Abstract

The use of femtosecond lasers to introduce controlled stress states has recently been demonstrated in silica glass. We use this technique, in combination with chemical etching, to generate and control stress-induced birefringence over a well-defined region of interest, demonstrating direct-write wave plates with precisely tailored retardance levels. This tailoring enables the fabrication of laser-written polarization optics that can be tuned to any wavelength for which silica is transparent, and with a clear aperture free of any laser modifications. Using this approach, we achieve sufficient retardance to act as a quarter-wave plate. The stress distribution within the clear aperture is analyzed and modeled, providing a generic template that can be used as a set of design rules for laser-machined polarization devices.

© 2016 Optical Society of America

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2016 (1)

C.-E. Athanasiou and Y. Bellouard, “Investigation of the micro-mechanical properties of femtosecond laser-induced phases in amorphous silica,” Proc. SPIE 9740, 97401E (2016).
[Crossref]

2015 (8)

T. Yang and Y. Bellouard, “Monolithic transparent 3D dielectrophoretic micro-actuator fabricated by femtosecond laser,” J. Micromech. Microeng. 25(10), 105009 (2015).
[Crossref]

B. McMillen and Y. Bellouard, “On the anisotropy of stress-distribution induced in glasses and crystals by non-ablative femtosecond laser exposure,” Opt. Express 23(1), 86–100 (2015).
[Crossref] [PubMed]

Y. Bellouard, A. Champion, B. McMillen, S. Mukherjee, R. Thomson, and Y. Cheng, “Femtosecond laser-induced stress-state inversion and related anisotropies,” Opt. Express 23, 86–100 (2015).
[Crossref]

C.-E. Athanasiou and Y. Bellouard, “A monolithic micro-tensile tester for investigating silicon dioxide polymorph micromechanics, fabricated and operated using a femtosecond laser,” Micromachines (Basel) 6(9), 1365–1386 (2015).
[Crossref]

Y. Bellouard, “Non-contact sub-nanometer optical repositioning using femtosecond lasers,” Opt. Express 23(22), 29258–29267 (2015).
[Crossref] [PubMed]

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photonics Rev. 9(4), 363–384 (2015).
[Crossref]

J. Tang, J. Lin, J. Song, Z. Fang, M. Wang, Y. Liao, L. Qiao, and Y. Cheng, “On-chip tuning of the resonant wavelength in a high-Q microresonator integrated with a microheater,” Int. J. Optomechatronics 9(2), 187–194 (2015).
[Crossref]

L. A. Fernandes, J. R. Grenier, J. S. Aitchison, and P. R. Herman, “Fiber optic stress-independent helical torsion sensor,” Opt. Lett. 40(4), 657–660 (2015).
[Crossref] [PubMed]

2013 (2)

S. B. Mehta, M. Shribak, and R. Oldenbourg, “Polarized light imaging of birefringence and diattenuation at high resolution and high sensitivity,” J. Opt. 15(9), 094007 (2013).
[Crossref] [PubMed]

A. Champion, M. Beresna, P. Kazansky, and Y. Bellouard, “Stress distribution around femtosecond laser affected zones: effect of nanogratings orientation,” Opt. Express 21(21), 24942–24951 (2013).
[Crossref] [PubMed]

2012 (4)

Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
[Crossref]

A. Champion and Y. Bellouard, “Direct volume variation measurements in fused silica specimens exposed to femtosecond laser,” Opt. Mater. Express 2(6), 789–798 (2012).
[Crossref]

F. Hecht, “New development in FreeFem++,” J. Numer. Math. 20(3-4), 251–266 (2012), http://www.freefem.org .
[Crossref]

B. Lenssen and Y. Bellouard, “Optically transparent glass micro-actuator fabricated by femtosecond laser exposure and chemical etching,” Appl. Phys. Lett. 101(10), 103503 (2012).
[Crossref]

2011 (4)

A. Schaap, Y. Bellouard, and T. Rohrlack, “Optofluidic lab-on-a-chip for rapid algae population screening,” Biomed. Opt. Express 2(3), 658–664 (2011).
[Crossref] [PubMed]

Y. Hanada, K. Sugioka, I. Shihira-Ishikawa, H. Kawano, A. Miyawaki, and K. Midorikawa, “3D microfluidic chips with integrated functional microelements fabricated by a femtosecond laser for studying the gliding mechanism of cyanobacteria,” Lab Chip 11(12), 2109–2115 (2011).
[Crossref] [PubMed]

