Abstract

Volumetric computer-generated diffractive optics offer advantages over planar 2D implementations, including the generation of space-variant functions and the multiplexing of information in space or frequency domains. Unfortunately, despite remarkable progress, fabrication of high volumetric space-bandwidth micro- and nano-structures is still in its infancy. Furthermore, existing 3D diffractive optics implementations are static while programmable volumetric spatial light modulators (SLMs) are still years or decades away. In order to address these shortcomings, we propose the implementation of volumetric diffractive optics equivalent functionality via cascaded planar elements. To illustrate the principle, we design 3D diffractive optics and implement a two-layer continuous phase-only design on a single SLM with a folded setup. The system provides dynamic and efficient multiplexing capability. Numerical and experimental results show this approach improves system performance such as diffraction efficiency, spatial/spectral selectivity, and number of multiplexing functions relative to 2D devices while providing dynamic large space-bandwidth relative to current static volume diffractive optics. The limitations and capabilities of dynamic 3D diffractive optics are discussed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4, eaar2114 (2018).
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O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12, 368–374 (2018).
[Crossref]

2017 (6)

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

H. Yang, T. Yu, Q. Wang, and M. Lei, “Wave manipulation with magnetically tunable metasurfaces,” Sci. Rep. 7, 5441 (2017).
[Crossref]

E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces,” Optica 4, 625–632 (2017).
[Crossref]

H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11, 186–192 (2017).
[Crossref]

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[Crossref]

2016 (2)

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[Crossref]

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[Crossref]

2015 (1)

2014 (3)

2013 (1)

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13, 987–993 (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (2)

2009 (3)

2008 (2)

V. Nikolenko, B. O. Watson, R. Araya, A. Woodruff, D. S. Peterka, and R. Yuste, “SLM microscopy: scanless two-photon imaging and photostimulation with spatial light modulators,” Front. Neural Circuits 2, 5 (2008).
[Crossref]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
[Crossref]

2007 (4)

2006 (1)

2005 (2)

2004 (1)

2003 (3)

2002 (2)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

J. S. Liu and M. R. Taghizadeh, “Iterative algorithm for the design of diffractive phase elements for laser beam shaping,” Opt. Lett. 27, 1463–1465 (2002).
[Crossref]

2001 (1)

2000 (1)

1999 (1)

1996 (1)

1994 (1)

1992 (2)

1989 (1)

R. Aharoni and Y. Censor, “Block-iterative projection methods for parallel computation of solutions to convex feasibility problems,” Linear Algebra Appl. 120, 165–175 (1989).
[Crossref]

1988 (1)

1984 (1)

1972 (1)

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Opt. Jena 35, 237–246 (1972).

1967 (2)

L. G. Gubin, B. T. Polyyak, and E. V. Raik, “The method of projections for finding the common point of convex sets,” USSR Comput. Math. Math. Phys. 7, 1–24 (1967).
[Crossref]

A. W. Lohmann and D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
[Crossref]

Aharoni, R.

R. Aharoni and Y. Censor, “Block-iterative projection methods for parallel computation of solutions to convex feasibility problems,” Linear Algebra Appl. 120, 165–175 (1989).
[Crossref]

Antolini, R.

Araya, R.

V. Nikolenko, B. O. Watson, R. Araya, A. Woodruff, D. S. Peterka, and R. Yuste, “SLM microscopy: scanless two-photon imaging and photostimulation with spatial light modulators,” Front. Neural Circuits 2, 5 (2008).
[Crossref]

Arbabi, A.

Arbabi, E.

Arkhipov, S. N.

Backer, A. S.

Y. Shechtman, L. E. Weiss, A. S. Backer, M. Y. Lee, and W. E. Moerner, “Multicolour localization microscopy by point-spread-function engineering,” Nat. Photonics 10, 590–594 (2016).
[Crossref]

Backlund, M. P.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13, 987–993 (2013).
[Crossref]

Barbastathis, G.

G. Barbastathis and D. Psaltis, “Volume holographic multiplexing methods,” in Holographic Data Storage, Springer Series in Optical Sciences (Springer, 2000), pp. 21–62.

Bartelt, H.

Bernet, S.

Bonifazi, P.

S. Bovetti, C. Moretti, S. Zucca, M. D. Maschio, P. Bonifazi, and T. Fellin, “Simultaneous high-speed imaging and optogenetic inhibition in the intact mouse brain,” Sci. Rep. 7, 40041 (2017).
[Crossref]

Booth, M. J.

Borgsmüller, S.

Bovetti, S.

