Abstract

The combined effect of chromatic dispersion and conical diffraction (i.e., off-plane diffraction) in femtosecond laser inscription of fiber Bragg gratings using the phase mask technique is characterized by measuring the light intensity distribution after the phase mask. As the distance from the mask and the observation point grows, chromatic dispersion and conical diffraction introduced by the mask gradually decrease the peak intensity inside the line-shaped focal volume of the cylindrical lens that is used to focus the femtosecond pulses inside the fiber. We also show that at a certain distance from the mask spherical aberration introduced by the plane-parallel mask substrate is cancelled out by conical diffraction and, at a different distance, chromatic aberration of the cylindrical lens is cancelled out by chromatic dispersion of the mask. These two independent cancellation effects lead to sharpening of the line-shaped focus and the consequent growth of peak light intensity inside it. The above phenomena become especially pronounced for tightly focused femtosecond laser beams and small-pitch phase masks, which, in turn, allows one to choose experimental conditions to inscribe Bragg gratings in polymer-coated non-sensitized 50 µm fibers.

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

Full Article  |  PDF Article
OSA Recommended Articles
Through-the-coating writing of tilted fiber Bragg gratings with the phase mask technique

Nurmemet Abdukerim, Dan Grobnic, Cyril Hnatovsky, and Stephen J. Mihailov
Opt. Express 27(26) 38259-38269 (2019)

IR femtosecond pulsed laser-based fiber Bragg grating inscription in a photonic crystal fiber using a phase mask and a short focal length lens

Tigran Baghdasaryan, Thomas Geernart, Adriana Morana, Emmanuel Marin, Sylvain Girard, Mariusz Makara, Paweł Mergo, Hugo Thienpont, and Francis Berghmans
Opt. Express 26(11) 14741-14751 (2018)

High-temperature stable π-phase-shifted fiber Bragg gratings inscribed using infrared femtosecond pulses and a phase mask

Cyril Hnatovsky, Dan Grobnic, and Stephen J. Mihailov
Opt. Express 26(18) 23550-23564 (2018)