M. Beresna, M. Gecevičius, and P. G. Kazansky, “Polarization sensitive elements fabricated by femtosecond laser nanostructuring of glass [Invited],” Opt. Mater. Express 1(4), 783–795 (2011).
[Crossref]

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

2010 (3)

2007 (1)

2006 (1)

H. Zhang, S. M. Eaton, J. Li, and P. R. Herman, “Type II femtosecond laser writing of Bragg grating waveguides in bulk glass,” Electron. Lett. 42(21), 1223–1224 (2006).
[Crossref]

2005 (1)

2004 (3)

2003 (1)

Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
[Crossref] [PubMed]

2002 (1)

R. Osellame, S. Taccheo, G. Cerullo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Optical gain in Er-Yb doped waveguides fabricated by femtosecond laser pulses,” Electron. Lett. 38(17), 964–965 (2002).
[Crossref]

2001 (2)

1998 (1)

Y. Kondo, T. Suzuki, H. Inouye, K. Miura, T. Mitsuyu, and K. Hirao, “Three-dimensional microscopic crystallization in photosensitive glass by femtosecond laser pulses at nonresonant wavelength,” Jpn. J. Appl. Phys. 37(Part 2, No. 1A/B), L94–L96 (1998).
[Crossref]

1997 (1)

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71(23), 3329–3331 (1997).
[Crossref]

1996 (1)

1972 (1)

T. N. Vasudevan and R. S. Krishnan, “Dispersion of the stress-optic coefficient in glasses,” J. Phys. D Appl. Phys. 5(12), 2283–2287 (1972).
[Crossref]

1903 (1)

L. N. G. Filon, “On an approximate solution for the bending of a beam of rectangular cross-section under any system of load, with special reference to points of concentrated or discontinuous loading,” Philos. Trans. Royal Soc. London 201(331-345), 63–155 (1903).
[Crossref]

Aitchison, J. S.

Athanasiou, C.-E.

C.-E. Athanasiou and Y. Bellouard, “Investigation of the micro-mechanical properties of femtosecond laser-induced phases in amorphous silica,” Proc. SPIE 9740, 97401E (2016).
[Crossref]

C.-E. Athanasiou and Y. Bellouard, “A monolithic micro-tensile tester for investigating silicon dioxide polymorph micromechanics, fabricated and operated using a femtosecond laser,” Micromachines (Basel) 6(9), 1365–1386 (2015).
[Crossref]

Bado, P.

Barrot, F.

Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
[Crossref]

Bellini, N.

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

Bellouard, Y.

C.-E. Athanasiou and Y. Bellouard, “Investigation of the micro-mechanical properties of femtosecond laser-induced phases in amorphous silica,” Proc. SPIE 9740, 97401E (2016).
[Crossref]

C.-E. Athanasiou and Y. Bellouard, “A monolithic micro-tensile tester for investigating silicon dioxide polymorph micromechanics, fabricated and operated using a femtosecond laser,” Micromachines (Basel) 6(9), 1365–1386 (2015).
[Crossref]

T. Yang and Y. Bellouard, “Monolithic transparent 3D dielectrophoretic micro-actuator fabricated by femtosecond laser,” J. Micromech. Microeng. 25(10), 105009 (2015).
[Crossref]

Y. Bellouard, “Non-contact sub-nanometer optical repositioning using femtosecond lasers,” Opt. Express 23(22), 29258–29267 (2015).
[Crossref] [PubMed]

B. McMillen and Y. Bellouard, “On the anisotropy of stress-distribution induced in glasses and crystals by non-ablative femtosecond laser exposure,” Opt. Express 23(1), 86–100 (2015).
[Crossref] [PubMed]

Y. Bellouard, A. Champion, B. McMillen, S. Mukherjee, R. Thomson, and Y. Cheng, “Femtosecond laser-induced stress-state inversion and related anisotropies,” Opt. Express 23, 86–100 (2015).
[Crossref]

A. Champion, M. Beresna, P. Kazansky, and Y. Bellouard, “Stress distribution around femtosecond laser affected zones: effect of nanogratings orientation,” Opt. Express 21(21), 24942–24951 (2013).
[Crossref] [PubMed]

