Abstract

We demonstrate polarization selective computer-generated holograms (PSCGH) for visible light operation fabricated in glass by a femtosecond laser. For this purpose we create arrays of tailored micro-waveplates by controlling the laser formation of nanogratings embedded in fused silica. A birefringent cell-oriented encoding method adapted to the characteristics of the physical writing process is proposed and implemented. According to this method, each cell contains a micro-waveplate with controlled phase retardation and orientation. A detour of each micro-waveplate, combined with the orientation of its principal optical axis, simultaneously realizes a different phase function for each polarization. PSCGH’s are attractive for integration with other free-space and guided-wave devices embedded in glass.

© 2006 Optical Society of America

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    [CrossRef]
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2006

W. Cai, T. Reber, R. Piestun, "Computer generated volume holograms fabricated by femtosecond laser micromachining," Opt. Lett. 31 (2006)
[CrossRef] [PubMed]

2005

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, R. Bhardwaj, D. M. Rayner, P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87, 14104-12106 (2005).
[CrossRef]

2004

E. Bricchi, B. G. Klappauf, P. G. Kazansky, "Form birefringence and negative index change created by femtosecond direct writing in transparent materials," Opt. Lett 29, 119-121 (2004).
[CrossRef] [PubMed]

P. Yang, G. R. Burns, J. Guo, T. S. Luk, G. A. A Vawter, "Femtosecond laser-pulse-induced birefringence in optically isotropic glass," J. Appl. Phys. 95, 5280-5283 (2004).
[CrossRef]

M. Mirotznik, D. Pustai, D. Prather, and J. Mait, "Design of two-dimensional polarization-selective diffractive optical elements with form-birefringent microstructures," Appl. Opt. 43, 5947-5954 (2004)
[CrossRef] [PubMed]

U. Levy, C. Tsai, H. Kim, and Y. Fainman, "Design, fabrication, and characterization of subwavelength computer-generated holograms for spot array generation," Opt. Express 12, 5345-5355 (2004) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5345
[CrossRef] [PubMed]

2003

Y. Shimotsuma, P. Kazansky, J. Qui, K. Hirao, "Self-organized nanogratings in glass irradiated by ultrashort light pulses," Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

2002

2001

1999

U. Zeitner, B. Schnabel, E. Kley, and F. Wyrowski, "Polarization multiplexing of diffractive elements with metal-stripe grating pixels," Appl. Opt. 38, 2177-2181 (1999)
[CrossRef]

L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, "Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses," Opt. Commun. 171, 279-284 (1999)
[CrossRef]

1997

1996

1995

1994

1993

1967

Bhardwaj, R.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, R. Bhardwaj, D. M. Rayner, P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87, 14104-12106 (2005).
[CrossRef]

Bomzon, Z.

Bricchi, E.

E. Bricchi, B. G. Klappauf, P. G. Kazansky, "Form birefringence and negative index change created by femtosecond direct writing in transparent materials," Opt. Lett 29, 119-121 (2004).
[CrossRef] [PubMed]

Brodeur, A.

Burns, G. R.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, G. A. A Vawter, "Femtosecond laser-pulse-induced birefringence in optically isotropic glass," J. Appl. Phys. 95, 5280-5283 (2004).
[CrossRef]

Cai, W.

W. Cai, T. Reber, R. Piestun, "Computer generated volume holograms fabricated by femtosecond laser micromachining," Opt. Lett. 31 (2006)
[CrossRef] [PubMed]

Cheng, C.-C.

Corkum, P. B.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, R. Bhardwaj, D. M. Rayner, P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87, 14104-12106 (2005).
[CrossRef]

Davis, K. M.

Fainman, Y.

Ford, J.

Ford, J. E.

Franco, M.

L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, "Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses," Opt. Commun. 171, 279-284 (1999)
[CrossRef]

Fujimoto, J.

Garca, J. F.

Guo, J.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, G. A. A Vawter, "Femtosecond laser-pulse-induced birefringence in optically isotropic glass," J. Appl. Phys. 95, 5280-5283 (2004).
[CrossRef]

Hamamoto, T.