References

  • View by:
  • |
  • |
  • |

  1. S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser microfabrication of periodic structures using a microlens array,” Appl. Phys. A 80(4), 683–685 (2005).
    [Crossref]
  2. J.-I. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
    [Crossref]
  3. P. S. Salter and M. J. Booth, “Addressable microlens array for parallel laser microfabrication,” Opt. Lett. 36(12), 2302–2304 (2011).
    [Crossref]
  4. Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81(22), 4239–4241 (2002).
    [Crossref]
  5. Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
    [Crossref]
  6. S. Hasegawa, Y. Hayasaki, and N. Nishida, “Holographic femtosecond laser processing with multiplexed phase Fresnel lenses,” Opt. Lett. 31(11), 1705–1707 (2006).
    [Crossref]
  7. M. Yamaji, H. Kawashima, J. Suzuki, and S. Tanaka, “Three dimensional micromachining inside a transparent material by single pulse femtosecond laser through a hologram,” Appl. Phys. Lett. 93(4), 041116 (2008).
    [Crossref]
  8. Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
    [Crossref]
  9. Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
    [Crossref]
  10. K. Obata, J. Kuch, U. Hinze, and B. N. Chichkov, “Multi-focus two-photon polymerization technique based on individually controlled phase modulation,” Opt. Express 18(16), 17193–17200 (2010).
    [Crossref]
  11. J. Amako, K. Nagasaka, and N. Kazuhiro, “Chromatic-distortion compensation in splitting and focusing of femtosecond pulses by use of a pair of diffractive optical elements,” Opt. Lett. 27(11), 969–971 (2002).
    [Crossref]
  12. G. Li, C. Zhou, and E. Dai, “Splitting of femtosecond laser pulses by using a Dammann grating and compensating grating,” J. Opt. Soc. Am. A 22(4), 767–772 (2005).
    [Crossref]
  13. G. Mínguez-Vega, J. Lancis, J. Caraquitena, V. Torres-Company, and P. Andrés, “High spatiotemporal resolution in multifocal processing with femtosecond laser pulses,” Opt. Lett. 31(17), 2631–2633 (2006).
    [Crossref]
  14. G. Mínguez-Vega, E. Tajahuerce, M. Fernádez-Alonso, V. Climent, J. Lancis, J. Caraquitena, and P. Andres, “Dispersion-compensated beam-splitting of femtosecond light pulses: wave optics analysis,” Opt. Express 15(2), 278–288 (2007).
    [Crossref]
  15. A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express 18(20), 21090–21099 (2010).
    [Crossref]
  16. S. Torres-Peiro, J. Gonzalez-Ausejo, O. Mendoza-Yero, G. Minguez-Vega, P. Angres, and J. Lancis, “Parallel laser micromachining based on diffractive optical elements with dispersion compensated femtosecond pulses,” Opt. Express 21(26), 31830–31835 (2013).
    [Crossref]
  17. S. Hasegawa and Y. Hayasaki, “Dynamic control of spatial wavelength dispersion in holographic femtosecond laser processing,” Opt. Lett. 39(3), 478–481 (2014).
    [Crossref]
  18. S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, “Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation,” Opt. Lett. 28(12), 995–997 (2003).
    [Crossref]
  19. C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, “Inscription of high contrast volume Bragg gratings in fused silica with femtosecond laser pulses,” Appl. Phys. A 102(1), 35–38 (2011).
    [Crossref]
  20. D. Richter, C. Voigtländer, R. G. Krämer, J. U. Thomas, A. Tünnermann, and S. Nolte, “Discrete nonplanar reflections from an ultrashort pulse written volume Bragg grating,” Opt. Lett. 40(12), 2766–2769 (2015).
    [Crossref]
  21. J. C. Wyant and K. Creath, Basic Wavefront Aberration Theory for Optical Metrology. In: R. R. Shannon and J. C. Wyant (eds.), Applied Optics and Optical Engineering, Volume XI. (Academic Press, New York, 1992).
  22. P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12(2), 325–332 (1995).
    [Crossref]
  23. P. Török and P. Varga, “Electromagnetic diffraction of light focused through a stratified medium,” Appl. Opt. 36(11), 2305–2312 (1997).
    [Crossref]
  24. A. Martinez, I. Y. Khrushchev, and I. Bennion, “Direct inscription of Bragg gratings in coated fibers by an infrared femtosecond laser,” Opt. Lett. 31(11), 1603–1605 (2006).
    [Crossref]
  25. S. J. Mihailov, D. Grobnic, and C. W. Smelser, “Efficient grating writing through fibre coating with femtosecond IR radiation and phase mask,” Electron. Lett. 43(8), 442–443 (2007).
    [Crossref]
  26. J. Habel, T. Boilard, J.-S. Frenière, F. Trépanier, and M. Bernier, “Femtosecond FBG written through the coating for sensing applications,” Sensors 17(11), 2519 (2017).
    [Crossref]
  27. D. Grobnic, C. Hnatovsky, and S. J. Mihailov, “Thermally stable type II FBGs written through polyimide coatings of silica-based optical fiber,” IEEE Photonics Technol. Lett. 29(21), 1780–1783 (2017).
    [Crossref]
  28. C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “Through-the-coating femtosecond laser inscription of very short fiber Bragg gratings for acoustic and high temperature sensing applications,” Opt. Express 25(21), 25435–25446 (2017).
    [Crossref]
  29. G. W. Stroke, Diffraction Gratings. In: S. Flügge (eds) Optische Instrumente/Optical Instruments. Handbuch der Physik/Encyclopedia of Physics, Volume 5/29. (Springer, Berlin, Heidelberg1967).
  30. C. Palmer, Diffraction Grating Handbook, 4th ed. (Richardson Grating Laboratory, Rochester, N.Y., 2000).
  31. J. E. Harvey and C. L. Vernold, “Description of diffraction grating behavior in direction cosine space,” Appl. Opt. 37(34), 8158–8159 (1998).
    [Crossref]
  32. J. E. Harvey, D. Bogunovic, and A. Krywonos, “Aberrations of diffracted wave fields: distortion,” Appl. Opt. 42(7), 1167–1174 (2003).
    [Crossref]
  33. O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986).
    [Crossref]
  34. Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
    [Crossref]
  35. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, “How to make femtosecond pulses overlap,” Opt. Lett. 23(17), 1378–1380 (1998).
    [Crossref]
  36. J. D. Mills, C. W. J. Hillman, B. H. Blott, and W. S. Brocklesby, “Imaging of free-space interference patterns used to manufacture fiber bragg gratings,” Appl. Opt. 39(33), 6128–6135 (2000).
    [Crossref]
  37. C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding, and X. Dai, “Multiple-beam interference patterns in optical fiber generated with ultrafast pulses and a phase mask,” Opt. Lett. 29(13), 1458–1460 (2004).
    [Crossref]
  38. C. W. Smelser, D. Grobnic, and S. J. Mihailov, “Generation of pure two-beam interference grating structures in an optical fiber with a femtosecond infrared source and a phase mask,” Opt. Lett. 29(15), 1730–1732 (2004).
    [Crossref]
  39. C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “Nonlinear photoluminescence imaging applied to femtosecond laser manufacturing of fiber Bragg gratings,” Opt. Express 25(13), 14247–14259 (2017).
    [Crossref]
  40. C. Dorrer, “Comment on: Novel method for ultrashort laser pulse-width measurement based on the self-diffraction effect,” Opt. Express 11(1), 79–80 (2003).
    [Crossref]
  41. I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308–437 (2009).
    [Crossref]
  42. H. Zhao, Z. Wang, G. Jia, Y. Zhang, and Z. Xu, “Chromatic aberrations correction for imaging spectrometer based on acousto-optic tunable filter with two transducers,” Opt. Express 25(20), 23809–23825 (2017).
    [Crossref]
  43. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 6th ed. (Pergamon, Oxford, UK, 1980).
  44. S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14(7), 1482–1490 (1997).
    [Crossref]
  45. S. H. Wiersma, T. D. Visser, and P. Török, “Annular focusing through a dielectric interface: scanning and confining the intensity,” Pure Appl. Opt. 7(5), 1237–1248 (1998).
    [Crossref]
  46. C. Braig, L. Fritzsch, T. Käsebier, E.-B. Kley, C. Laubis, Y. Liu, F. Scholze, and A. Tünnermann, “An EUV beamsplitter based on conical grazing incidence diffraction,” Opt. Express 20(2), 1825–1838 (2012).
    [Crossref]
  47. C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “High-temperature stable π-phase-shifted fiber Bragg gratings inscribed using infrared femtosecond pulses and a phase mask,” Opt. Express 26(18), 23550–23564 (2018).
    [Crossref]
  48. R. K Lüneburg, Mathematical Theory of Optics (Cambridge University Press, 1964).
  49. J. E. Greivenkamp, Field Guide to Geometric Optics (SPIE Press, 2004).
  50. A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68(12), 4309–4341 (1997).
    [Crossref]
  51. C. Smelser, S. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13(14), 5377–5386 (2005).
    [Crossref]
  52. C. Hnatovsky, D. Grobnic, D. Coulas, M. Barnes, and S. J. Mihailov, “Self-organized nanostructure formation during femtosecond-laser inscription of fiber Bragg gratings,” Opt. Lett. 42(3), 399–402 (2017).
    [Crossref]
  53. M. Kempe, U. Stamm, B. Wilhelmi, and W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 9(7), 1158–1165 (1992).
    [Crossref]
  54. M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. B 48(6), 4721–4729 (1993).
    [Crossref]
  55. Z. L. Horváth, Z. Benkő, A. P. Kovács, H. A. Hazim, and Z. Bor, “Propagation of femtosecond pulses through lenses, gratings, and slits,” Opt. Eng. 32(10), 2491–2500 (1993).
    [Crossref]
  56. Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94(4), 249–258 (1992).
    [Crossref]
  57. W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993).
    [Crossref]
  58. C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Characterization of Fourier components in type I infrared ultrafast laser induced fiber Bragg gratings,” Opt. Lett. 32(11), 1453–1455 (2007).
    [Crossref]

2018 (1)

2017 (6)

2015 (1)

2014 (1)

2013 (1)