A. Champion and Y. Bellouard, “Direct volume variation measurements in fused silica specimens exposed to femtosecond laser,” Opt. Mater. Express 2(6), 789–798 (2012).
[Crossref]

B. Lenssen and Y. Bellouard, “Optically transparent glass micro-actuator fabricated by femtosecond laser exposure and chemical etching,” Appl. Phys. Lett. 101(10), 103503 (2012).
[Crossref]

Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
[Crossref]

A. Schaap, Y. Bellouard, and T. Rohrlack, “Optofluidic lab-on-a-chip for rapid algae population screening,” Biomed. Opt. Express 2(3), 658–664 (2011).
[Crossref] [PubMed]

S. Rajesh and Y. Bellouard, “Towards fast femtosecond laser micromachining of fused silica: The effect of deposited energy,” Opt. Express 18(20), 21490–21497 (2010).
[Crossref] [PubMed]

Y. Bellouard, A. Said, and P. Bado, “Integrating optics and micro-mechanics in a single substrate: a step toward monolithic integration in fused silica,” Opt. Express 13(17), 6635–6644 (2005).
[Crossref] [PubMed]

Y. Bellouard, A. Said, M. Dugan, and P. Bado, “Fabrication of high-aspect ratio, micro-fluidic channels and tunnels using femtosecond laser pulses and chemical etching,” Opt. Express 12(10), 2120–2129 (2004).
[Crossref] [PubMed]

Beresna, M.

A. Champion, M. Beresna, P. Kazansky, and Y. Bellouard, “Stress distribution around femtosecond laser affected zones: effect of nanogratings orientation,” Opt. Express 21(21), 24942–24951 (2013).
[Crossref] [PubMed]

Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
[Crossref]

M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

M. Beresna, M. Gecevičius, and P. G. Kazansky, “Polarization sensitive elements fabricated by femtosecond laser nanostructuring of glass [Invited],” Opt. Mater. Express 1(4), 783–795 (2011).
[Crossref]

Bottinelli, S.

Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
[Crossref]

Boukenter, A.

Bragheri, F.

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

Breguet, J. M.

Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
[Crossref]

Bricchi, E.

Brown, T. G.

Burakov, I. M.

Cerullo, G.

R. Osellame, S. Taccheo, G. Cerullo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Optical gain in Er-Yb doped waveguides fabricated by femtosecond laser pulses,” Electron. Lett. 38(17), 964–965 (2002).
[Crossref]

Champion, A.

Chappuis, O.

Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
[Crossref]

Cheng, G.

Cheng, Y.

Clavel, R.

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Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
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S. B. Mehta, M. Shribak, and R. Oldenbourg, “Polarized light imaging of birefringence and diattenuation at high resolution and high sensitivity,” J. Opt. 15(9), 094007 (2013).
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Y. Hanada, K. Sugioka, I. Shihira-Ishikawa, H. Kawano, A. Miyawaki, and K. Midorikawa, “3D microfluidic chips with integrated functional microelements fabricated by a femtosecond laser for studying the gliding mechanism of cyanobacteria,” Lab Chip 11(12), 2109–2115 (2011).
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Minzioni, P.

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
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Y. Kondo, T. Suzuki, H. Inouye, K. Miura, T. Mitsuyu, and K. Hirao, “Three-dimensional microscopic crystallization in photosensitive glass by femtosecond laser pulses at nonresonant wavelength,” Jpn. J. Appl. Phys. 37(Part 2, No. 1A/B), L94–L96 (1998).
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K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71(23), 3329–3331 (1997).
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Y. Kondo, T. Suzuki, H. Inouye, K. Miura, T. Mitsuyu, and K. Hirao, “Three-dimensional microscopic crystallization in photosensitive glass by femtosecond laser pulses at nonresonant wavelength,” Jpn. J. Appl. Phys. 37(Part 2, No. 1A/B), L94–L96 (1998).
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K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71(23), 3329–3331 (1997).
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Y. Hanada, K. Sugioka, I. Shihira-Ishikawa, H. Kawano, A. Miyawaki, and K. Midorikawa, “3D microfluidic chips with integrated functional microelements fabricated by a femtosecond laser for studying the gliding mechanism of cyanobacteria,” Lab Chip 11(12), 2109–2115 (2011).
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Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
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S. B. Mehta, M. Shribak, and R. Oldenbourg, “Polarized light imaging of birefringence and diattenuation at high resolution and high sensitivity,” J. Opt. 15(9), 094007 (2013).
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F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
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R. Osellame, S. Taccheo, G. Cerullo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Optical gain in Er-Yb doped waveguides fabricated by femtosecond laser pulses,” Electron. Lett. 38(17), 964–965 (2002).
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T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photonics Rev. 9(4), 363–384 (2015).
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R. Osellame, S. Taccheo, G. Cerullo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Optical gain in Er-Yb doped waveguides fabricated by femtosecond laser pulses,” Electron. Lett. 38(17), 964–965 (2002).
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J. Tang, J. Lin, J. Song, Z. Fang, M. Wang, Y. Liao, L. Qiao, and Y. Cheng, “On-chip tuning of the resonant wavelength in a high-Q microresonator integrated with a microheater,” Int. J. Optomechatronics 9(2), 187–194 (2015).
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Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
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K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71(23), 3329–3331 (1997).
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Ramponi, R.

