Abstract

Throughout optics and photonics, phase is normally controlled via an optical path difference. Although much less common, an alternative means for phase control exists: a geometric phase (GP) shift occurring when a light wave is transformed through one parameter space, e.g., polarization, in such a way as to create a change in a second parameter, e.g., phase. In thin films and surfaces where only the GP varies spatially—which may be called GP holograms (GPHs)—the phase profile of nearly any (physical or virtual) object can in principle be embodied as an inhomogeneous anisotropy manifesting exceptional diffraction and polarization behavior. Pure GP elements have had poor efficiency and utility up to now, except in isolated cases, due to the lack of fabrication techniques producing elements with an arbitrary spatially varying GP shift at visible and near-infrared wavelengths. Here, we describe two methods to create high-fidelity GPHs, one interferometric and another direct-write, capable of recording the wavefront of nearly any physical or virtual object. We employ photoaligned liquid crystals to record the patterns as an inhomogeneous optical axis profile in thin films with a few μm thickness. We report on eight representative examples, including a GP lens with F/2.3 (at 633 nm) and 99% diffraction efficiency across visible wavelengths, and several GP vortex phase plates with excellent modal purity and remarkably small central defect size (e.g., 0.7 and 7 μm for topological charges of 1 and 8, respectively). We also report on a GP Fourier hologram, a fan-out grid with dozens of far-field spots, and an elaborate phase profile, which showed excellent fidelity and very low leakage wave transmittance and haze. Together, these techniques are the first practical bases for arbitrary GPHs with essentially no loss, high phase gradients (rad/μm), novel polarization functionality, and broadband behavior.

© 2015 Optical Society of America

Full Article  |  PDF Article

Corrections

4 November 2015: A correction was made to the supplementary material.


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References

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2015 (4)

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10, 308–312 (2015).
[Crossref]

M. N. Miskiewicz and M. J. Escuti, “Optimization of direct-write polarization gratings,” Opt. Eng. 54, 025101 (2015).
[Crossref]

X. Xiang, M. N. Miskiewicz, and M. J. Escuti, “Distortion-free broadband holograms: a novel class of elements utilizing the wavelength-independent geometric phase,” Proc. SPIE 9386, 938609 (2015).
[Crossref]

J. Kim, M. Miskiewicz, S. Serati, and M. Escuti, “Nonmechanical laser beam steering based on polymer polarization gratings: design optimization and demonstration,” J. Lightwave Technol. 33, 2068–2077 (2015).
[Crossref]

2014 (1)

2013 (7)

P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013).

S. R. Nersisyan, N. V. Tabiryan, D. Mawet, and E. Serabyn, “Improving vector vortex waveplates for high-contrast coronagraphy,” Opt. Express 21, 8205–8213 (2013).
[Crossref]

R. K. Komanduri, K. F. Lawler, and M. J. Escuti, “Multi-twist retarders: broadband retardation control using self-aligning reactive liquid crystal layers,” Opt. Express 21, 404–420 (2013).
[Crossref]

D. Maluenda, I. Juvells, R. Martnez-Herrero, and A. Carnicer, “Reconfigurable beams with arbitrary polarization and shape distributions at a given plane,” Opt. Express 21, 5432–5439 (2013).
[Crossref]

U. Ruiz, P. Pagliusi, C. Provenzano, K. Volke-Sepúlveda, and G. Cipparrone, “Polarization holograms allow highly efficient generation of complex light beams,” Opt. Express 21, 7505–7510 (2013).
[Crossref]

2012 (6)

U. Ruiz, C. Provenzano, P. Pagliusi, and G. Cipparrone, “Single-step polarization holographic method for programmable microlens arrays,” Opt. Lett. 37, 4958–4960 (2012).
[Crossref]

M. Kang, T. Feng, H.-T. Wang, and J. Li, “Wave front engineering from an array of thin aperture antennas,” Opt. Express 20, 15882–15890 (2012).
[Crossref]

S. Larouche, Y.-J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nat. Mater. 11, 450–454 (2012).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref]

H. Ono, T. Wada, and N. Kawatsuki, “Polarization imaging screen using vector gratings fabricated by photocrosslinkable polymer liquid crystals,” Jpn. J. Appl. Phys. 51, 030202 (2012).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

2011 (3)

2009 (3)

2008 (3)

2006 (5)

M. J. Escuti, C. Oh, C. Sánchez, C. Bastiaansen, and D. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

C. Provenzano, P. Pagliusi, and G. Cipparrone, “Highly efficient liquid crystal based diffraction grating induced by polarization holograms at the aligning surfaces,” Appl. Phys. Lett. 89, 121105 (2006).
[Crossref]

W. Cai, A. R. Libertun, and R. Piestun, “Polarization selective computer-generated holograms realized in glass by femtosecond laser induced nanogratings,” Opt. Express 14, 3785–3791 (2006).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (2006).
[Crossref]

P. Ramanujam, C. Dam-Hansen, R. Berg, S. Hvilsted, and L. Nikolova, “Polarisation-sensitive optical elements in azobenzene polyesters and peptides,” Opt. Laser Eng. 44, 912–925 (2006).
[Crossref]