2012 (1)

2011 (2)

P. S. Salter and M. J. Booth, “Addressable microlens array for parallel laser microfabrication,” Opt. Lett. 36(12), 2302–2304 (2011).
[Crossref]

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, “Inscription of high contrast volume Bragg gratings in fused silica with femtosecond laser pulses,” Appl. Phys. A 102(1), 35–38 (2011).
[Crossref]

2010 (2)

2009 (2)

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308–437 (2009).
[Crossref]

2008 (2)

M. Yamaji, H. Kawashima, J. Suzuki, and S. Tanaka, “Three dimensional micromachining inside a transparent material by single pulse femtosecond laser through a hologram,” Appl. Phys. Lett. 93(4), 041116 (2008).
[Crossref]

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

2007 (3)

2006 (3)

2005 (5)

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser microfabrication of periodic structures using a microlens array,” Appl. Phys. A 80(4), 683–685 (2005).
[Crossref]

J.-I. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

G. Li, C. Zhou, and E. Dai, “Splitting of femtosecond laser pulses by using a Dammann grating and compensating grating,” J. Opt. Soc. Am. A 22(4), 767–772 (2005).
[Crossref]

C. Smelser, S. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13(14), 5377–5386 (2005).
[Crossref]

2004 (2)

2003 (3)

2002 (2)

J. Amako, K. Nagasaka, and N. Kazuhiro, “Chromatic-distortion compensation in splitting and focusing of femtosecond pulses by use of a pair of diffractive optical elements,” Opt. Lett. 27(11), 969–971 (2002).
[Crossref]

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81(22), 4239–4241 (2002).
[Crossref]

2000 (1)

1998 (3)

1997 (3)

1995 (1)

1993 (4)

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[Crossref]

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. B 48(6), 4721–4729 (1993).
[Crossref]

Z. L. Horváth, Z. Benkő, A. P. Kovács, H. A. Hazim, and Z. Bor, “Propagation of femtosecond pulses through lenses, gratings, and slits,” Opt. Eng. 32(10), 2491–2500 (1993).
[Crossref]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993).
[Crossref]

1992 (2)

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94(4), 249–258 (1992).
[Crossref]

M. Kempe, U. Stamm, B. Wilhelmi, and W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 9(7), 1158–1165 (1992).
[Crossref]

1986 (1)

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986).
[Crossref]

Adachi, Y.

J.-I. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Amako, J.

Andres, P.

Andrés, P.

Angres, P.

Barnes, M.

Bayon, J. F.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993).
[Crossref]

Benko, Z.

Z. L. Horváth, Z. Benkő, A. P. Kovács, H. A. Hazim, and Z. Bor, “Propagation of femtosecond pulses through lenses, gratings, and slits,” Opt. Eng. 32(10), 2491–2500 (1993).
[Crossref]

Bennion, I.

Bernage, P.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993).
[Crossref]

Bernier, M.

J. Habel, T. Boilard, J.-S. Frenière, F. Trépanier, and M. Bernier, “Femtosecond FBG written through the coating for sensing applications,” Sensors 17(11), 2519 (2017).
[Crossref]

Blott, B. H.

Bogunovic, D.

Boilard, T.

J. Habel, T. Boilard, J.-S. Frenière, F. Trépanier, and M. Bernier, “Femtosecond FBG written through the coating for sensing applications,” Sensors 17(11), 2519 (2017).
[Crossref]

Booker, G. R.

Booth, M. J.

Bor, Z.

Z. L. Horváth, Z. Benkő, A. P. Kovács, H. A. Hazim, and Z. Bor, “Propagation of femtosecond pulses through lenses, gratings, and slits,” Opt. Eng. 32(10), 2491–2500 (1993).
[Crossref]

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[Crossref]

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94(4), 249–258 (1992).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 6th ed. (Pergamon, Oxford, UK, 1980).

Braig, C.

Brocklesby, W. S.

Caraquitena, J.

Chichkov, B. N.

Climent, V.

Coulas, D.

Creath, K.

J. C. Wyant and K. Creath, Basic Wavefront Aberration Theory for Optical Metrology. In: R. R. Shannon and J. C. Wyant (eds.), Applied Optics and Optical Engineering, Volume XI. (Academic Press, New York, 1992).

Crimmins, T. F.

Dai, E.

Dai, X.

Dearden, G.

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Ding, H.

Dorrer, C.

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308–437 (2009).
[Crossref]

C. Dorrer, “Comment on: Novel method for ultrashort laser pulse-width measurement based on the self-diffraction effect,” Opt. Express 11(1), 79–80 (2003).
[Crossref]

Douay, M.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993).
[Crossref]

Edwardson, S.

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

Edwardson, S. P.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Fearon, E.

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

Fernádez-Alonso, M.

Frenière, J.-S.

J. Habel, T. Boilard, J.-S. Frenière, F. Trépanier, and M. Bernier, “Femtosecond FBG written through the coating for sensing applications,” Sensors 17(11), 2519 (2017).
[Crossref]

Fritzsch, L.

Georges, T.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993).
[Crossref]

Gonzalez-Ausejo, J.

Greivenkamp, J. E.

J. E. Greivenkamp, Field Guide to Geometric Optics (SPIE Press, 2004).

Grobnic, D.