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
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R. Osellame, S. Taccheo, G. Cerullo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Optical gain in Er-Yb doped waveguides fabricated by femtosecond laser pulses,” Electron. Lett. 38(17), 964–965 (2002).
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[Crossref] [PubMed]

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Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
[Crossref] [PubMed]

Shribak, M.

S. B. Mehta, M. Shribak, and R. Oldenbourg, “Polarized light imaging of birefringence and diattenuation at high resolution and high sensitivity,” J. Opt. 15(9), 094007 (2013).
[Crossref] [PubMed]

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J. Tang, J. Lin, J. Song, Z. Fang, M. Wang, Y. Liao, L. Qiao, and Y. Cheng, “On-chip tuning of the resonant wavelength in a high-Q microresonator integrated with a microheater,” Int. J. Optomechatronics 9(2), 187–194 (2015).
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Steel, M. J.

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photonics Rev. 9(4), 363–384 (2015).
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Y. Hanada, K. Sugioka, I. Shihira-Ishikawa, H. Kawano, A. Miyawaki, and K. Midorikawa, “3D microfluidic chips with integrated functional microelements fabricated by a femtosecond laser for studying the gliding mechanism of cyanobacteria,” Lab Chip 11(12), 2109–2115 (2011).
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Y. Cheng, K. Sugioka, and K. Midorikawa, “Microfluidic laser embedded in glass by three-dimensional femtosecond laser microprocessing,” Opt. Lett. 29(17), 2007–2009 (2004).
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T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photonics Rev. 9(4), 363–384 (2015).
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R. Osellame, S. Taccheo, G. Cerullo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Optical gain in Er-Yb doped waveguides fabricated by femtosecond laser pulses,” Electron. Lett. 38(17), 964–965 (2002).
[Crossref]

Tang, J.

J. Tang, J. Lin, J. Song, Z. Fang, M. Wang, Y. Liao, L. Qiao, and Y. Cheng, “On-chip tuning of the resonant wavelength in a high-Q microresonator integrated with a microheater,” Int. J. Optomechatronics 9(2), 187–194 (2015).
[Crossref]

Thomson, R.

Vasudevan, T. N.

T. N. Vasudevan and R. S. Krishnan, “Dispersion of the stress-optic coefficient in glasses,” J. Phys. D Appl. Phys. 5(12), 2283–2287 (1972).
[Crossref]

Vishnubhatla, K. C.

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

Wang, M.

J. Tang, J. Lin, J. Song, Z. Fang, M. Wang, Y. Liao, L. Qiao, and Y. Cheng, “On-chip tuning of the resonant wavelength in a high-Q microresonator integrated with a microheater,” Int. J. Optomechatronics 9(2), 187–194 (2015).
[Crossref]

Watanabe, M.

Withford, M. J.

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photonics Rev. 9(4), 363–384 (2015).
[Crossref]

Yang, T.

T. Yang and Y. Bellouard, “Monolithic transparent 3D dielectrophoretic micro-actuator fabricated by femtosecond laser,” J. Micromech. Microeng. 25(10), 105009 (2015).
[Crossref]

Zhang, H.

