Abstract

In the past years, several examples of waveguides or gratings manufactured by laser radiation in various glasses or transparent polymers have been demonstrated. As these devices rely on a modification of the refractive index in the vicinity of the focal point of a writing laser, phase retrieval methods are well suited to determine the induced phase change inside the material experimentally. Thus, phase retrieval can assist parameter-studies and reveal information about the internal structure of the modifications which can hardly be obtained using other methods. Here, we demonstrate the application of a modified phase retrieval technique especially suited to determine the optical properties of phase objects such as femtosecond written gratings or waveguide arrays inscribed in transparent materials. Using the presented algorithm, we quantify the correlation between pulse energy and phase deviation as well as the structure width for femtosecond laser induced refractive index modifications in poly(methyl methacrylate) which, in the future, can be used to create tailored micro-optical structures for sensing applications.

© 2016 Optical Society of America

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References

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  1. K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239(1), 91–95 (1998).
    [Crossref]
  2. A. Y. Naumov, C. Przygodzki, X. Zhu, and P. Corkum, “Microstructuring with femtosecond laser inside silica glasses,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, 356–357 (1999).
  3. L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171(4), 279–284 (1999).
    [Crossref]
  4. S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77(1), 109–111 (2003).
    [Crossref]
  5. R. Osellame, V. Maselli, R. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett. 90(23), 231118 (2007).
    [Crossref]
  6. A. Zoubir, C. Lopez, M. Richardson, and K. Richardson, “Femtosecond laser fabrication of tubular waveguides in poly (methyl methacrylate),” Opt. Lett. 29(16), 1840–1842 (2004).
    [Crossref] [PubMed]
  7. S. Sowa, W. Watanabe, T. Tamaki, J. Nishii, and K. Itoh, “Symmetric waveguides in poly (methyl methacrylate) fabricated by femtosecond laser pulses,” Opt. Express 14(1), 291–297 (2006).
    [Crossref] [PubMed]
  8. W. M. Pätzold, C. Reinhardt, A. Demircan, and U. Morgner, “Cascaded-focus laser writing of low-loss waveguides in polymers,” Opt. Lett. 41(6), 1269–1272 (2016).
    [Crossref] [PubMed]
  9. W. Watanabe, K. Matsuda, S. Hirono, and H. Mochizuki, “Fabrication of diffractive optical elements in polymers by 400 nm femtosecond laser pulses,” J. Laser Micro. Nanoen. 7, 58 (2012).
    [Crossref]
  10. M. Rahlves, M. Rezem, K. Boroz, S. Schlangen, E. Reithmeier, and B. Roth, “Flexible, fast, and low-cost production process for polymer based diffractive optics,” Opt. Express 23(3), 3614–3622 (2015).
    [Crossref] [PubMed]
  11. C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
    [Crossref]
  12. M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE 1535, 34–42 (1991).
    [Crossref]
  13. R. Berlich, J. Choi, C. Mazuir, W. V. Schoenfeld, S. Nolte, and M. Richardson, “Spatially resolved measurement of femtosecond laser induced refractive index changes in transparent materials,” Opt. Lett. 37(14), 3003–3005 (2012).
    [Crossref] [PubMed]
  14. G. Palmer, M. Schultze, M. Emons, A. L. Lindemann, M. Pospiech, D. Steingrube, M. Lederer, and U. Morgner, “12 MW peak power from a two-crystal Yb: KYW chirped-pulse oscillator with cavity-dumping,” Opt. Express 18(18), 19095–19100 (2010).
    [Crossref] [PubMed]

2016 (2)

W. M. Pätzold, C. Reinhardt, A. Demircan, and U. Morgner, “Cascaded-focus laser writing of low-loss waveguides in polymers,” Opt. Lett. 41(6), 1269–1272 (2016).
[Crossref] [PubMed]

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

2015 (1)

2012 (2)

R. Berlich, J. Choi, C. Mazuir, W. V. Schoenfeld, S. Nolte, and M. Richardson, “Spatially resolved measurement of femtosecond laser induced refractive index changes in transparent materials,” Opt. Lett. 37(14), 3003–3005 (2012).
[Crossref] [PubMed]

W. Watanabe, K. Matsuda, S. Hirono, and H. Mochizuki, “Fabrication of diffractive optical elements in polymers by 400 nm femtosecond laser pulses,” J. Laser Micro. Nanoen. 7, 58 (2012).
[Crossref]

2010 (1)

2007 (1)

R. Osellame, V. Maselli, R. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett. 90(23), 231118 (2007).
[Crossref]

2006 (1)

2004 (1)

2003 (1)

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77(1), 109–111 (2003).
[Crossref]

1999 (1)

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171(4), 279–284 (1999).
[Crossref]

1998 (1)

K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239(1), 91–95 (1998).
[Crossref]

1991 (1)

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE 1535, 34–42 (1991).
[Crossref]

Berlich, R.