C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “High-temperature stable π-phase-shifted fiber Bragg gratings inscribed using infrared femtosecond pulses and a phase mask,” Opt. Express 26(18), 23550–23564 (2018).
[Crossref]

C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “Nonlinear photoluminescence imaging applied to femtosecond laser manufacturing of fiber Bragg gratings,” Opt. Express 25(13), 14247–14259 (2017).
[Crossref]

C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “Through-the-coating femtosecond laser inscription of very short fiber Bragg gratings for acoustic and high temperature sensing applications,” Opt. Express 25(21), 25435–25446 (2017).
[Crossref]

C. Hnatovsky, D. Grobnic, D. Coulas, M. Barnes, and S. J. Mihailov, “Self-organized nanostructure formation during femtosecond-laser inscription of fiber Bragg gratings,” Opt. Lett. 42(3), 399–402 (2017).
[Crossref]

D. Grobnic, C. Hnatovsky, and S. J. Mihailov, “Thermally stable type II FBGs written through polyimide coatings of silica-based optical fiber,” IEEE Photonics Technol. Lett. 29(21), 1780–1783 (2017).
[Crossref]

S. J. Mihailov, D. Grobnic, and C. W. Smelser, “Efficient grating writing through fibre coating with femtosecond IR radiation and phase mask,” Electron. Lett. 43(8), 442–443 (2007).
[Crossref]

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Characterization of Fourier components in type I infrared ultrafast laser induced fiber Bragg gratings,” Opt. Lett. 32(11), 1453–1455 (2007).
[Crossref]

C. Smelser, S. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13(14), 5377–5386 (2005).
[Crossref]

C. W. Smelser, D. Grobnic, and S. J. Mihailov, “Generation of pure two-beam interference grating structures in an optical fiber with a femtosecond infrared source and a phase mask,” Opt. Lett. 29(15), 1730–1732 (2004).
[Crossref]

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding, and X. Dai, “Multiple-beam interference patterns in optical fiber generated with ultrafast pulses and a phase mask,” Opt. Lett. 29(13), 1458–1460 (2004).
[Crossref]

S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, “Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation,” Opt. Lett. 28(12), 995–997 (2003).
[Crossref]

Habel, J.

J. Habel, T. Boilard, J.-S. Frenière, F. Trépanier, and M. Bernier, “Femtosecond FBG written through the coating for sensing applications,” Sensors 17(11), 2519 (2017).
[Crossref]

Harvey, J. E.

Hasegawa, S.

Hayasaki, Y.

Hazim, H. A.

Z. L. Horváth, Z. Benkő, A. P. Kovács, H. A. Hazim, and Z. Bor, “Propagation of femtosecond pulses through lenses, gratings, and slits,” Opt. Eng. 32(10), 2491–2500 (1993).
[Crossref]

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[Crossref]

Henderson, G.

Hilbert, M.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[Crossref]

Hillman, C. W. J.

Hinze, U.

Hnatovsky, C.

Horváth, Z. L.

Z. L. Horváth, Z. Benkő, A. P. Kovács, H. A. Hazim, and Z. Bor, “Propagation of femtosecond pulses through lenses, gratings, and slits,” Opt. Eng. 32(10), 2491–2500 (1993).
[Crossref]

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94(4), 249–258 (1992).
[Crossref]

Jesacher, A.

Jia, G.

Juodkazis, S.

S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser microfabrication of periodic structures using a microlens array,” Appl. Phys. A 80(4), 683–685 (2005).
[Crossref]

Käsebier, T.

Kato, J.-I.

J.-I. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Kawashima, H.

M. Yamaji, H. Kawashima, J. Suzuki, and S. Tanaka, “Three dimensional micromachining inside a transparent material by single pulse femtosecond laser through a hologram,” Appl. Phys. Lett. 93(4), 041116 (2008).
[Crossref]

Kawata, S.

J.-I. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Kazuhiro, N.

Kempe, M.

Khrushchev, I. Y.

Kley, E.-B.

Kovács, A. P.

Z. L. Horváth, Z. Benkő, A. P. Kovács, H. A. Hazim, and Z. Bor, “Propagation of femtosecond pulses through lenses, gratings, and slits,” Opt. Eng. 32(10), 2491–2500 (1993).
[Crossref]

Krämer, R. G.

Krywonos, A.

Kuang, Z.

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Kuch, J.

Laczik, Z.

Lancis, J.

Laubis, C.

Leach, J.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Li, G.

Liu, D.

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

Liu, Y.

Lu, P.

Lüneburg, R. K

R. K Lüneburg, Mathematical Theory of Optics (Cambridge University Press, 1964).

Maeda, M.

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81(22), 4239–4241 (2002).
[Crossref]

Martinez, A.

Martinez, O. E.

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986).
[Crossref]

Matsuo, S.

S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser microfabrication of periodic structures using a microlens array,” Appl. Phys. A 80(4), 683–685 (2005).
[Crossref]

Maznev, A. A.

Mendoza-Yero, O.

Mihailov, S.

Mihailov, S. J.

C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “High-temperature stable π-phase-shifted fiber Bragg gratings inscribed using infrared femtosecond pulses and a phase mask,” Opt. Express 26(18), 23550–23564 (2018).
[Crossref]

C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “Nonlinear photoluminescence imaging applied to femtosecond laser manufacturing of fiber Bragg gratings,” Opt. Express 25(13), 14247–14259 (2017).
[Crossref]

D. Grobnic, C. Hnatovsky, and S. J. Mihailov, “Thermally stable type II FBGs written through polyimide coatings of silica-based optical fiber,” IEEE Photonics Technol. Lett. 29(21), 1780–1783 (2017).
[Crossref]

C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “Through-the-coating femtosecond laser inscription of very short fiber Bragg gratings for acoustic and high temperature sensing applications,” Opt. Express 25(21), 25435–25446 (2017).
[Crossref]

C. Hnatovsky, D. Grobnic, D. Coulas, M. Barnes, and S. J. Mihailov, “Self-organized nanostructure formation during femtosecond-laser inscription of fiber Bragg gratings,” Opt. Lett. 42(3), 399–402 (2017).
[Crossref]

S. J. Mihailov, D. Grobnic, and C. W. Smelser, “Efficient grating writing through fibre coating with femtosecond IR radiation and phase mask,” Electron. Lett. 43(8), 442–443 (2007).
[Crossref]

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Characterization of Fourier components in type I infrared ultrafast laser induced fiber Bragg gratings,” Opt. Lett. 32(11), 1453–1455 (2007).
[Crossref]

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding, and X. Dai, “Multiple-beam interference patterns in optical fiber generated with ultrafast pulses and a phase mask,” Opt. Lett. 29(13), 1458–1460 (2004).
[Crossref]

C. W. Smelser, D. Grobnic, and S. J. Mihailov, “Generation of pure two-beam interference grating structures in an optical fiber with a femtosecond infrared source and a phase mask,” Opt. Lett. 29(15), 1730–1732 (2004).
[Crossref]

S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, “Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation,” Opt. Lett. 28(12), 995–997 (2003).
[Crossref]

Mills, J. D.