H. Zhang, S. M. Eaton, J. Li, and P. R. Herman, “Type II femtosecond laser writing of Bragg grating waveguides in bulk glass,” Electron. Lett. 42(21), 1223–1224 (2006).
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Appl. Opt. (1)

Appl. Phys. Lett. (3)

K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, and K. Hirao, “Photowritten optical waveguides in various glasses with ultrashort pulse laser,” Appl. Phys. Lett. 71(23), 3329–3331 (1997).
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M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

B. Lenssen and Y. Bellouard, “Optically transparent glass micro-actuator fabricated by femtosecond laser exposure and chemical etching,” Appl. Phys. Lett. 101(10), 103503 (2012).
[Crossref]

Biomed. Opt. Express (1)

Electron. Lett. (2)

R. Osellame, S. Taccheo, G. Cerullo, M. Marangoni, D. Polli, R. Ramponi, P. Laporta, and S. De Silvestri, “Optical gain in Er-Yb doped waveguides fabricated by femtosecond laser pulses,” Electron. Lett. 38(17), 964–965 (2002).
[Crossref]

H. Zhang, S. M. Eaton, J. Li, and P. R. Herman, “Type II femtosecond laser writing of Bragg grating waveguides in bulk glass,” Electron. Lett. 42(21), 1223–1224 (2006).
[Crossref]

Int. J. Optomechatronics (1)

J. Tang, J. Lin, J. Song, Z. Fang, M. Wang, Y. Liao, L. Qiao, and Y. Cheng, “On-chip tuning of the resonant wavelength in a high-Q microresonator integrated with a microheater,” Int. J. Optomechatronics 9(2), 187–194 (2015).
[Crossref]

J. Biophotonics (1)

F. Bragheri, L. Ferrara, N. Bellini, K. C. Vishnubhatla, P. Minzioni, R. Ramponi, R. Osellame, and I. Cristiani, “Optofluidic chip for single cell trapping and stretching fabricated by a femtosecond laser,” J. Biophotonics 3(4), 234–243 (2010).
[Crossref] [PubMed]

J. Laser Micro Nanoeng. (1)

Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevičius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The femtoprint project,” J. Laser Micro Nanoeng. 7(1), 1–10 (2012).
[Crossref]

J. Micromech. Microeng. (1)

T. Yang and Y. Bellouard, “Monolithic transparent 3D dielectrophoretic micro-actuator fabricated by femtosecond laser,” J. Micromech. Microeng. 25(10), 105009 (2015).
[Crossref]

J. Numer. Math. (1)

F. Hecht, “New development in FreeFem++,” J. Numer. Math. 20(3-4), 251–266 (2012), http://www.freefem.org .
[Crossref]

J. Opt. (1)

S. B. Mehta, M. Shribak, and R. Oldenbourg, “Polarized light imaging of birefringence and diattenuation at high resolution and high sensitivity,” J. Opt. 15(9), 094007 (2013).
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J. Phys. D Appl. Phys. (1)

T. N. Vasudevan and R. S. Krishnan, “Dispersion of the stress-optic coefficient in glasses,” J. Phys. D Appl. Phys. 5(12), 2283–2287 (1972).
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Jpn. J. Appl. Phys. (1)

Y. Kondo, T. Suzuki, H. Inouye, K. Miura, T. Mitsuyu, and K. Hirao, “Three-dimensional microscopic crystallization in photosensitive glass by femtosecond laser pulses at nonresonant wavelength,” Jpn. J. Appl. Phys. 37(Part 2, No. 1A/B), L94–L96 (1998).
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Lab Chip (1)

Y. Hanada, K. Sugioka, I. Shihira-Ishikawa, H. Kawano, A. Miyawaki, and K. Midorikawa, “3D microfluidic chips with integrated functional microelements fabricated by a femtosecond laser for studying the gliding mechanism of cyanobacteria,” Lab Chip 11(12), 2109–2115 (2011).
[Crossref] [PubMed]

Laser Photonics Rev. (1)

T. Meany, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photonics Rev. 9(4), 363–384 (2015).
[Crossref]

Micromachines (Basel) (1)

C.-E. Athanasiou and Y. Bellouard, “A monolithic micro-tensile tester for investigating silicon dioxide polymorph micromechanics, fabricated and operated using a femtosecond laser,” Micromachines (Basel) 6(9), 1365–1386 (2015).
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Opt. Express (8)

