Abstract

Direct laser writing is widely used for fabrication of subsurface, three dimensional structures in transparent media. However, the accessible volume is limited by distortion of the focussed beam at the sample edge. We determine the aberrated focal intensity distribution for light focused close to the edge of the substrate. Aberrations are modelled by dividing the pupil into two regions, each corresponding to light passing through the top and side facets. Aberration correction is demonstrated experimentally using a liquid crystal spatial light modulator for femtosecond microfabrication in fused silica. This technique allows controlled subsurface fabrication right up to the edge of the substrate. This can benefit a wide range of applications using direct laser writing, including the manufacture of waveguides and photonic crystals.

© 2012 OSA

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References

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    [CrossRef]
  2. S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
    [CrossRef]
  3. R. Osellame, V. Maselli, R. M. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett.90, 231118 (2007).
    [CrossRef]
  4. M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
    [CrossRef]
  5. Y. Y. Cao, N. Takeyasu, T. Tanaka, X. M. Duan, and S. Kawata, “3d metallic nanostructure fabrication by surfactant-assisted multiphoton-induced reduction,” Small5, 1144–1148 (2009).
    [PubMed]
  6. G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. OBrien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
    [CrossRef] [PubMed]
  7. G. D. Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A, Pure Appl. Opt.11, 013001 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. C. Mauclair, A. Mermillod-Blondin, N. Huot, E. Audouard, and R. Stoian, “Ultrafast laser writing of homogeneous longitudinal waveguides in glasses using dynamic wavefront correction,” Opt. Express16, 5481–5492 (2008).
    [CrossRef] [PubMed]
  13. B. P. Cumming, A. Jesacher, M. J. Booth, T. Wilson, and M. Gu, “Adaptive aberration compensation for three-dimensional micro-fabrication of photonic crystals in lithium niobate,” Opt. Express19, 9419–9425 (2011).
    [CrossRef] [PubMed]
  14. R. R. Thomson, A. S. Bockelt, E. Ramsay, S. Beecher, A. H. Greenaway, A. K. Kar, and D. T. Reid, “Shaping ultrafast laser inscribed optical waveguides using a deformable mirror,” Opt. Express16, 12786–12793 (2008).
    [CrossRef] [PubMed]
  15. A. R. de la Cruz, A. Ferrer, W. Gawelda, D. Puerto, M. G. Sosa, J. Siegel, and J. Solis, “Independent control of beam astigmatism and ellipticity using a slm for fs-laser waveguide writing,” Opt. Express17, 20853–20859 (2009).
    [CrossRef]
  16. M. Pospiech, M. Emons, A. Steinmann, G. Palmer, R. Osellame, N. Bellini, G. Cerullo, and U. Morgner, “Double waveguide couplers produced by simultaneous femtosecond writing,” Opt. Express17, 3555–3563 (2009).
    [CrossRef] [PubMed]
  17. P. S. Salter, A. Jesacher, J. B. Spring, B. J. Metcalf, N. Thomas-Peter, R. D. Simmonds, N. K. Langford, I. A. Walmsley, and M. J. Booth, “Adaptive slit beam shaping for direct laser written waveguides,” Opt. Lett.37, 470–472 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  21. J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

2012

2011

2010

2009

A. R. de la Cruz, A. Ferrer, W. Gawelda, D. Puerto, M. G. Sosa, J. Siegel, and J. Solis, “Independent control of beam astigmatism and ellipticity using a slm for fs-laser waveguide writing,” Opt. Express17, 20853–20859 (2009).
[CrossRef]

M. Pospiech, M. Emons, A. Steinmann, G. Palmer, R. Osellame, N. Bellini, G. Cerullo, and U. Morgner, “Double waveguide couplers produced by simultaneous femtosecond writing,” Opt. Express17, 3555–3563 (2009).
[CrossRef] [PubMed]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
[CrossRef]

Y. Y. Cao, N. Takeyasu, T. Tanaka, X. M. Duan, and S. Kawata, “3d metallic nanostructure fabrication by surfactant-assisted multiphoton-induced reduction,” Small5, 1144–1148 (2009).
[PubMed]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. OBrien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
[CrossRef] [PubMed]

G. D. Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A, Pure Appl. Opt.11, 013001 (2009).
[CrossRef]

2008

2007

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A365, 2829–2843 (2007).
[CrossRef] [PubMed]

R. Osellame, V. Maselli, R. M. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett.90, 231118 (2007).
[CrossRef]

2006

S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
[CrossRef]

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett.88, 031109 (2006).
[CrossRef]

2003

1998

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192, 90–98 (1998).
[CrossRef]

1995

Ams, M.