Minguez-Vega, G.

Mínguez-Vega, G.

Misawa, H.

S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser microfabrication of periodic structures using a microlens array,” Appl. Phys. A 80(4), 683–685 (2005).
[Crossref]

Nagasaka, K.

Nakata, Y.

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81(22), 4239–4241 (2002).
[Crossref]

Nelson, K. A.

Niay, P.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993).
[Crossref]

Nishida, N.

S. Hasegawa, Y. Hayasaki, and N. Nishida, “Holographic femtosecond laser processing with multiplexed phase Fresnel lenses,” Opt. Lett. 31(11), 1705–1707 (2006).
[Crossref]

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

Nolte, S.

D. Richter, C. Voigtländer, R. G. Krämer, J. U. Thomas, A. Tünnermann, and S. Nolte, “Discrete nonplanar reflections from an ultrashort pulse written volume Bragg grating,” Opt. Lett. 40(12), 2766–2769 (2015).
[Crossref]

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, “Inscription of high contrast volume Bragg gratings in fused silica with femtosecond laser pulses,” Appl. Phys. A 102(1), 35–38 (2011).
[Crossref]

Obata, K.

Okada, T.

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81(22), 4239–4241 (2002).
[Crossref]

Othonos, A.

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68(12), 4309–4341 (1997).
[Crossref]

Padgett, M.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Palmer, C.

C. Palmer, Diffraction Grating Handbook, 4th ed. (Richardson Grating Laboratory, Rochester, N.Y., 2000).

Perrie, W.

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Racz, B.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[Crossref]

Richter, D.

D. Richter, C. Voigtländer, R. G. Krämer, J. U. Thomas, A. Tünnermann, and S. Nolte, “Discrete nonplanar reflections from an ultrashort pulse written volume Bragg grating,” Opt. Lett. 40(12), 2766–2769 (2015).
[Crossref]

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, “Inscription of high contrast volume Bragg gratings in fused silica with femtosecond laser pulses,” Appl. Phys. A 102(1), 35–38 (2011).
[Crossref]

Rudolph, W.

Salter, P. S.

Scholze, F.

Sharp, M.

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Smelser, C.

Smelser, C. W.

Stamm, U.

Stroke, G. W.

G. W. Stroke, Diffraction Gratings. In: S. Flügge (eds) Optische Instrumente/Optical Instruments. Handbuch der Physik/Encyclopedia of Physics, Volume 5/29. (Springer, Berlin, Heidelberg1967).

Sugimoto, T.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

Sun, H.-B.

J.-I. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Suzuki, J.

M. Yamaji, H. Kawashima, J. Suzuki, and S. Tanaka, “Three dimensional micromachining inside a transparent material by single pulse femtosecond laser through a hologram,” Appl. Phys. Lett. 93(4), 041116 (2008).
[Crossref]

Szabo, G.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[Crossref]

Tajahuerce, E.

Takeyasu, N.

J.-I. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Takita, A.

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

Tanaka, S.

M. Yamaji, H. Kawashima, J. Suzuki, and S. Tanaka, “Three dimensional micromachining inside a transparent material by single pulse femtosecond laser through a hologram,” Appl. Phys. Lett. 93(4), 041116 (2008).
[Crossref]

Thomas, J.

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, “Inscription of high contrast volume Bragg gratings in fused silica with femtosecond laser pulses,” Appl. Phys. A 102(1), 35–38 (2011).
[Crossref]

Thomas, J. U.

Török, P.

Torres-Company, V.

Torres-Peiro, S.

Trépanier, F.

J. Habel, T. Boilard, J.-S. Frenière, F. Trépanier, and M. Bernier, “Femtosecond FBG written through the coating for sensing applications,” Sensors 17(11), 2519 (2017).
[Crossref]

Tünnermann, A.

Unruh, J.

Varga, P.

Vernold, C. L.

Visser, T. D.

S. H. Wiersma, T. D. Visser, and P. Török, “Annular focusing through a dielectric interface: scanning and confining the intensity,” Pure Appl. Opt. 7(5), 1237–1248 (1998).
[Crossref]

S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14(7), 1482–1490 (1997).
[Crossref]

Voigtländer, C.

D. Richter, C. Voigtländer, R. G. Krämer, J. U. Thomas, A. Tünnermann, and S. Nolte, “Discrete nonplanar reflections from an ultrashort pulse written volume Bragg grating,” Opt. Lett. 40(12), 2766–2769 (2015).
[Crossref]

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, “Inscription of high contrast volume Bragg gratings in fused silica with femtosecond laser pulses,” Appl. Phys. A 102(1), 35–38 (2011).
[Crossref]

Walker, R. B.

Walmsley, I. A.

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308–437 (2009).
[Crossref]

Wang, Z.

Watkins, K.

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

Watkins, K. G.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Wiersma, S. H.

S. H. Wiersma, T. D. Visser, and P. Török, “Annular focusing through a dielectric interface: scanning and confining the intensity,” Pure Appl. Opt. 7(5), 1237–1248 (1998).
[Crossref]

S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14(7), 1482–1490 (1997).
[Crossref]

Wilhelmi, B.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 6th ed. (Pergamon, Oxford, UK, 1980).

Wyant, J. C.

J. C. Wyant and K. Creath, Basic Wavefront Aberration Theory for Optical Metrology. In: R. R. Shannon and J. C. Wyant (eds.), Applied Optics and Optical Engineering, Volume XI. (Academic Press, New York, 1992).

Xie, W. X.

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993).
[Crossref]

Xu, Z.

Yamaji, M.

M. Yamaji, H. Kawashima, J. Suzuki, and S. Tanaka, “Three dimensional micromachining inside a transparent material by single pulse femtosecond laser through a hologram,” Appl. Phys. Lett. 93(4), 041116 (2008).
[Crossref]

Zhang, Y.

Zhao, H.

Zhou, C.