Hasman, E.

Hirao, K.

Y. Shimotsuma, P. Kazansky, J. Qui, K. Hirao, "Self-organized nanogratings in glass irradiated by ultrashort light pulses," Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

K. M. Davis, K. Miura, N. Sugimoto, K. Hirao, "Writing waveguides in glass with a femtosecond laser," Opt. Lett. 21, 1729-1731 (1996).
[CrossRef] [PubMed]

Hnatovsky, C.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, R. Bhardwaj, D. M. Rayner, P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87, 14104-12106 (2005).
[CrossRef]

Ichioka, Y.

Ippen, E.

Kazansky, P.

Y. Shimotsuma, P. Kazansky, J. Qui, K. Hirao, "Self-organized nanogratings in glass irradiated by ultrashort light pulses," Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

Kazansky, P. G.

E. Bricchi, B. G. Klappauf, P. G. Kazansky, "Form birefringence and negative index change created by femtosecond direct writing in transparent materials," Opt. Lett 29, 119-121 (2004).
[CrossRef] [PubMed]

Kim, H.

Kirk, A.

Klappauf, B. G.

E. Bricchi, B. G. Klappauf, P. G. Kazansky, "Form birefringence and negative index change created by femtosecond direct writing in transparent materials," Opt. Lett 29, 119-121 (2004).
[CrossRef] [PubMed]

Kleiner, V.

Kley, E.

Konishi, T.

Kowalevicz, A.

Levy, U.

Lohmann, A. W.

Luk, T. S.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, G. A. A Vawter, "Femtosecond laser-pulse-induced birefringence in optically isotropic glass," J. Appl. Phys. 95, 5280-5283 (2004).
[CrossRef]

Mait, J.

Mazur, E.

Minoshima, K.

Mirotznik, M.

Miura, K.

Morlion, B.

Mysyrowicz, A.

L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, "Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses," Opt. Commun. 171, 279-284 (1999)
[CrossRef]

Nieuborg, N.

Paris, D. P.

Piestun, R.

Prade, B.

L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, "Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses," Opt. Commun. 171, 279-284 (1999)
[CrossRef]

Prather, D.

Pustai, D.

Qui, J.

Y. Shimotsuma, P. Kazansky, J. Qui, K. Hirao, "Self-organized nanogratings in glass irradiated by ultrashort light pulses," Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

Rajeev, P. P.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, R. Bhardwaj, D. M. Rayner, P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87, 14104-12106 (2005).
[CrossRef]

Rayner, D. M.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, R. Bhardwaj, D. M. Rayner, P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87, 14104-12106 (2005).
[CrossRef]

Reber, T.

W. Cai, T. Reber, R. Piestun, "Computer generated volume holograms fabricated by femtosecond laser micromachining," Opt. Lett. 31 (2006)
[CrossRef] [PubMed]

Schaffer, C. B.

Scherer, A.

Schnabel, B.

Shamir, J.

Shimotsuma, Y.

Y. Shimotsuma, P. Kazansky, J. Qui, K. Hirao, "Self-organized nanogratings in glass irradiated by ultrashort light pulses," Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

Simova, E.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, R. Bhardwaj, D. M. Rayner, P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87, 14104-12106 (2005).
[CrossRef]

Spektor, B.

Sudrie, L.

L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, "Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses," Opt. Commun. 171, 279-284 (1999)
[CrossRef]

Sugimoto, N.

Sun, P.-C.

Taylor, R. S.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, R. Bhardwaj, D. M. Rayner, P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87, 14104-12106 (2005).
[CrossRef]

Thienpont, H.

Toyota, H.

Tsai, C.

Tyan, R.-C.

Urquhart, K.

Vawter, G. A. A

P. Yang, G. R. Burns, J. Guo, T. S. Luk, G. A. A Vawter, "Femtosecond laser-pulse-induced birefringence in optically isotropic glass," J. Appl. Phys. 95, 5280-5283 (2004).
[CrossRef]

Veretennicoff, I.

