Abstract

We study the performance of amplitude computer-generated volume holograms (CGVH) in terms of efficiency and angular/frequency selectivity. We compare CGVHs to interferometrically-recorded amplitude volume holograms. Theoretical results show that amplitude CGVHs can increase the efficiency as well as the angular and wavelength selectivity relative to optically recorded amplitude volume holograms. We fabricate the CGVHs using femtosecond laser pulse micromachining in the bulk of glass and demonstrate results consistent with the theory. These results show that aperiodic three-dimensional structures provide the degrees of freedom necessary to improve the performance of volume diffractive optics. They suggest that, under certain circumstances, a departure from the Bragg paradigm provides enhanced volume diffraction properties.

© 2007 Optical Society of America

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2006

2005

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87,014104 (2005).
[CrossRef]

2004

M. Deubel, M. Wegener, A. Kaso, and S. John, "Direct laser writing and characterization of "Slanted Pore" Photonic Crystals," Appl. Phys. Lett. 85,1895-1897 (2004).
[CrossRef]

2003

S.-Y. Lin, J. G. Fleming, and I. El-Kady, "Experimental observation of photonic-crystal emission near a photonic band edge," Appl. Phys. Lett. 83,593-595 (2003).
[CrossRef]

S. Borgsmüller, S. Noehte, C. Dietrich, T. Kresse, and R. Männer, "Computer-generated stratified diffractive optical elements," Appl. Opt. 42,5274-5283 (2003).
[CrossRef] [PubMed]

2002

2001

2000

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53 (2000).
[CrossRef] [PubMed]

1999

1997

R. Piestun, B. Spektor, and J. Shamir, "On-axis binary-amplitude computer generated holograms," Opt. Commun. 136,85-92 (1997).
[CrossRef]

1996

1994

1992

1989

1988

1987

1984

B. Y. Zel’dovich, D. I. Mirovitski, N. V. Rostovtseva, and O. B. Serov, "Characteristics of two-layer phase holograms," Sov. J. Quantum Electron 14,364-369 (1984).
[CrossRef]

1980

A. P. Yakimovich, "Multilayer volume holographic lattices," Optika I Spektroskopiya 49,158-164 (1980).

1976

J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser beams in the atmosphere," Appl. Phys. A. 10,129-160 (1976).

1969

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48,2909 (1969).

Balberg, M.

Barbastathis, G.

Bhardwaj, V. R.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87,014104 (2005).
[CrossRef]

Borgsmüller, S.

Brady, D.

Brady, D. J.

Bryngdahl, O.

Cai, W.

Callan, J. P.

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53 (2000).
[CrossRef] [PubMed]

Chambers, D. M.

Corkum, P. B.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87,014104 (2005).
[CrossRef]

Davis, K. M.

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53 (2000).
[CrossRef] [PubMed]

Deubel, M.

M. Deubel, M. Wegener, A. Kaso, and S. John, "Direct laser writing and characterization of "Slanted Pore" Photonic Crystals," Appl. Phys. Lett. 85,1895-1897 (2004).
[CrossRef]

Dietrich, C.

El-Kady, I.

S.-Y. Lin, J. G. Fleming, and I. El-Kady, "Experimental observation of photonic-crystal emission near a photonic band edge," Appl. Phys. Lett. 83,593-595 (2003).
[CrossRef]

Feit, M. D.

J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser beams in the atmosphere," Appl. Phys. A. 10,129-160 (1976).

Finlay, R. J.

Fleck, J. A.

J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser beams in the atmosphere," Appl. Phys. A. 10,129-160 (1976).

Fleming, J. G.

S.-Y. Lin, J. G. Fleming, and I. El-Kady, "Experimental observation of photonic-crystal emission near a photonic band edge," Appl. Phys. Lett. 83,593-595 (2003).
[CrossRef]

Glezer, E. N.

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53 (2000).
[CrossRef] [PubMed]

Her, T.-H.

Hirao, K.

Hnatovsky, C.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87,014104 (2005).
[CrossRef]

Huang, L.

Itoh, K.

John, S.

M. Deubel, M. Wegener, A. Kaso, and S. John, "Direct laser writing and characterization of "Slanted Pore" Photonic Crystals," Appl. Phys. Lett. 85,1895-1897 (2004).
[CrossRef]

Johnson, R. V.

Kaso, A.

M. Deubel, M. Wegener, A. Kaso, and S. John, "Direct laser writing and characterization of "Slanted Pore" Photonic Crystals," Appl. Phys. Lett. 85,1895-1897 (2004).
[CrossRef]

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48,2909 (1969).

Kresse, T.

Kuroda, D.

Libertun, A. R.

Lin, S.-Y.

S.-Y. Lin, J. G. Fleming, and I. El-Kady, "Experimental observation of photonic-crystal emission near a photonic band edge," Appl. Phys. Lett. 83,593-595 (2003).
[CrossRef]

Männer, R.

Mazur, E.

Milosavljevic, M.

Mirovitski, D. I.

B. Y. Zel’dovich, D. I. Mirovitski, N. V. Rostovtseva, and O. B. Serov, "Characteristics of two-layer phase holograms," Sov. J. Quantum Electron 14,364-369 (1984).
[CrossRef]

Miura, K.

Morris, J. R.

J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser beams in the atmosphere," Appl. Phys. A. 10,129-160 (1976).

Nishii, J.

Noehte, S.

Nordin, G. P.

Piestun, R.

Psaltis, D.

Rajeev, P. P.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87,014104 (2005).
[CrossRef]

Rayner, D. M.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87,014104 (2005).
[CrossRef]

Reber, T. J.

Rostovtseva, N. V.