S. Rajesh and Y. Bellouard, “Towards fast femtosecond laser micromachining of fused silica: The effect of deposited energy,” Opt. Express 18(20), 21490–21497 (2010).
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K. Mishchik, G. Cheng, G. Huo, I. M. Burakov, C. Mauclair, A. Mermillod-Blondin, A. Rosenfeld, Y. Ouerdane, A. Boukenter, O. Parriaux, and R. Stoian, “Nanosize structural modifications with polarization functions in ultrafast laser irradiated bulk fused silica,” Opt. Express 18(24), 24809–24824 (2010).
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Y. Bellouard, A. Said, M. Dugan, and P. Bado, “Fabrication of high-aspect ratio, micro-fluidic channels and tunnels using femtosecond laser pulses and chemical etching,” Opt. Express 12(10), 2120–2129 (2004).
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A. Champion, M. Beresna, P. Kazansky, and Y. Bellouard, “Stress distribution around femtosecond laser affected zones: effect of nanogratings orientation,” Opt. Express 21(21), 24942–24951 (2013).
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B. McMillen and Y. Bellouard, “On the anisotropy of stress-distribution induced in glasses and crystals by non-ablative femtosecond laser exposure,” Opt. Express 23(1), 86–100 (2015).
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Y. Bellouard, A. Champion, B. McMillen, S. Mukherjee, R. Thomson, and Y. Cheng, “Femtosecond laser-induced stress-state inversion and related anisotropies,” Opt. Express 23, 86–100 (2015).
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Y. Bellouard, A. Said, and P. Bado, “Integrating optics and micro-mechanics in a single substrate: a step toward monolithic integration in fused silica,” Opt. Express 13(17), 6635–6644 (2005).
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Y. Bellouard, “Non-contact sub-nanometer optical repositioning using femtosecond lasers,” Opt. Express 23(22), 29258–29267 (2015).
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Philos. Trans. Royal Soc. London (1)

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Y. Shimotsuma, P. G. Kazansky, J. Qiu, and K. Hirao, “Self-organized nanogratings in glass irradiated by ultrashort light pulses,” Phys. Rev. Lett. 91(24), 247405 (2003).
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Proc. SPIE (1)

C.-E. Athanasiou and Y. Bellouard, “Investigation of the micro-mechanical properties of femtosecond laser-induced phases in amorphous silica,” Proc. SPIE 9740, 97401E (2016).
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Figures (8)

Fig. 1
Fig. 1 Microscope image of a laser-machined waveplate. In this arrangement, a clear aperture (c) is defined by a pair of horizontal cuts (a), fabricated using a wet-etch-assisted laser machining process [31]. Stress-induced birefringence is then generated in this aperture by writing a set of vertical lines (labeled ‘stressor bar’, (b)) within the bulk of the substrate at each end of the device, using exposure conditions sufficient to generate nanogratings. Here, the writing polarization, and hence the orientation of the nanogratings, is chosen such that the generated stress behaves like a quasi-uniaxial loading, as indicated by the red arrows.
Fig. 2
Fig. 2 (a) Retardance as a function of the energy deposited for a pulse energy of 250 nJ and a line spacing of 10 μm. All devices were written with 16 stressors per side (32 stressors total per device). For these writing conditions, it was found that the stress peaks for a deposited energy of 20 J/mm2. The images in (b)-(d) show a magnified view of the retardance map for three waveplates spanning the range over the peak shown in (a), with deposited energy values of 10, 20, and 30 J/mm2 respectively.
Fig. 3
Fig. 3 Waveplate retardance as a function of the number of stressors and stressor spacing. (a) and (b) show retardance maps for a stressor spacing of 10 μm, with 16 and 32 stressors per side, respectively. Devices (c) and (d) are similar, but for a stressor spacing of 5 um and 32 and 64 stressors per side, respectively. All devices were written with a deposited energy of 20 J/mm2, with the laser polarization fixed parallel to the long axis of each device. For comparison, the device shown in (a) has a peak center retardance of ~15 nm, while the device in (d) is considerably higher at ~55 nm.
Fig. 4
Fig. 4 (a) 3D visualization of a waveplate, highlighting the various regions taken into consideration in the 1D spring model. (b) Expanded view of the stressor region, showing the composite nature of the structure. (c) Lumped spring model used to predict the retardance in the center of the clear aperture as a function of the number of stressors.
Fig. 5
Fig. 5 Prediction of waveplate retardance as a function of the number and spacing of machined stressors using the 1D stiffness model outlined in section 4.1. Here, the individual data points the developed retardance in each waveplate (measured in the center of the clear aperture for each device shown in Fig. 3), while the curves are the predicted values based on the model. For each measured data point, the error was estimated from the measurement noise, which on average was not greater than ± 1 nm. The reader should note that the measured data points shown in the above graph compare different sizes of clear aperture. The devices written with 32 stressors 10 μm spacing and 64 stressors 5 μm spacing have the same clear aperture size, while conversely the second two data points are also comparable.
Fig. 6
Fig. 6 Schematic representation of the loading case considered for the two-dimensional model. The terms here represent the dimensions of the waveplate (c, l), as well as the applied load (qo) and the area over which it is distributed (a).
Fig. 7
Fig. 7 Simulated retardance profile of a laser-written waveplate using a computed displacement on the boundaries of the stressors. The resulting average strain required to produce a maximum center retardance of 55 nm was ~0.16%. For clarity, the loading along the edges of the plate is shown by red arrows.
Fig. 8
Fig. 8 (a) Retardance map for the peak device shown in Fig. 3(d) (55 nm, 128 stressors, 5 μm spacing). (b) 3D view of the retardance profile calculated using the 2D analytical model (only half the computed map is shown). (c-d) comparison between retardance data obtained for experimental measurements, FEM simulation, and the 2D analytical model for the y and x profile directions respectively. (e-g) Contour maps of the measured retardance, 2D analytical model, and FEM simulation respectively.