S. Bovetti, C. Moretti, S. Zucca, M. D. Maschio, P. Bonifazi, and T. Fellin, “Simultaneous high-speed imaging and optogenetic inhibition in the intact mouse brain,” Sci. Rep. 7, 40041 (2017).
[Crossref]

Brady, D.

Cai, W.

Caley, A. J.

Caravaca-Aguirre, A. M.

O. Tzang, A. M. Caravaca-Aguirre, K. Wagner, and R. Piestun, “Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres,” Nat. Photonics 12, 368–374 (2018).
[Crossref]

Censor, Y.

R. Aharoni and Y. Censor, “Block-iterative projection methods for parallel computation of solutions to convex feasibility problems,” Linear Algebra Appl. 120, 165–175 (1989).
[Crossref]

Chavel, P.

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

Chen, J.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Chen, J.-W.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Chong, A.

Choudhury, A.

Chu, C. H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Colburn, S.

S. Colburn, A. Zhan, and A. Majumdar, “Metasurface optics for full-color computational imaging,” Sci. Adv. 4, eaar2114 (2018).
[Crossref]

Conkey, D. B.

Cooper, J.

Courtial, J.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

Dannberg, P.

Dantus, M.

Denolle, B.

Dietrich, C.

Ducin, I.

Emiliani, V.

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[Crossref]

Fajst, A.

Farah, N.

L. Golan, I. Reutsky, N. Farah, and S. Shoham, “Design and characteristics of holographic neural photo-stimulation systems,” J. Neural Eng. 6, 066004 (2009).
[Crossref]

Faraon, A.

Fellin, T.

S. Bovetti, C. Moretti, S. Zucca, M. D. Maschio, P. Bonifazi, and T. Fellin, “Simultaneous high-speed imaging and optogenetic inhibition in the intact mouse brain,” Sci. Rep. 7, 40041 (2017).
[Crossref]

Fidelin, K.

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[Crossref]

Froner, E.

Fürhapter, S.

Gahlmann, A.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13, 987–993 (2013).
[Crossref]

Genevaux, P.

Gerchberg, R.

R. Gerchberg and W. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Opt. Jena 35, 237–246 (1972).

Gerke, T. D.

Golan, L.

L. Golan, I. Reutsky, N. Farah, and S. Shoham, “Design and characteristics of holographic neural photo-stimulation systems,” J. Neural Eng. 6, 066004 (2009).
[Crossref]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

Grover, G.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13, 987–993 (2013).
[Crossref]

Gubin, L. G.

L. G. Gubin, B. T. Polyyak, and E. V. Raik, “The method of projections for finding the common point of convex sets,” USSR Comput. Math. Math. Phys. 7, 1–24 (1967).
[Crossref]

Harm, W.

Hernandez, O.

O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7, 11928 (2016).
[Crossref]

Hirao, K.

Horie, Y.

Ito, T.

T. Shimobaba, A. Shiraki, N. Masuda, and T. Ito, “An electroholographic colour reconstruction by time division switching of reference lights,” J. Opt. A 9, 757–760 (2007).
[Crossref]

Jesacher, A.

Jian, P.

Johnson, R. V.

Jordan, P.

Kakarenko, K.

Kamali, S. M.

Kämpfe, T.

Kang, H.

Kley, E.-B.

Kolodziejczyk, A.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002).
[Crossref]

Kresse, T.

Kuan, C.-H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Kuroiwa, Y.

Labroille, G.

Lai, Y.-C.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, C. H. Chu, J.-W. Chen, S.-H. Lu, J. Chen, B. Xu, C.-H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8, 187 (2017).
[Crossref]

Lalanne, P.

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

Lee, K.

H. Yu, K. Lee, J. Park, and Y. Park, “Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields,” Nat. Photonics 11, 186–192 (2017).
[Crossref]

Lee, M. K.

A. Gahlmann, J. L. Ptacin, G. Grover, S. Quirin, A. R. S. von Diezmann, M. K. Lee, M. P. Backlund, L. Shapiro, R. Piestun, and W. E. Moerner, “Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions,” Nano Lett. 13, 987–993 (2013).
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Supplementary Material (4)

NameDescription
» Supplement 1       Supplementary document
» Visualization 1       2D implementation of volume diffractive optics. Simulation results for frequency multiplexing with 2-layer diffractive optics implemented on a single SLM. The letters in the word “boulder”? are reconstructed with wavelength 460 nm, 496 nm, 532 nm, 568 nm.
» Visualization 2       Investigation of lateral misalignment tolerance. Visualization 2 shows the reconstructed pattern under both 633 nm and 532 nm illumination as the second layer is misaligned from −20 to 20 micron.
» Visualization 3       Investigation of longitudinal misalignment tolerance. Visualization 3 shows the reconstructed pattern, under both 633 nm and 532 nm illumination, when the second layer is misaligned from −50 to 50 micron.

