Abstract

We report on a novel method to create waveguide coupler devices in fused silica by combining the technique of beam shaping with femtosecond laser writing. The method is based on a programmable phase modulator and a dynamic variation of the phase-pattern during the writing process. The major advantage is the possibility to create complex devices in a single sweep by simultaneously writing two or more waveguides with changing separation. The guiding properties and the coupling behavior between the waveguides are investigated.

© 2009 Optical Society of America

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  1. K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, "Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing," Opt. Express 10, 645-652 (2002). http://www.opticsexpress.org/abstract.cfm?URI=oe-10-15-645.
    [PubMed]
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  3. R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
    [CrossRef]
  4. D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, "Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses," Opt. Lett. 24, 1311-1313 (1999). http://ol.osa.org/abstract.cfm?URI=ol-24-18-1311.
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    [CrossRef]
  6. J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, "Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser," Opt. Commun. 253, 315-319 (2005). http://www.sciencedirect.com/science/article/B6TVF-4G6J7BK-4/2/edea39cc51bbd43d00faaaa0733ae52c.
    [CrossRef]
  7. C. Florea and K. A. Winick, "Fabrication and Characterization of PhotonicDevices Directly Written in Glass using Femtosecond Laser Pulses," J. Lightwave Technol. 21, 246-253 (2003). http://jlt.osa.org/abstract.cfm?URI=JLT-21-1-246.
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  10. 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. Express 16, 5481-5492 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-8-5481.
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    [CrossRef]
  12. G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. Lederer, and U. Morgner, "Passively modelocked and cavity-dumped Yb:KY(WO4)2 oscillator with positive dispersion," Opt. Express 15, 16017-16021 (2007). http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16017.
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2008 (3)

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. Express 16, 12,786-12,793 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-12786.

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. Express 16, 5481-5492 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-8-5481.
[CrossRef] [PubMed]

A. Steinmann, G. Palmer, M. Emons, M. Siegel, and U. Morgner, "Generation of 9-μJ 420-fs Pulses by Fiber-Based Amplification of a Cavity-Dumped Yb:KYW Laser Oscillator," Laser Phys. 18, 527-529 (2008).
[CrossRef]

2007 (1)

2005 (4)

S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, "Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate," Opt. Express 13, 4708-4716 (2005). http://www.opticsexpress.org/abstract.cfm?URI=oe-13-12-4708.
[CrossRef] [PubMed]

R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
[CrossRef]

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, "Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser," Opt. Commun. 253, 315-319 (2005). http://www.sciencedirect.com/science/article/B6TVF-4G6J7BK-4/2/edea39cc51bbd43d00faaaa0733ae52c.
[CrossRef]

L. Shah, A. Arai, S. Eaton, and P. Herman, "Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate," Opt. Express 13, 1999-2006 (2005). http://www.opticsexpress.org/abstract.cfm?URI=oe-13-6-1999.
[CrossRef] [PubMed]

2004 (1)

2003 (3)

S. Nolte, M. Will, J. Burghoff, and A. Tunnermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A 77, 109-111 (2003).
[CrossRef]

C. Florea and K. A. Winick, "Fabrication and Characterization of PhotonicDevices Directly Written in Glass using Femtosecond Laser Pulses," J. Lightwave Technol. 21, 246-253 (2003). http://jlt.osa.org/abstract.cfm?URI=JLT-21-1-246.
[CrossRef]

C. Schaffer, J. Garcia, and E. Mazur, "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

2002 (1)

2001 (1)

1999 (1)

1972 (1)

Apter, B.

Arai, A.

Audouard, E.

Bahat-Treidel, E.

Beecher, S.

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. Express 16, 12,786-12,793 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-12786.

Bockelt, A. S.

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. Express 16, 12,786-12,793 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-12786.

Boivin, L. P.

Borrelli, N. F.

Bovatsek, J.

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tunnermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A 77, 109-111 (2003).
[CrossRef]

Cerullo, G.