Equations (16)

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R=Cσt ( E Si O 2 ) Material ( ε LAZ ) Laser [ nt α ( 1+ L WP L INT λ ) ] Geometry
λ= 1 n [ 2( 1β ) α+( 1 1 n ) + β καγ+( 1 1 n ) ] 1 n [ 2( 1β ) α+1 + β καγ+1 ]
4 φ x 4 +2 4 φ x 2 y 2 + 4 φ y 2 =0.
φ( x,y )=sin mπx l f( y )
sin( αx )[ f ( 4 ) ( y )2 α 2 f ( 2 ) ( y )+ α 4 f( y ) ]=0.
φ( x,y )=sin( αx )[ C 1 cosh( αy )+ C 2 sinh( αy )+ C 3 ycosh( αy )+ C 4 ysinh( αy ) ]
q( x )= A o + m=1 A m sin( αx ) + m=1 A m cos( αx ),
A o = q o a l , A m = 1 l a a q o cos( αx )x = 2 q o mπ sin( αa ).
σ xx = 2 φ y 2 , σ yy = 2 φ x 2 , an d τ xy = 2 φ xy
σ xx = q o a l + 4 q o D π m=1 sin( αa ) m [ αcch( αc )sh( αc ) ]ch( αy )αysh( αy )ch( αc ) sh( 2αc )+2αc cos( αx ) σ yy = q o a l 4 q o D π m=1 sin( αa ) m [ αcch( αc )+sh( αc ) ]ch( αy )αysh( αy )ch( αc ) sh( 2αc )+2αc cos( αx ) τ xy = q o a l + 4 q o D π m=1 sin( αa ) m αcch( αc )sh( αy )αych( αy )sh( αc ) sh( 2αc )+2αc sin( αx ) wit h α= mπ l , ch=cosh , an d sh=sinh.
ζ ij = π ijkl σ kl where i,j,k,l=1,2,3...
ζ ( 1..6 ) =[ π 11 π 12 π 12 0 0 0 π 12 π 11 π 12 0 0 0 π 12 π 12 π 11 0 0 0 0 0 0 π 14 0 0 0 0 0 0 π 14 0 0 0 0 0 0 π 14 ][ σ 1 σ 2 0 0 0 0 ]=[ π 11 σ 1 + π 12 σ 2 π 12 σ 1 + π 11 σ 2 π 12 σ 1 + π 12 σ 2 0 0 0 ]
( Δn ) 3 =| ( n o n o 3 2 ζ 1 )( n o n o 3 2 ζ 2 ) |
( Δn ) 3 = n o 3 2 | ( σ 1 σ 2 )( π 11 π 12 ) |
R=C| σ 1 σ 2 | t an d C= n o 3 2 ( π 11 π 12 )
σ 1 , σ 2 = σ xx + σ yy 2 ± ( σ xx σ yy 2 ) 2 + τ xy 2

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