Audouard, E.

Beecher, S.

Bellini, N.

Bockelt, A. S.

Booker, G. R.

Booth, M. J.

Cao, Y. Y.

Y. Y. Cao, N. Takeyasu, T. Tanaka, X. M. Duan, and S. Kawata, “3d metallic nanostructure fabrication by surfactant-assisted multiphoton-induced reduction,” Small5, 1144–1148 (2009).
[PubMed]

Cerullo, G.

M. Pospiech, M. Emons, A. Steinmann, G. Palmer, R. Osellame, N. Bellini, G. Cerullo, and U. Morgner, “Double waveguide couplers produced by simultaneous femtosecond writing,” Opt. Express17, 3555–3563 (2009).
[CrossRef] [PubMed]

R. Osellame, V. Maselli, R. M. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett.90, 231118 (2007).
[CrossRef]

Chin, S. L.

Cumming, B. P.

de la Cruz, A. R.

Dekker, P.

Deubel, M.

S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
[CrossRef]

Duan, X. M.

Y. Y. Cao, N. Takeyasu, T. Tanaka, X. M. Duan, and S. Kawata, “3d metallic nanostructure fabrication by surfactant-assisted multiphoton-induced reduction,” Small5, 1144–1148 (2009).
[PubMed]

Emons, M.

Ferrer, A.

Freymann, G.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
[CrossRef]

Gattass, R. R.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics2, 219–225 (2008).
[CrossRef]

Gawelda, W.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

Greenaway, A. H.

Gu, M.

Huot, N.

Jesacher, A.

John, S.

S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
[CrossRef]

Kar, A. K.

Kawata, S.

Y. Y. Cao, N. Takeyasu, T. Tanaka, X. M. Duan, and S. Kawata, “3d metallic nanostructure fabrication by surfactant-assisted multiphoton-induced reduction,” Small5, 1144–1148 (2009).
[PubMed]

Kawata, Y.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett.88, 031109 (2006).
[CrossRef]

Laczik, Z.

Langford, N. K.

Laporta, P.

G. D. Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A, Pure Appl. Opt.11, 013001 (2009).
[CrossRef]

Linden, S.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
[CrossRef]

Liu, W.

Marshall, G. D.

Maselli, V.

R. Osellame, V. Maselli, R. M. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett.90, 231118 (2007).
[CrossRef]

Matthews, J. C. F.

Mauclair, C.

Mazur, E.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics2, 219–225 (2008).
[CrossRef]

Mermillod-Blondin, A.

Metcalf, B. J.

Miyata, S.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett.88, 031109 (2006).
[CrossRef]

Morgner, U.

Nakabayashi, M.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett.88, 031109 (2006).
[CrossRef]

Nakano, M.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett.88, 031109 (2006).
[CrossRef]

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192, 90–98 (1998).
[CrossRef]

Nguyen, N. T.

OBrien, J. L.

Osellame, R.

G. D. Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A, Pure Appl. Opt.11, 013001 (2009).
[CrossRef]

M. Pospiech, M. Emons, A. Steinmann, G. Palmer, R. Osellame, N. Bellini, G. Cerullo, and U. Morgner, “Double waveguide couplers produced by simultaneous femtosecond writing,” Opt. Express17, 3555–3563 (2009).
[CrossRef] [PubMed]

R. Osellame, V. Maselli, R. M. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett.90, 231118 (2007).
[CrossRef]

Ozin, G. A.

S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
[CrossRef]

Palmer, G.

Plet, C.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
[CrossRef]

Politi, A.

Pospiech, M.

Prez-Willard, F.

S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
[CrossRef]

Puerto, D.

Ramponi, R.

R. Osellame, V. Maselli, R. M. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett.90, 231118 (2007).
[CrossRef]

Ramsay, E.

Reid, D. T.

Rill, M. S.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
[CrossRef]

Saliminia, A.

Salter, P. S.

Schwertner, M.

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett.88, 031109 (2006).
[CrossRef]

Siegel, J.

Simmonds, R. D.

Solis, J.

Sosa, M. G.

Spring, J. B.

Staude, I.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
[CrossRef]

Steinmann, A.

Stoian, R.

Takeyasu, N.

Y. Y. Cao, N. Takeyasu, T. Tanaka, X. M. Duan, and S. Kawata, “3d metallic nanostructure fabrication by surfactant-assisted multiphoton-induced reduction,” Small5, 1144–1148 (2009).
[PubMed]

Tanaka, T.