R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
[CrossRef]

Chang, S.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, "Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser," Opt. Commun. 253, 315-319 (2005). http://www.sciencedirect.com/science/article/B6TVF-4G6J7BK-4/2/edea39cc51bbd43d00faaaa0733ae52c.
[CrossRef]

Chiodo, N.

R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
[CrossRef]

Eaton, S.

Efron, U.

Emons, M.

A. Steinmann, G. Palmer, M. Emons, M. Siegel, and U. Morgner, "Generation of 9-μJ 420-fs Pulses by Fiber-Based Amplification of a Cavity-Dumped Yb:KYW Laser Oscillator," Laser Phys. 18, 527-529 (2008).
[CrossRef]

G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. Lederer, and U. Morgner, "Passively modelocked and cavity-dumped Yb:KY(WO4)2 oscillator with positive dispersion," Opt. Express 15, 16017-16021 (2007). http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16017.
[CrossRef] [PubMed]

Florea, C.

Flueraru, C.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, "Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser," Opt. Commun. 253, 315-319 (2005). http://www.sciencedirect.com/science/article/B6TVF-4G6J7BK-4/2/edea39cc51bbd43d00faaaa0733ae52c.
[CrossRef]

Fujimoto, J. G.

Gaeta, A. L.

Garcia, J.

C. Schaffer, J. Garcia, and E. Mazur, "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

Greenaway, A. H.

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. Express 16, 12,786-12,793 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-12786.

Grover, C. P.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, "Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser," Opt. Commun. 253, 315-319 (2005). http://www.sciencedirect.com/science/article/B6TVF-4G6J7BK-4/2/edea39cc51bbd43d00faaaa0733ae52c.
[CrossRef]

Herman, P.

Homoelle, D.

Huot, N.

Ippen, E. P.

Kar, A. K.

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. Express 16, 12,786-12,793 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-12786.

Kowalevicz, A. M.

Lederer, M.

Liu, J.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, "Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser," Opt. Commun. 253, 315-319 (2005). http://www.sciencedirect.com/science/article/B6TVF-4G6J7BK-4/2/edea39cc51bbd43d00faaaa0733ae52c.
[CrossRef]

Maselli, V.

R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
[CrossRef]

Mauclair, C.

Mazur, E.

C. Schaffer, J. Garcia, and E. Mazur, "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

Mermillod-Blondin, A.

Minoshima, K.

Morgner, U.

A. Steinmann, G. Palmer, M. Emons, M. Siegel, and U. Morgner, "Generation of 9-μJ 420-fs Pulses by Fiber-Based Amplification of a Cavity-Dumped Yb:KYW Laser Oscillator," Laser Phys. 18, 527-529 (2008).
[CrossRef]

G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. Lederer, and U. Morgner, "Passively modelocked and cavity-dumped Yb:KY(WO4)2 oscillator with positive dispersion," Opt. Express 15, 16017-16021 (2007). http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16017.
[CrossRef] [PubMed]

Nolte, S.

S. Nolte, M. Will, J. Burghoff, and A. Tunnermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A 77, 109-111 (2003).
[CrossRef]

Osellame, R.

R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
[CrossRef]

Palmer, G.

A. Steinmann, G. Palmer, M. Emons, M. Siegel, and U. Morgner, "Generation of 9-μJ 420-fs Pulses by Fiber-Based Amplification of a Cavity-Dumped Yb:KYW Laser Oscillator," Laser Phys. 18, 527-529 (2008).
[CrossRef]

G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. Lederer, and U. Morgner, "Passively modelocked and cavity-dumped Yb:KY(WO4)2 oscillator with positive dispersion," Opt. Express 15, 16017-16021 (2007). http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16017.
[CrossRef] [PubMed]

Polli, D.

R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
[CrossRef]

Ramponi, R.

R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
[CrossRef]

Ramsay, E.

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. Express 16, 12,786-12,793 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-12786.

Reid, D. T.

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. Express 16, 12,786-12,793 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-12786.

Schaffer, C.

C. Schaffer, J. Garcia, and E. Mazur, "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

Schultze, M.

Shah, L.

Siegel, M.