Boroz, K.

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77(1), 109–111 (2003).
[Crossref]

Cerullo, G.

R. Osellame, V. Maselli, R. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett. 90(23), 231118 (2007).
[Crossref]

Choi, J.

Corkum, P.

A. Y. Naumov, C. Przygodzki, X. Zhu, and P. Corkum, “Microstructuring with femtosecond laser inside silica glasses,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, 356–357 (1999).

Demircan, A.

Emons, M.

Farn, M. W.

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE 1535, 34–42 (1991).
[Crossref]

Franco, M.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171(4), 279–284 (1999).
[Crossref]

Hinkelmann, M.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

Hirao, K.

K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239(1), 91–95 (1998).
[Crossref]

Hirono, S.

W. Watanabe, K. Matsuda, S. Hirono, and H. Mochizuki, “Fabrication of diffractive optical elements in polymers by 400 nm femtosecond laser pulses,” J. Laser Micro. Nanoen. 7, 58 (2012).
[Crossref]

Itoh, K.

Kelb, C.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

Lederer, M.

Lindemann, A. L.

Lopez, C.

Maselli, V.

R. Osellame, V. Maselli, R. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett. 90(23), 231118 (2007).
[Crossref]

Matsuda, K.

W. Watanabe, K. Matsuda, S. Hirono, and H. Mochizuki, “Fabrication of diffractive optical elements in polymers by 400 nm femtosecond laser pulses,” J. Laser Micro. Nanoen. 7, 58 (2012).
[Crossref]

Mazuir, C.

Miura, K.

K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239(1), 91–95 (1998).
[Crossref]

Mochizuki, H.

W. Watanabe, K. Matsuda, S. Hirono, and H. Mochizuki, “Fabrication of diffractive optical elements in polymers by 400 nm femtosecond laser pulses,” J. Laser Micro. Nanoen. 7, 58 (2012).
[Crossref]

Morgner, U.

Müller, C.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

Mysyrowicz, A.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171(4), 279–284 (1999).
[Crossref]

Naumov, A. Y.

A. Y. Naumov, C. Przygodzki, X. Zhu, and P. Corkum, “Microstructuring with femtosecond laser inside silica glasses,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, 356–357 (1999).

Nishii, J.

Nolte, S.

R. Berlich, J. Choi, C. Mazuir, W. V. Schoenfeld, S. Nolte, and M. Richardson, “Spatially resolved measurement of femtosecond laser induced refractive index changes in transparent materials,” Opt. Lett. 37(14), 3003–3005 (2012).
[Crossref] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77(1), 109–111 (2003).
[Crossref]

Osellame, R.

R. Osellame, V. Maselli, R. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett. 90(23), 231118 (2007).
[Crossref]

Palmer, G.

Pätzold, W. M.

Pospiech, M.

Prade, B.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171(4), 279–284 (1999).
[Crossref]

Prucker, O.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

Przygodzki, C.

A. Y. Naumov, C. Przygodzki, X. Zhu, and P. Corkum, “Microstructuring with femtosecond laser inside silica glasses,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, 356–357 (1999).

Rahlves, M.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

M. Rahlves, M. Rezem, K. Boroz, S. Schlangen, E. Reithmeier, and B. Roth, “Flexible, fast, and low-cost production process for polymer based diffractive optics,” Opt. Express 23(3), 3614–3622 (2015).
[Crossref] [PubMed]

Ramponi, R.

R. Osellame, V. Maselli, R. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett. 90(23), 231118 (2007).
[Crossref]

Reinhardt, C.

Reithmeier, E.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

M. Rahlves, M. Rezem, K. Boroz, S. Schlangen, E. Reithmeier, and B. Roth, “Flexible, fast, and low-cost production process for polymer based diffractive optics,” Opt. Express 23(3), 3614–3622 (2015).
[Crossref] [PubMed]

Rezem, M.

Richardson, K.

Richardson, M.

Roth, B.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

M. Rahlves, M. Rezem, K. Boroz, S. Schlangen, E. Reithmeier, and B. Roth, “Flexible, fast, and low-cost production process for polymer based diffractive optics,” Opt. Express 23(3), 3614–3622 (2015).
[Crossref] [PubMed]

Rother, R.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

Rühe, J.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

Schlangen, S.

Schoenfeld, W. V.

Schuler, A. K.

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

Schultze, M.

Sowa, S.

Steingrube, D.

Sudrie, L.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171(4), 279–284 (1999).
[Crossref]

Tamaki, T.

Tuennermann, A.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77(1), 109–111 (2003).
[Crossref]

Vazquez, R.

