Goebel, C. Matzdorf, A. Liem, T. Schreiber, A. Tünnermann, and S. Nolte, “Mitigation of stimulated Raman scattering in high power fiber lasers using transmission gratings,”, Proc. SPIE LASE 10512–53, (2018).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 (a) Evolution of coupling coefficients κ l,m for an increasing displacement dx. Displayed is the behavior for different azimuthal indices l. In (b) a schematic sketch of the induced modification displaced to the core/cladding boundary is shown. The red star is indicating the center of the induced modification. (c) Shows the corresponding calculated spectrum for different displacements dx. The transmittance is flipped for better overview. Some resonances are labeled with their corresponding higher order modes.
Fig. 2
Fig. 2 (a) Schematic sketch of the induced modifications for different extents with displacement dx. The black star indicates the core center while the yellow star indicates the center of RI change. In (b) the calculated coupling coefficients are shown for l = 0 and 2 ≤ m ≤ 20 modes (neglecting self-coupling) corresponding to the RI shapes from (a) with 100% (blue dots), 75% (green dots) and 50% (red dots) extent. In (c) and (d) the calculated coupling coefficients for l = 1, 2 and 1 ≤ m ≤ 20 modes are displayed.
Fig. 3
Fig. 3 Schematic of the axial LPFG line by line inscription setup. The fiber is translated in z-direction at a constant speed while the microscope objective is kept fixed.
Fig. 4
Fig. 4 (a) Measured RI cross section showing a homogeneous modified core (laser incident from top). (b) Shows the corresponding measured (green line) and simulated (black dashed line) spectrum.
Fig. 5
Fig. 5 (a) Measured RI cross section showing a centered modification in the fiber core (laser incidence from top). (b) Shows the corresponding measured (green line) and simulated (black dashed line) spectrum.
Fig. 6
Fig. 6 (a) Measured RI cross section showing a decentered modification in the fiber core (laser incidence from top). (b) Shows the corresponding measured (green line) and simulated (black dashed line) spectrum.

Equations (4)

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β 0,1 β l,m 2π Λ =0, 
λ LPFG = ( n 0,1 n l,m )Λ.
β l,m ( λ )  ( n 2 2 ( 2π λ ) 2 A l,m ) 1/2 with A l,m =  ( l+2m+ 1 2 ) 2 π 2 4 a 2 2 ,
κ l,m = ω 4 0 2π dϕ 0 dr rΔε( r,ϕ ) E 0,1 T E l,m T* .

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