Wyrowski, F.

Xu, F.

Yang, P.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, G. A. A Vawter, "Femtosecond laser-pulse-induced birefringence in optically isotropic glass," J. Appl. Phys. 95, 5280-5283 (2004).
[CrossRef]

Yotsuya, T.

Yu, W.

Zeitner, U.

Appl. Opt.

Appl. Phys. Lett.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, R. Bhardwaj, D. M. Rayner, P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87, 14104-12106 (2005).
[CrossRef]

J. Appl. Phys.

P. Yang, G. R. Burns, J. Guo, T. S. Luk, G. A. A Vawter, "Femtosecond laser-pulse-induced birefringence in optically isotropic glass," J. Appl. Phys. 95, 5280-5283 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, "Writing of permanent birefringent microlayers in bulk fused silica with femtosecond laser pulses," Opt. Commun. 171, 279-284 (1999)
[CrossRef]

Opt. Express

Opt. Lett

E. Bricchi, B. G. Klappauf, P. G. Kazansky, "Form birefringence and negative index change created by femtosecond direct writing in transparent materials," Opt. Lett 29, 119-121 (2004).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

Y. Shimotsuma, P. Kazansky, J. Qui, K. Hirao, "Self-organized nanogratings in glass irradiated by ultrashort light pulses," Phys. Rev. Lett. 91, 247405 (2003).
[CrossRef] [PubMed]

Other

W. Cai, T. Reber, R. Piestun, "Computer Generated Holograms Embedded in Glass Fabricated with a Femtosecond Laser," Proceedings of the Conference on Lasers and Electro Optics (CLEO) 2005, paper number CTuEE3, Baltimore, USA. ISBN: 1-55752-770-9.

Supplementary Material (1)

» Media 1: AVI (3805 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the PSCGH cell design according to Eq. (2). Two phase functions are encoded by shifting a square birefringent window within each cell (φ detour) and by rotating the micro-waveplate axis.

Fig. 2.
Fig. 2.

(a) Microscope image of a 2 × 9 array of 5 μm side micro-waveplates placed between two crossed polarizers. The principal axes of neighboring squares are rotated by 20 degrees. b) Measured retardance between fast and slow axes, Δφ, for double layers as a function of layer separation in depth (black). The retardance for single layers fabricated at the same depths, 40 μm (red) and 45–65 μm (green), are shown for reference. Given all parameters, like pulse energy, duration, and translation speed, the graph shows that the total retardance can be controlled by the separation between the two layers. Measurements were performed at 514 nm.

Fig. 3.
Fig. 3.

Left: Microscope image of a detail of the fabricated PSCGH. Right: far field reconstruction. Note that the reconstruction is asymmetric. When the polarization is changed between two orthogonal states, the reconstruction switches the +1 and -1 orders.

Fig. 4.
Fig. 4.

Top-simulation of the reconstruction at +1 order for each of two orthogonal linear polarizations. Bottom-experimental reconstruction at +1 order for different polarizations. From left to right, the polarization angles are rotated clockwise 0, 30, 60, and 90 degrees. See 576KB movie of this reconstruction when the polarization is gradually rotated.

Equations (7)

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φ x i y j = φ x i y j ± Δ φ .
φ x i y j = φ det our x i y j + φ slow, if φ x i y j = φ x i y j + Δ φ ,
φ x i y j = φ det our x i y j + φ fast, if φ x i y j = φ x i y j Δ φ .
φ x i y j = φ det our x i y j , if φ x i y j = φ x i y j + Δφ ,
φ x i y j = φ det our x i y j + Δφ , if φ x i y j = φ x i y j Δφ .
φ ( + 1 ) = φ x i y j = { φ detour x i y j or φ detour x i y j + Δ φ ,
φ ( 1 ) = { φ det our x i y j = φ x i y j or [ φ detour x i y j Δ φ ] = [ φ x i y j 2 Δ φ ] } = [ φ x i y j Δ φ ] ,

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