R. Osellame, V. Maselli, R. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett. 90(23), 231118 (2007).
[Crossref]

Watanabe, W.

W. Watanabe, K. Matsuda, S. Hirono, and H. Mochizuki, “Fabrication of diffractive optical elements in polymers by 400 nm femtosecond laser pulses,” J. Laser Micro. Nanoen. 7, 58 (2012).
[Crossref]

S. Sowa, W. Watanabe, T. Tamaki, J. Nishii, and K. Itoh, “Symmetric waveguides in poly (methyl methacrylate) fabricated by femtosecond laser pulses,” Opt. Express 14(1), 291–297 (2006).
[Crossref] [PubMed]

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77(1), 109–111 (2003).
[Crossref]

Zhu, X.

A. Y. Naumov, C. Przygodzki, X. Zhu, and P. Corkum, “Microstructuring with femtosecond laser inside silica glasses,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, 356–357 (1999).

Zoubir, A.

Appl. Phys. A (1)

S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, “Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics,” Appl. Phys. A 77(1), 109–111 (2003).
[Crossref]

Appl. Phys. Lett. (1)

R. Osellame, V. Maselli, R. Vazquez, R. Ramponi, and G. Cerullo, “Integration of optical waveguides and microfluidic channels both fabricated by femtosecond laser irradiation,” Appl. Phys. Lett. 90(23), 231118 (2007).
[Crossref]

J. Laser Micro. Nanoen. (1)

W. Watanabe, K. Matsuda, S. Hirono, and H. Mochizuki, “Fabrication of diffractive optical elements in polymers by 400 nm femtosecond laser pulses,” J. Laser Micro. Nanoen. 7, 58 (2012).
[Crossref]

J. Non-Cryst. Solids (1)

K. Hirao and K. Miura, “Writing waveguides and gratings in silica and related materials by a femtosecond laser,” J. Non-Cryst. Solids 239(1), 91–95 (1998).
[Crossref]

Opt. Commun. (1)

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses,” Opt. Commun. 171(4), 279–284 (1999).
[Crossref]

Opt. Eng. (1)

C. Kelb, R. Rother, A. K. Schuler, M. Hinkelmann, M. Rahlves, O. Prucker, C. Müller, J. Rühe, E. Reithmeier, and B. Roth, “Manufacturing of embedded multimode waveguides by reactive lamination of cyclic olefin polymer and polymethylmethacrylate,” Opt. Eng. 55(3), 037103 (2016).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Proc. SPIE (1)

M. W. Farn, “New iterative algorithm for the design of phase-only gratings,” Proc. SPIE 1535, 34–42 (1991).
[Crossref]

Other (1)

A. Y. Naumov, C. Przygodzki, X. Zhu, and P. Corkum, “Microstructuring with femtosecond laser inside silica glasses,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, 356–357 (1999).

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Figures (7)

Fig. 1
Fig. 1 Sketch of the optomechanical writing setup: the specimen is moved underneath an aspheric lens along the x-axis with a constant feedrate v.
Fig. 2
Fig. 2 Sketch of the optical characterization setup: the specimen is illuminated with a HeNe Laser and the intensities of the diffraction orders are monitored with a laser power meter.
Fig. 3
Fig. 3 a) Sequential function chart of the phase retrieval algorithm; b) Constructed start phase function φ0(k); c) Two-dimensional error map displaying the RMS-error between actually measured diffraction intensities and intensities as produced by the start phase function. The red dot marks the minimum RMS error.
Fig. 4
Fig. 4 Cross-sections of material modifications in PMMA: a) schematic of the measured sectional plane. b)–d) Microscope images of written modifications using pulse energies ranging from 100 nJ to 300 nJ.
Fig. 5
Fig. 5 Phase given in radians over lateral distance of one grating period.
Fig. 6
Fig. 6 Maximum phase deviation over pulse energy. An increase can be observed for increasing pulse energies over the monitored energy band, the maximum value being φmax = 0.43 rad. Comparing lower (left in Fig. 7) pulse energies to higher (right part of Fig. 7) pulse energies, the increased scattering prohibits the further growth of the destroyed region while the refocused fraction of the beam would be strong enough to write a second modification once a certain energy threshold in the second focus is reached. This would then lead to a saturation in maximum phase deviation as long as no second modification develops.
Fig. 7
Fig. 7 Assumed internal structure of the written modifications for low (left) and increased (right) pulse energies.

Equations (3)

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c ( n ) = 1 K k = 0 K 1 e i φ ( k ) e i 2 π n k / K = | c ( n ) | e i α ( n )
M = n w ( n ) | c ( n ) |
e i φ ( k ) = n w ( n ) e i α ( n ) e i 2 π n k / K

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