Adv. Opt. Photonics (1)

I. A. Walmsley and C. Dorrer, “Characterization of ultrashort electromagnetic pulses,” Adv. Opt. Photonics 1(2), 308–437 (2009).
[Crossref]

Appl. Opt. (4)

Appl. Phys. A (2)

S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser microfabrication of periodic structures using a microlens array,” Appl. Phys. A 80(4), 683–685 (2005).
[Crossref]

C. Voigtländer, D. Richter, J. Thomas, A. Tünnermann, and S. Nolte, “Inscription of high contrast volume Bragg gratings in fused silica with femtosecond laser pulses,” Appl. Phys. A 102(1), 35–38 (2011).
[Crossref]

Appl. Phys. Lett. (4)

J.-I. Kato, N. Takeyasu, Y. Adachi, H.-B. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86(4), 044102 (2005).
[Crossref]

Y. Nakata, T. Okada, and M. Maeda, “Fabrication of dot matrix, comb, and nanowire structures using laser ablation by interfered femtosecond laser beams,” Appl. Phys. Lett. 81(22), 4239–4241 (2002).
[Crossref]

Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005).
[Crossref]

M. Yamaji, H. Kawashima, J. Suzuki, and S. Tanaka, “Three dimensional micromachining inside a transparent material by single pulse femtosecond laser through a hologram,” Appl. Phys. Lett. 93(4), 041116 (2008).
[Crossref]

Appl. Surf. Sci. (2)

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Z. Kuang, D. Liu, W. Perrie, S. Edwardson, M. Sharp, E. Fearon, G. Dearden, and K. Watkins, “Fast parallel diffractive multi-beam femtosecond laser surface micro-structuring,” Appl. Surf. Sci. 255(13-14), 6582–6588 (2009).
[Crossref]

Electron. Lett. (1)

S. J. Mihailov, D. Grobnic, and C. W. Smelser, “Efficient grating writing through fibre coating with femtosecond IR radiation and phase mask,” Electron. Lett. 43(8), 442–443 (2007).
[Crossref]

IEEE Photonics Technol. Lett. (1)

D. Grobnic, C. Hnatovsky, and S. J. Mihailov, “Thermally stable type II FBGs written through polyimide coatings of silica-based optical fiber,” IEEE Photonics Technol. Lett. 29(21), 1780–1783 (2017).
[Crossref]

J. Opt. Soc. Am. A (3)

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

Opt. Commun. (3)

Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94(4), 249–258 (1992).
[Crossref]

W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993).
[Crossref]

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986).
[Crossref]

Opt. Eng. (2)

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[Crossref]

Z. L. Horváth, Z. Benkő, A. P. Kovács, H. A. Hazim, and Z. Bor, “Propagation of femtosecond pulses through lenses, gratings, and slits,” Opt. Eng. 32(10), 2491–2500 (1993).
[Crossref]

Opt. Express (11)

G. Mínguez-Vega, E. Tajahuerce, M. Fernádez-Alonso, V. Climent, J. Lancis, J. Caraquitena, and P. Andres, “Dispersion-compensated beam-splitting of femtosecond light pulses: wave optics analysis,” Opt. Express 15(2), 278–288 (2007).
[Crossref]

C. Braig, L. Fritzsch, T. Käsebier, E.-B. Kley, C. Laubis, Y. Liu, F. Scholze, and A. Tünnermann, “An EUV beamsplitter based on conical grazing incidence diffraction,” Opt. Express 20(2), 1825–1838 (2012).
[Crossref]

C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “Nonlinear photoluminescence imaging applied to femtosecond laser manufacturing of fiber Bragg gratings,” Opt. Express 25(13), 14247–14259 (2017).
[Crossref]

C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “High-temperature stable π-phase-shifted fiber Bragg gratings inscribed using infrared femtosecond pulses and a phase mask,” Opt. Express 26(18), 23550–23564 (2018).
[Crossref]

C. Smelser, S. Mihailov, and D. Grobnic, “Formation of Type I-IR and Type II-IR gratings with an ultrafast IR laser and a phase mask,” Opt. Express 13(14), 5377–5386 (2005).
[Crossref]

A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express 18(20), 21090–21099 (2010).
[Crossref]

K. Obata, J. Kuch, U. Hinze, and B. N. Chichkov, “Multi-focus two-photon polymerization technique based on individually controlled phase modulation,” Opt. Express 18(16), 17193–17200 (2010).
[Crossref]

C. Hnatovsky, D. Grobnic, and S. J. Mihailov, “Through-the-coating femtosecond laser inscription of very short fiber Bragg gratings for acoustic and high temperature sensing applications,” Opt. Express 25(21), 25435–25446 (2017).
[Crossref]

C. Dorrer, “Comment on: Novel method for ultrashort laser pulse-width measurement based on the self-diffraction effect,” Opt. Express 11(1), 79–80 (2003).
[Crossref]

S. Torres-Peiro, J. Gonzalez-Ausejo, O. Mendoza-Yero, G. Minguez-Vega, P. Angres, and J. Lancis, “Parallel laser micromachining based on diffractive optical elements with dispersion compensated femtosecond pulses,” Opt. Express 21(26), 31830–31835 (2013).
[Crossref]

H. Zhao, Z. Wang, G. Jia, Y. Zhang, and Z. Xu, “Chromatic aberrations correction for imaging spectrometer based on acousto-optic tunable filter with two transducers,” Opt. Express 25(20), 23809–23825 (2017).
[Crossref]

Opt. Lett. (13)

D. Richter, C. Voigtländer, R. G. Krämer, J. U. Thomas, A. Tünnermann, and S. Nolte, “Discrete nonplanar reflections from an ultrashort pulse written volume Bragg grating,” Opt. Lett. 40(12), 2766–2769 (2015).
[Crossref]

S. Hasegawa, Y. Hayasaki, and N. Nishida, “Holographic femtosecond laser processing with multiplexed phase Fresnel lenses,” Opt. Lett. 31(11), 1705–1707 (2006).
[Crossref]

G. Mínguez-Vega, J. Lancis, J. Caraquitena, V. Torres-Company, and P. Andrés, “High spatiotemporal resolution in multifocal processing with femtosecond laser pulses,” Opt. Lett. 31(17), 2631–2633 (2006).
[Crossref]

P. S. Salter and M. J. Booth, “Addressable microlens array for parallel laser microfabrication,” Opt. Lett. 36(12), 2302–2304 (2011).
[Crossref]