A. Steinmann, G. Palmer, M. Emons, M. Siegel, and U. Morgner, "Generation of 9-μJ 420-fs Pulses by Fiber-Based Amplification of a Cavity-Dumped Yb:KYW Laser Oscillator," Laser Phys. 18, 527-529 (2008).
[CrossRef]

G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. Lederer, and U. Morgner, "Passively modelocked and cavity-dumped Yb:KY(WO4)2 oscillator with positive dispersion," Opt. Express 15, 16017-16021 (2007). http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16017.
[CrossRef] [PubMed]

Smith, C.

Steinmann, A.

A. Steinmann, G. Palmer, M. Emons, M. Siegel, and U. Morgner, "Generation of 9-μJ 420-fs Pulses by Fiber-Based Amplification of a Cavity-Dumped Yb:KYW Laser Oscillator," Laser Phys. 18, 527-529 (2008).
[CrossRef]

G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. Lederer, and U. Morgner, "Passively modelocked and cavity-dumped Yb:KY(WO4)2 oscillator with positive dispersion," Opt. Express 15, 16017-16021 (2007). http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16017.
[CrossRef] [PubMed]

Stoian, R.

Streltsov, A. M.

T¨unnermann, A.

S. Nolte, M. Will, J. Burghoff, and A. Tunnermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A 77, 109-111 (2003).
[CrossRef]

Thomson, R. R.

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. Express 16, 12,786-12,793 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-12786.

Vazquez, R. M.

R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
[CrossRef]

Wielandy, S.

Will, M.

S. Nolte, M. Will, J. Burghoff, and A. Tunnermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A 77, 109-111 (2003).
[CrossRef]

Winick, K. A.

Yoshino, F.

Zhang, H.

Zhang, Z.

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, "Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser," Opt. Commun. 253, 315-319 (2005). http://www.sciencedirect.com/science/article/B6TVF-4G6J7BK-4/2/edea39cc51bbd43d00faaaa0733ae52c.
[CrossRef]

Appl. Opt. (2)

Appl. Phys. A (2)

C. Schaffer, J. Garcia, and E. Mazur, "Bulk heating of transparent materials using a high-repetition-rate femtosecond laser," Appl. Phys. A 76, 351-354 (2003).
[CrossRef]

S. Nolte, M. Will, J. Burghoff, and A. Tunnermann, "Femtosecond waveguide writing: a new avenue to threedimensional integrated optics," Appl. Phys. A 77, 109-111 (2003).
[CrossRef]

Electron. Lett. (1)

R. Osellame, V. Maselli, N. Chiodo, D. Polli, R. M. Vazquez, R. Ramponi, and G. Cerullo, "Fabrication of 3D photonic devices at 1.55 μm wavelength by femtosecond Ti:Sapphire oscillator," Electron. Lett. 41, 315-317 (2005).
[CrossRef]

J. Lightwave Technol. (1)

Laser Phys. (1)

A. Steinmann, G. Palmer, M. Emons, M. Siegel, and U. Morgner, "Generation of 9-μJ 420-fs Pulses by Fiber-Based Amplification of a Cavity-Dumped Yb:KYW Laser Oscillator," Laser Phys. 18, 527-529 (2008).
[CrossRef]

Opt. Commun. (1)

J. Liu, Z. Zhang, S. Chang, C. Flueraru, and C. P. Grover, "Directly writing of 1-to-N optical waveguide power splitters in fused silica glass using a femtosecond laser," Opt. Commun. 253, 315-319 (2005). http://www.sciencedirect.com/science/article/B6TVF-4G6J7BK-4/2/edea39cc51bbd43d00faaaa0733ae52c.
[CrossRef]

Opt. Express (6)

K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, "Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing," Opt. Express 10, 645-652 (2002). http://www.opticsexpress.org/abstract.cfm?URI=oe-10-15-645.
[PubMed]

G. Palmer, M. Emons, M. Siegel, A. Steinmann, M. Schultze, M. Lederer, and U. Morgner, "Passively modelocked and cavity-dumped Yb:KY(WO4)2 oscillator with positive dispersion," Opt. Express 15, 16017-16021 (2007). http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16017.
[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. Express 16, 12,786-12,793 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-17-12786.