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Figures (7)

Fig. 1.
Fig. 1. 3D diffractive optics implementation via 2D optics. (a) Decomposition in stratified layers. (b) Equivalent cascaded system using imaging optics. (c) 3D diffractive optics folded implementation on single spatially multiplexed DOE (e.g., SLM) with spherical mirrors.
Fig. 2.
Fig. 2. Flowchart of projection onto constraint sets with a distribution-on-layers algorithm. h1,h2,,hN are layers to be designed, and are set random prior to the computation. R1(kx,ky,),R2(kx,ky,),,RK(kx,ky,) are user-defined output multiplexed fields with the corresponding input multiplexing fields E1(x,y,z1),E2(x,y,z1),,EK(x,y,z1). The input field and output field are forward- and backward-propagated, respectively, to the field before and after the layer to be designed. The modulation function is updated during several iterations for each multiplexing pair and for each layer in the 3D diffractive optics. The process is followed by a parallel projection to ensure that all the information is being encrypted and evenly distributed among all the N layers. The optimization algorithm ends when the target quality or the preset iteration number is reached.
Fig. 3.
Fig. 3. Simulation results for multiplexing 3D diffractive optics. (a) The letters “C” and “U” in the CU logo are the target images. (b) Phase patterns designed for angular multiplexing. (c) Reconstructed images with incident angle at 7° and 10° showing angular multiplexing. (d) Phase patterns designed for frequency multiplexing. (e) Reconstructed images with 633 nm and 532 nm illumination showing frequency multiplexing.
Fig. 4.
Fig. 4. Characterization of 3D diffractive optics in the case of frequency multiplexing. (a) Diffraction efficiency of the letter “C” under 633 nm illumination and “U” under 532 nm illumination as a function of the number of pixels and the number of layers. (b) Wavelength selectivity for the letters “C” and “U” as a function of the number of pixels and the number of layers. (c) Diffraction efficiency of the letters “C” and “U” as a function of layer separation. (d) Wavelength selectivity of the letters “C” and “U” at layer separation of 50 μm, 486 μm, and 1000 μm. Pixel numbers (n) represent side size of a square matrix of size n×n.
Fig. 5.
Fig. 5. Experimental setup for 2D implementation and characterization of dynamic 3D diffractive optics. A supercontinuum source together with an acousto-optic tunable filter (AOTF) provide narrowband laser output in the visible spectrum. The designed layers are implemented on a single high-resolution liquid-crystal SLM, which is spatially divided into two sections. The first layer is imaged at a small distance in front of the second layer, with an imaging system formed by a concave spherical mirror with focal length of 200 mm. A color CMOS sensor is placed on the reconstruction plane after a Fourier lens to record the image.
Fig. 6.
Fig. 6. Experimental results for angular multiplexing. (a) Reconstruction image with incident angle at 7°. (b) Reconstruction image with incident angle at 10°. (c) Speckle field with one layer blocked, indicating that the 3D encryption is successful.
Fig. 7.
Fig. 7. Experimental results for frequency multiplexing with two-layer diffractive optics implemented on a single SLM. The letters in the word “boulder” are reconstructed with wavelength 460 nm, 496 nm, 532 nm, 568 nm, 600 nm, 633 nm, and 694 nm, respectively. See Visualization 1.

Equations (12)

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hk(x,y)=|hk(x,y)|exp[jϕk(x,y)],
E(x,y,zk+)=hk(x,y)E(x,y,zk),
E(x,y,zk+1)=F1{ejk02kx2ky2·Δz·F[E(x,y,zk+)·ej2πλ(x2+y2)·2f]},
R(kx,ky,)=F{E(x,y,zN+)}.
h˜r(x,y)=E(x,y,zr+)E(x,y,zr).
hr(x,y)=exp{h˜r(x,y)}.
Ep(x,y,z1)={Aexp{i2πλxsinϕp},angular  multiplexingAexp{i2πλp},frequency  multiplexing,p=1,2,,KAexp{iϕp(x,y)},phase  multiplexing,
hr(x,y)=exp{cr1Kp=1Kh˜r,p(x,y)},
DE=|UR(kx,ky,)|2vb(kx,ky)dkxdky|E(x,y,z1)|2dxdy,
Err=||UR(kx,ky,)|2civb(kx,ky)|2dkxdky|UR(kx,ky,)|2vb(kx,ky)dkxdky,
ϕ(V,λ)=2πdλn(V,λ),
ϕk(x,y)=1Ni=1Nβλiϕλi(x,y),