Y. Y. Cao, N. Takeyasu, T. Tanaka, X. M. Duan, and S. Kawata, “3d metallic nanostructure fabrication by surfactant-assisted multiphoton-induced reduction,” Small5, 1144–1148 (2009).
[PubMed]

Thiel, M.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
[CrossRef]

Thomas-Peter, N.

Thomson, R. R.

Torok, P.

Valle, G. D.

G. D. Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A, Pure Appl. Opt.11, 013001 (2009).
[CrossRef]

Vallee, R.

Varga, P.

Vazquez, R. M.

R. Osellame, V. Maselli, R. M. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett.90, 231118 (2007).
[CrossRef]

von Freymann, G.

S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
[CrossRef]

Walmsley, I. A.

Wegener, M.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
[CrossRef]

S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
[CrossRef]

Wilson, T.

B. P. Cumming, A. Jesacher, M. J. Booth, T. Wilson, and M. Gu, “Adaptive aberration compensation for three-dimensional micro-fabrication of photonic crystals in lithium niobate,” Opt. Express19, 9419–9425 (2011).
[CrossRef] [PubMed]

A. Jesacher, G. D. Marshall, T. Wilson, and M. J. Booth, “Adaptive optics for direct laser writing with plasma emission aberration sensing,” Opt. Express18, 656–661 (2010).
[CrossRef] [PubMed]

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett.88, 031109 (2006).
[CrossRef]

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192, 90–98 (1998).
[CrossRef]

Withford, M. J.

Wong, S.

S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
[CrossRef]

Adv. Mater.

S. Wong, M. Deubel, F. Prez-Willard, S. John, G. A. Ozin, M. Wegener, and G. von Freymann, “Direct laser writing of three-dimensional photonic crystals with a complete photonic bandgap in chalcogenide glasses,” Adv. Mater.18, 265–269 (2006).
[CrossRef]

Appl. Phys. Lett.

R. Osellame, V. Maselli, R. M. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett.90, 231118 (2007).
[CrossRef]

M. J. Booth, M. Schwertner, T. Wilson, M. Nakano, Y. Kawata, M. Nakabayashi, and S. Miyata, “Predictive aberration correction for multilayer optical data storage,” Appl. Phys. Lett.88, 031109 (2006).
[CrossRef]

J. Microsc.

M. J. Booth, M. A. A. Neil, and T. Wilson, “Aberration correction for confocal imaging in refractive-index-mismatched media,” J. Microsc.192, 90–98 (1998).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

G. D. Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A, Pure Appl. Opt.11, 013001 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Mater.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater.7, 543–546 (2009).
[CrossRef]

Nat. Photonics

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics2, 219–225 (2008).
[CrossRef]

Opt. Express

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. OBrien, “Laser written waveguide photonic quantum circuits,” Opt. Express17, 12546–12554 (2009).
[CrossRef] [PubMed]

A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express18, 21090–21099 (2010).
[CrossRef] [PubMed]

C. Mauclair, A. Mermillod-Blondin, N. Huot, E. Audouard, and R. Stoian, “Ultrafast laser writing of homogeneous longitudinal waveguides in glasses using dynamic wavefront correction,” Opt. Express16, 5481–5492 (2008).
[CrossRef] [PubMed]

B. P. Cumming, A. Jesacher, M. J. Booth, T. Wilson, and M. Gu, “Adaptive aberration compensation for three-dimensional micro-fabrication of photonic crystals in lithium niobate,” Opt. Express19, 9419–9425 (2011).
[CrossRef] [PubMed]

R. R. Thomson, A. S. Bockelt, E. Ramsay, S. Beecher, A. H. Greenaway, A. K. Kar, and D. T. Reid, “Shaping ultrafast laser inscribed optical waveguides using a deformable mirror,” Opt. Express16, 12786–12793 (2008).
[CrossRef] [PubMed]

A. R. de la Cruz, A. Ferrer, W. Gawelda, D. Puerto, M. G. Sosa, J. Siegel, and J. Solis, “Independent control of beam astigmatism and ellipticity using a slm for fs-laser waveguide writing,” Opt. Express17, 20853–20859 (2009).
[CrossRef]

M. Pospiech, M. Emons, A. Steinmann, G. Palmer, R. Osellame, N. Bellini, G. Cerullo, and U. Morgner, “Double waveguide couplers produced by simultaneous femtosecond writing,” Opt. Express17, 3555–3563 (2009).
[CrossRef] [PubMed]

A. Jesacher, G. D. Marshall, T. Wilson, and M. J. Booth, “Adaptive optics for direct laser writing with plasma emission aberration sensing,” Opt. Express18, 656–661 (2010).
[CrossRef] [PubMed]

Opt. Lett.