A. A. Maznev, T. F. Crimmins, and K. A. Nelson, “How to make femtosecond pulses overlap,” Opt. Lett. 23(17), 1378–1380 (1998).
[Crossref]

S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, “Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation,” Opt. Lett. 28(12), 995–997 (2003).
[Crossref]

S. Hasegawa and Y. Hayasaki, “Dynamic control of spatial wavelength dispersion in holographic femtosecond laser processing,” Opt. Lett. 39(3), 478–481 (2014).
[Crossref]

J. Amako, K. Nagasaka, and N. Kazuhiro, “Chromatic-distortion compensation in splitting and focusing of femtosecond pulses by use of a pair of diffractive optical elements,” Opt. Lett. 27(11), 969–971 (2002).
[Crossref]

C. W. Smelser, S. J. Mihailov, D. Grobnic, P. Lu, R. B. Walker, H. Ding, and X. Dai, “Multiple-beam interference patterns in optical fiber generated with ultrafast pulses and a phase mask,” Opt. Lett. 29(13), 1458–1460 (2004).
[Crossref]

C. W. Smelser, D. Grobnic, and S. J. Mihailov, “Generation of pure two-beam interference grating structures in an optical fiber with a femtosecond infrared source and a phase mask,” Opt. Lett. 29(15), 1730–1732 (2004).
[Crossref]

C. W. Smelser, S. J. Mihailov, and D. Grobnic, “Characterization of Fourier components in type I infrared ultrafast laser induced fiber Bragg gratings,” Opt. Lett. 32(11), 1453–1455 (2007).
[Crossref]

C. Hnatovsky, D. Grobnic, D. Coulas, M. Barnes, and S. J. Mihailov, “Self-organized nanostructure formation during femtosecond-laser inscription of fiber Bragg gratings,” Opt. Lett. 42(3), 399–402 (2017).
[Crossref]

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Direct inscription of Bragg gratings in coated fibers by an infrared femtosecond laser,” Opt. Lett. 31(11), 1603–1605 (2006).
[Crossref]

Phys. Rev. B (1)

M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. B 48(6), 4721–4729 (1993).
[Crossref]

Pure Appl. Opt. (1)

S. H. Wiersma, T. D. Visser, and P. Török, “Annular focusing through a dielectric interface: scanning and confining the intensity,” Pure Appl. Opt. 7(5), 1237–1248 (1998).
[Crossref]

Rev. Sci. Instrum. (1)

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68(12), 4309–4341 (1997).
[Crossref]

Sensors (1)

J. Habel, T. Boilard, J.-S. Frenière, F. Trépanier, and M. Bernier, “Femtosecond FBG written through the coating for sensing applications,” Sensors 17(11), 2519 (2017).
[Crossref]

Other (6)

G. W. Stroke, Diffraction Gratings. In: S. Flügge (eds) Optische Instrumente/Optical Instruments. Handbuch der Physik/Encyclopedia of Physics, Volume 5/29. (Springer, Berlin, Heidelberg1967).

C. Palmer, Diffraction Grating Handbook, 4th ed. (Richardson Grating Laboratory, Rochester, N.Y., 2000).

J. C. Wyant and K. Creath, Basic Wavefront Aberration Theory for Optical Metrology. In: R. R. Shannon and J. C. Wyant (eds.), Applied Optics and Optical Engineering, Volume XI. (Academic Press, New York, 1992).