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. Express 16, 5481-5492 (2008). http://www.opticsexpress.org/abstract.cfm?URI=oe-16-8-5481.
[CrossRef] [PubMed]

L. Shah, A. Arai, S. Eaton, and P. Herman, "Waveguide writing in fused silica with a femtosecond fiber laser at 522 nm and 1 MHz repetition rate," Opt. Express 13, 1999-2006 (2005). http://www.opticsexpress.org/abstract.cfm?URI=oe-13-6-1999.
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S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, "Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate," Opt. Express 13, 4708-4716 (2005). http://www.opticsexpress.org/abstract.cfm?URI=oe-13-12-4708.
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Opt. Lett. (2)

Other (3)

Y. Gu, J.-H. Chung, and J. G. Fujimoto, "Femtosecond Laser Fabrication of Directional Couplers and Mach-Zehnder Interferometers," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, p. CThS3 (Optical Society of America, 2007).http://www.opticsinfobase.org/abstract.cfm?URI=URI=CLEO-2007-CThS3.
[PubMed]

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W. J. Reichman, D. M. Krol, L. Shah, F. Yoshino, A. Arai, S. M. Eaton, and P. R. Herman, "A spectroscopic comparison of femtosecond-laser-modified fused silica using kilohertz and megahertz laser systems," Journal of Applied Physics 99, 123112 (pages 5) (2006).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

aveguide writing setup.

Fig. 2.
Fig. 2.

Diffraction at rectangular phase grating for multiple periods. The left image shows the evolution of intensity in diffraction orders and the right one the separation into two foci at π-phase.

Fig. 3.
Fig. 3.

1) 175.3 μm (10 px), 2) 87.7 μm (20 px), 3) 43.8 μm (40 px), 4) 21.9 μm (80 px), 5) 11.0 μm (160 px), 6) 7.2 μm (240 px). The numbers in brackets indicate the phase grating period in pixels. The scaling is equal in all images.

Fig. 4.
Fig. 4.

Separation between double waveguides depending on the applied phase grating period. The separation was measured using the calibrated microscope images, see figure 3.

Fig. 5.
Fig. 5.

Left panel: guided mode near field of one of the waveguides shown in Fig.3.1; fabrication parameters: 500 nJ and 500 μm/s. Right panel: intensity profiles in the x- and z-axis; comparison between the waveguide mode (solid line) and that of a standard telecom fiber (dashed line).

Fig. 6.
Fig. 6.

Coupler Setup. The variables D and d indicate the maximum and minimum separation. See text for a detailed description of the coupler layout.

Fig. 7.
Fig. 7.

Left panel: simulated phase variation applied to the SLM for the coupler fabrication. Right panel: simulation by the Fourier transform of each grating in steps of 10 ms of the time dependent position of the different foci. Numbers 1 to 5 indicate the sections introduced in Fig. 6.

Fig. 8.
Fig. 8.

Microscope images of the couplers written in glass. The image is composed by stitching together several images, each scaled down in width by a factor of 20. The image on the left shows couplers with an outer separation of 175 μm and a center separation of 11 μm and 22 μm. The image on the right shows couplers with an outer separation of 88 ¼m and center separations of 8 μm , 11 μm and 22 μm.

Fig. 9.
Fig. 9.

Near fields of the coupler outputs with light launched into the left waveguide. The writing parameters were 500 nJ per waveguide and 100 μm/s. Left panel: coupler with center separation of 11 μm. The cross-coupling-ratio is 45 %. Right panel: coupler with center separation of 8 μm. The cross-coupling-ratio is 94 %.

Equations (2)

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P 1 ( z ) P 0 = cos 2 ( γz ) + ( Δ β 2 γ ) 2 sin 2 ( γz )
P 2 ( z ) P 0 = C 2 γ 2 sin 2 ( γz ) with γ 2 = C 2 + ( Δ β 2 ) 2

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