B. Y. Zel’dovich, D. I. Mirovitski, N. V. Rostovtseva, and O. B. Serov, "Characteristics of two-layer phase holograms," Sov. J. Quantum Electron 14,364-369 (1984).
[CrossRef]

Schonbrun, E.

E. Schonbrun and R. Piestun, "Optical vortices for localized optical lattice site manipulation," Optical Engineering 45,028001 (2006).
[CrossRef]

Serov, O. B.

B. Y. Zel’dovich, D. I. Mirovitski, N. V. Rostovtseva, and O. B. Serov, "Characteristics of two-layer phase holograms," Sov. J. Quantum Electron 14,364-369 (1984).
[CrossRef]

Shamir, J.

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53 (2000).
[CrossRef] [PubMed]

Simova, E.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87,014104 (2005).
[CrossRef]

Spektor, B.

R. Piestun, B. Spektor, and J. Shamir, "On-axis binary-amplitude computer generated holograms," Opt. Commun. 136,85-92 (1997).
[CrossRef]

R. Piestun, B. Spektor, and J. Shamir, "Wave fields in three dimensions: analysis and synthesis," J. Opt. Soc. Am. A 13,1837-1848 (1996).
[CrossRef]

Sugimoto, N.

Tanguay, A. R.

Taylor, R. S.

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87,014104 (2005).
[CrossRef]

Toma, T.

Tricoles, G.

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53 (2000).
[CrossRef] [PubMed]

Watanabe, W.

Wegener, M.

M. Deubel, M. Wegener, A. Kaso, and S. John, "Direct laser writing and characterization of "Slanted Pore" Photonic Crystals," Appl. Phys. Lett. 85,1895-1897 (2004).
[CrossRef]

Wyrowski, F.

Yakimovich, A. P.

A. P. Yakimovich, "Multilayer volume holographic lattices," Optika I Spektroskopiya 49,158-164 (1980).

Yamada, K.

Zel’dovich, B. Y.

B. Y. Zel’dovich, D. I. Mirovitski, N. V. Rostovtseva, and O. B. Serov, "Characteristics of two-layer phase holograms," Sov. J. Quantum Electron 14,364-369 (1984).
[CrossRef]

Appl. Opt.

Appl. Phys. A.

J. A. Fleck, Jr., J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser beams in the atmosphere," Appl. Phys. A. 10,129-160 (1976).

Appl. Phys. Lett.

S.-Y. Lin, J. G. Fleming, and I. El-Kady, "Experimental observation of photonic-crystal emission near a photonic band edge," Appl. Phys. Lett. 83,593-595 (2003).
[CrossRef]

M. Deubel, M. Wegener, A. Kaso, and S. John, "Direct laser writing and characterization of "Slanted Pore" Photonic Crystals," Appl. Phys. Lett. 85,1895-1897 (2004).
[CrossRef]

C. Hnatovsky, R. S. Taylor, P. P. Rajeev, E. Simova, V. R. Bhardwaj, D. M. Rayner, and P. B. Corkum, "Pulse duration dependence of femtosecond-laser-fabricated nanogratings in fused silica," Appl. Phys. Lett. 87,014104 (2005).
[CrossRef]

Bell Syst. Tech. J.

H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48,2909 (1969).

J. Opt. Soc. Am. A

Nature

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404,53 (2000).
[CrossRef] [PubMed]

Opt. Commun.

R. Piestun, B. Spektor, and J. Shamir, "On-axis binary-amplitude computer generated holograms," Opt. Commun. 136,85-92 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Optical Engineering

E. Schonbrun and R. Piestun, "Optical vortices for localized optical lattice site manipulation," Optical Engineering 45,028001 (2006).
[CrossRef]

Optika I Spektroskopiya

A. P. Yakimovich, "Multilayer volume holographic lattices," Optika I Spektroskopiya 49,158-164 (1980).

Sov. J. Quantum Electron

B. Y. Zel’dovich, D. I. Mirovitski, N. V. Rostovtseva, and O. B. Serov, "Characteristics of two-layer phase holograms," Sov. J. Quantum Electron 14,364-369 (1984).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

H. J. Caulfield and S. Lu, The Applications of Holography (Wiley-Interscience, 1970).

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Figures (5)

Fig. 1.
Fig. 1.

Propagation model through an N-layer structure: propagation between layers is modeled by a scalar angular spectrum technique described in (1), and propagation through each layer is modeled by multiplication of the transmission function of the layer.

Fig. 2.
Fig. 2.

Example of a 4-layer CGVH. Black denotes no transmission while white denotes full transmission. Individual lines are 3μm wide.

Fig. 3.
Fig. 3.

Simulated far-field intensity pattern for propagation through the 4 layer structure depicted in Fig. 2. The x-axis is the normalized transverse wavevector, i.e., normalized far-field transverse location.

Fig. 4.
Fig. 4.

Diffraction efficiency as a function of the number of layers for a CGVH of 100μm total thickness. Comparison maxima for an optimal thin element and an optimal optically recorded amplitude transmission volume hologram are the labeled horizontal dashed lines.

Fig. 5.
Fig. 5.

(a) Diffraction efficiency as a function of incident angle. The blue line is experimental data and the dashed red line is the simulated result. The dotted black line is the response of an equivalent (same 3D size and diffraction angle) optically recorded amplitude volume hologram (ORAVH). (b) Simulated diffraction efficiency as a function of the illumination wavelength for a 100 micron (solid red) and 200 micron (dashed blue) thick, 4-layer structure designed for 632.8nm illumination. The dotted lines correspond to the selectivity for equivalent 100 and 200μm thick optically recorded amplitude volume holograms for comparison.

Equations (1)

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E ( x , y ; z + Δ z ) = 𝓕 xy 1 { e j k o 2 k t 2 Δ z 𝓕 xy [ E x y ; z ] } ,

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