R. K Lüneburg, Mathematical Theory of Optics (Cambridge University Press, 1964).

J. E. Greivenkamp, Field Guide to Geometric Optics (SPIE Press, 2004).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 6th ed. (Pergamon, Oxford, UK, 1980).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1.
Fig. 1. Interference of ultrashort pulses after a phase mask that produces four diffraction orders (m = 0,..3). M denotes the phase mask, CL is the cylindrical lens, ΔT is the transverse walk-off, ΔL is the longitudinal walk-off, L is the distance from M to the observation point (O), l is the distance from M to the pulse front of the 0th diffraction order. The pulse phase fronts are normal to the propagation direction of the respective diffraction orders.
Fig. 2.
Fig. 2. Focal elongation caused by chromatic dispersion of the mask (a) and chromatic aberration of the cylindrical lens (b). In (a), $\Delta {\theta _1}$ is the angular spread of the spectrum of the 1st diffraction order corresponding to a pulse bandwidth Δλ. For clarity, the mask produces only the 0th and 1st diffraction orders. Note that ‘red’ light is focused closer to M in (a) and farther from M in (b).
Fig. 3.
Fig. 3. Focal elongation caused by the plane parallel mask substrate. Note that marginal rays are focused farther from the mask than paraxial rays (compare with Fig. 4(b)).
Fig. 4.
Fig. 4. Focal elongation caused by conical (off-plane) diffraction. (a) Visualization of the direction cosine space for conical diffraction by a phase mask (i.e., transmission diffraction grating). (b) Ray propagation in the yz-plane plane (βγ-plane in (a)). In (b), F0,0 denotes the paraxial focus of the 0th diffraction order, Fm,0 and Fm,φ respectively denote the paraxial and marginal foci of the mth diffraction order, L and l respectively denote the distance from M and Fm,0 (observation point O coincides with Fm,0) and the distance from M to F0,0. The mask produces only 0th and 1st diffraction orders. Note that the marginal focus (i.e., Fm,φ) lies closer to the mask than the paraxial focus (i.e., Fm,0).(Compare with Fig. 3.)
Fig. 5.
Fig. 5. Focal intensity distributions in the yz-plane of the RA-1 beam (a) and the RA-2 beam (b) when the phase mask is removed from the beam path. The focusing is performed using the 12 mm-focal-length acylindrical lens whose effective numerical aperture is sin(φ) = 0.26 for (a) and sin(φ) = 0.30 for (b). In (a) and (b), the beam propagation is from left to right.
Fig. 6.
Fig. 6. Focal intensity distributions in the yz-plane of the RA-1 beam (a) and (c) and the RA-2 beam (b) and (d) when the beam is focused through the phase mask substrate without intercepting the mask grooves. (a) and (b) correspond to t = 2.1 mm, while (c) and (d) correspond to t = 3.4 mm. The focusing is performed using the 12 mm-focal-length acylindrical lens. sin(φ) = 0.26 and 0.30 for RA-1 and RA-2, respectively. In all the panels, the beam propagation is from left to right.
Fig. 7.
Fig. 7. Focal peak intensity as a function of distance L from the 1.07 µm-pitch 2.1 mm-thick phase mask.
Fig. 8.
Fig. 8. Focal intensity distributions in the xy- and yz-planes of the RA-1 beam (a, c, e and g) and RA-2 beam (b, d, f and h) when the beams are focused through the 1.07 µm-pitch 2.1 mm-thick phase mask. The focusing is performed using the 12 mm-focal-length acylindrical lens. sin(φ) = 0.26 and 0.30 for RA-1 and RA-2, respectively. In all the panels corresponding to the yz-plane the beam propagation is from left to right.
Fig. 9.
Fig. 9. Focal intensity distributions of the RA-1 and RA-2 beams when the beams are focused through the 1.07 µm-pitch 3.4 mm-thick phase mask. (a) Focal peak intensity as a function of distance L from the mask. (b) and (c), focal intensity distributions in the xy- and yz-planes of RA-1 and RA-2 recorded respectively at L = 570 µm and L = 400 µm. The focusing is performed using the 12 mm-focal-length acylindrical lens. sin(φ) = 0.26 and 0.30 for RA-1 and RA-2, respectively. In all the panels corresponding to the yz-plane the beam propagation is from left to right.
Fig. 10.
Fig. 10. A procedure to compensate for substrate-induced negative spherical aberration using a plano-convex cylindrical lens (CL1) placed in front of the acylindrical lens.
Fig. 11.
Fig. 11. Focal intensity distributions of the RA-1 and RA-2 beams when the beams are focused through the 1.07 µm-pitch 3.4 mm-thick phase mask and substrate-induced negative spherical aberration has been corrected using the technique depicted in Figs. 10(a) and (b), focal intensity distributions in the yz-planes of RA-1 and RA-2, respectively, when the beams are focused through the phase mask substrate without intercepting the mask grooves. (c) Focal peak intensity as a function of distance L from the mask. The focusing is performed using the 12 mm-focal-length acylindrical lens. For RA-1 and RA-2, the effective numerical aperture is estimated at 0.25 < sin(φ) < 0.28. In (a) and (b), the beam propagation is from left to right.
Fig. 12.
Fig. 12. Focal intensity distributions of the RA-1 beam when the beam is focused through the 2.14 µm-pitch 2.4 mm-thick phase mask. (a) Focal peak intensity as a function of distance L from the mask. (b) Focal intensity distributions the 1st diffraction order in the xy- and yz-planes. In the panel corresponding to the yz-plane, the beam propagation is from left to right. The focusing is performed using the 12 mm-focal-length acylindrical lens at sin(φ) = 0.26.
Fig. 13.
Fig. 13. (a) FBGs written in uncoated SMF-28 fiber. (b) Inferred refractive index change Δn for the corresponding FBGs.
Fig. 14.
Fig. 14. (a) Reflection spectrum (∼6 dB in transmission, Δn ∼ 1.5×10−4) of an FBG written in a 50 µm fiber through the polyimide coating. (b) An optical microscopy image of the 50 µm fiber containing the FBG whose spectrum is shown in (a). To visualize the FBG, red light at 637 nm was coupled into the fiber core [52].

Equations (16)

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

L λ 0 2 Δ λ cos [ arcsin ( m λ 0 / d ) ] cos [ arcsin [ ( m 1 ) λ 0 / d ] ] cos [ arcsin ( m λ 0 / d ) ] ,
Δ z mask chrom . = L sin ( θ m ) cos ( θ m ) Δ θ m = m L Δ λ d sin [ arcsin ( | m | λ 0 / d ) ] cos 2 [ arcsin ( | m | λ 0 / d ) ] ,
Δ z substr . chrom . = t n 1 2 ( d n 1 / d λ ) Δ λ ,
Δ z lens chrom . = f n L 1 ( d n L / d λ ) Δ λ ,
Δ z lens chrom . = f cos ( θ m ) n L 1 ( d n L / d λ ) Δ λ .
Δ z mask chrom . = m 2 λ 0 L Δ λ d 2 m 2 λ 0 2 .
Δ z substr . sph . aberr . = t n 1 { 1 [ n 1 2 ( 1 sin 2 ( φ ) ) n 1 2 sin 2 ( φ ) ] 1 / 2 } .
Δ z substr . sph . aberr . ( n 1 2 1 ) t φ 2 2 n 1 3 .
Δ z substr . sph . aberr . = t cos ( θ m ) n 1 { 1 [ n 1 2 ( 1 sin 2 ( φ ) ) n 1 2 sin 2 ( φ ) ] 1 / 2 } .
Δ z substr . sph . aberr . ( n 1 2 1 ) t cos ( θ m ) φ 2 2 n 1 3 .
α i = sin ( χ ) cos ( φ ) ; β i = sin ( φ ) ; γ i = cos ( χ ) cos ( φ ) with α i 2 + β i 2 + γ i 2 = 1 ,
α m α i = m λ 0 / d , α m = sin ( θ m ) cos ( φ ) ; β m = β i = sin ( φ ) with α m 2 + β m 2 + γ m 2 = 1.
γ m = [ 1 m 2 λ 0 2 / d 2 sin 2 ( φ ) ] 1 / 2 ; tan ( Ψ m , φ ) = sin ( φ ) [ 1 m 2 λ 0 2 / d 2 sin 2 ( φ ) ] 1 / 2 .
Δ z mask con . diffr . = L { 1 [ cos 2 ( φ ) m 2 λ 0 2 / d 2 cos 2 ( φ ) ( 1 m 2 λ 0 2 / d 2 ) ] 1 / 2 } ,
Δ z mask con . diffr . m 2 λ 0 2 L φ 2 2 ( d 2 m 2 λ 0 2 ) .
R 0 tanh 2 [ π Δ n W η ( V ) / λ B ] ,

Metrics