Phil. Trans. R. Soc. A

M. J. Booth, “Adaptive optics in microscopy,” Phil. Trans. R. Soc. A365, 2829–2843 (2007).
[CrossRef] [PubMed]

Small

Y. Y. Cao, N. Takeyasu, T. Tanaka, X. M. Duan, and S. Kawata, “3d metallic nanostructure fabrication by surfactant-assisted multiphoton-induced reduction,” Small5, 1144–1148 (2009).
[PubMed]

Other

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company, 2005).

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Figures (7)

Fig. 1
Fig. 1

Ray trace diagrams showing the refraction of rays focussed through the top (blue) and side (red) surfaces of a substrate with differing refractive index (n2) to that of the lens immersion medium (n1). The diagrams provide a view of a plane perpendicular to the focal plane and containing the optical axis of the lens. As the lateral distance g between the edge of the substrate and the optic axis decreases, the focal splitting between red and blue rays becomes more severe.

Fig. 2
Fig. 2

Light is focused to a point F at a depth d beneath the upper surface T of a substrate, and a distance g from the side facet Σ. The line CC′ divides the focusing cone into rays that pass through and are refracted by the top surface T and the side facet Σ. The line OPF is the optical axis for the focusing lens, while the perpendicular line OQF represents the optical axis for a virtual pupil, which is used to describe rays passing through the side facet.

Fig. 3
Fig. 3

Pupil phase distributions required to maintain an aberration free geometric focus for 790 nm wavelength light focused 50 μm beneath the surface of fused silica by a 0.85 NA air objective. The phase maps are for a focus at a distances (a) g = 0 μm, (b) g = 10 μm, (c) g = 20 μm and (d) g = 30 μm from the side facet Σ.

Fig. 4
Fig. 4

(a) Experimental schematic for microfabrication demonstrations. Lens focal lengths are in mm. (b), (c) and (d): Images of focal splitting in void fabrication of fused silica after exposure to a single pulse at a nominal depth of 50μm and 5μm from the substrate edge. The optical axis is the z direction. (c) and (d) are cross-sectional images focused at planes Z1 and Z2 respectively.

Fig. 5
Fig. 5

Measurements of the net intensity of plasma emission from the focal volume when focussing at a nominal depth dnom = 50 μm in fused silica, at nominal distances of gnom = 5 μm, 10 μm and 15 μm from the edge of the substrate. In (a) the phase pattern in region A of the SLM is altered by varying g in Eq. (10), while in (b) the phase distribution in region B is modified by varying d in Eq. (3). The boundary CC′ separating region A and B varies according to Eq. (2) in both plots. A background phase is added to the calculated phase distributions, which takes into account any system aberrations including the initial flatness correction for the SLM. The inset shows a typical CCD image of the plasma emission. The weak signal on the left is a ghost image formed by light reflecting off the internal side surface of the silica block.

Fig. 6
Fig. 6

Differential interference contrast (DIC) images showing voids fabricated at a depth of 50 μm in fused silica, 10 μm from the edge of the substrate. The optical axis was along the z direction and the voids were fabricated by a burst of 100 pulses from the laser.

Fig. 7
Fig. 7

DIC images showing tracks fabricated at a depth of 50 μm in fused silica, by translating the sample at a speed of 0.5 μm/s in the positive x direction. The tracks in image (a) were written at a constant power without (i) and with (ii) correction of the edge aberration. The tracks in images (b) and (c) were written adapting the SLM to modify the laser power incident on the objective lens, and in image (b) the SLM additionally provided correction of the edge aberration. The optical axis was along the z direction. Also shown are the instantaneous phase patterns displayed on the SLM at the points indicated.

Equations (10)

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ρ = 1 sin α 1 1 + ( d / r t ) 2
ρ = 1 sin α 1 1 + ( d g ) 2 cos 2 θ
Ψ ( ρ , θ ) = 2 π λ d N A ( cosec 2 α 2 ρ 2 cosec 2 α 1 ρ 2 )
Ψ ( ρ , θ ) = 2 π λ g N A ( cosec 2 α 2 ρ 2 cosec 2 α 1 ρ 2 )
R 2 = R 2 g 2 + d 2
g cos α 1 = d cos α 1
cos 2 ϕ + cos 2 ξ + sin 2 ϕ sin 2 θ = 1
ρ = 1 ρ 2 sin α 1 2 cos 2 θ sin α 1
= 1 ρ 2 sin α 1 2 cos 2 θ 1 ( g / d ) 2 cos 2 α 1
Ψ ( ρ , θ ) = 2 π λ g n 1 ( ( n 2 n 1 + ρ 2 sin α 1 2 cos 2 θ 1 ) ρ sin α 1 cos θ )

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