2005 (1)

G. Crawford, J. Eakin, M. Radcliffe, A. Callan-Jones, and R. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[Crossref]

2004 (2)

2003 (2)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
[Crossref]

R. W. Batterman, “Falling cats, parallel parking, and polarized light,” Stud. Hist. Philos. Sci. B 34, 527–557 (2003).
[Crossref]

2002 (2)

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures,” Opt. Commun. 209, 45–54 (2002).
[Crossref]

M. Hasegawa, “Fabrication of freely patterned aligned nematic liquid crystal cells using UV laser scanning photoalignment,” Jpn. J. Appl. Phys. 41, L201–L202 (2002).
[Crossref]

1999 (1)

1998 (1)

J.-M. Vigoureux and D. Van Labeke, “A geometric phase in optical multilayers,” J. Mod. Opt. 45, 2409–2416 (1998).
[Crossref]

1997 (1)

R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 281, 1–64 (1997).
[Crossref]

1996 (1)

M. Ferstl and A.-M. Frisch, “Static and dynamic Fresnel zone lenses for optical interconnections,” J. Mod. Opt. 43, 1451–1462 (1996).
[Crossref]

1992 (1)

J. Anandan, “The geometric phase,” Nature 360, 307–313 (1992).
[Crossref]

1986 (1)

R. Chiao and Y.-S. Wu, “Manifestations of Berry’s topological phase for the photon,” Phys. Rev. Lett. 57, 933–936 (1986).
[Crossref]

1985 (1)

1984 (2)

M. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
[Crossref]

L. Nikolova and T. Todorov, “Diffraction efficiency and selectivity of polarization holographic recording,” Opt. Acta 31, 579–588 (1984).
[Crossref]

1972 (2)

O. Bryngdahl, “Polarization-grating moire,” J. Opt. Soc. Am. 62, 839–848 (1972).
[Crossref]

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

1956 (1)

S. Pancharatnam, “Generalized theory of interference, and its applications. Part i. Coherent pencils,” Proc. Indian Acad. Sci. A 44, 247–262 (1956).

Aieta, F.

P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Anandan, J.

J. Anandan, “The geometric phase,” Nature 360, 307–313 (1992).
[Crossref]

Aoust, G.

P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

Bai, B.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
[Crossref]

Bastiaansen, C.

M. J. Escuti, C. Oh, C. Sánchez, C. Bastiaansen, and D. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Batterman, R. W.

R. W. Batterman, “Falling cats, parallel parking, and polarized light,” Stud. Hist. Philos. Sci. B 34, 527–557 (2003).
[Crossref]

Berg, R.

P. Ramanujam, C. Dam-Hansen, R. Berg, S. Hvilsted, and L. Nikolova, “Polarisation-sensitive optical elements in azobenzene polyesters and peptides,” Opt. Laser Eng. 44, 912–925 (2006).
[Crossref]

Berry, M.

M. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London Ser. A 392, 45–57 (1984).
[Crossref]

Bhandari, R.

R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 281, 1–64 (1997).
[Crossref]

Biener, G.

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
[Crossref]

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures,” Opt. Commun. 209, 45–54 (2002).
[Crossref]

Blanchard, R.

P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Bomzon, Z.

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, “Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures,” Opt. Commun. 209, 45–54 (2002).
[Crossref]

Boulé, J.

Broer, D.

M. J. Escuti, C. Oh, C. Sánchez, C. Bastiaansen, and D. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Bryngdahl, O.

Cai, W.

Callan-Jones, A.

G. Crawford, J. Eakin, M. Radcliffe, A. Callan-Jones, and R. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98, 123102 (2005).
[Crossref]

Capasso, F.

P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012).
[Crossref]

Carnicer, A.

Cheah, K.-W.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

Chen, S.

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Appl. Opt. (3)

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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. Geometric phase holograms. (a) Illustration of GP lens behavior. (b) Example of GPH cross-section with LC and LPP. (c) New modified Mach–Zehnder interferometric fabrication. (d) New direct-write fabrication. Note that ψ ( x , y ) is the linear polarization orientation angle, Φ ( x , y ) is the optical axis angle, and δ ( x , y ) is the phase angle.
Fig. 2.
Fig. 2. Interference GPH. (a) Lens. (b) Axicon. (c) Large period prism (i.e., polarization grating). Columns: i, Simulated (curve) and measured (circles) primary (magenta) and conjugate (cyan) phases, where measurement error is less than ± 0.02 rad . ii, Theoretical optical axis profile, with simulated cross-polarizer texture. iii, Measured polarizing optical micrograph under crossed polarizers. iv, Far-field result. Scale bars in column iii indicate 500 μm.
Fig. 3.
Fig. 3. Detailed Results from GP Lens. (a) Measured (dots) focused beam profile of GP lens (blue) and recorded lens (red), compared with perfect Gaussian result. (b) Measured transmittance of primary + conjugate (solid) and leakage (dashed) waves; inset: chromatic dispersion of focal spot. (c) Predicted replay versus recorded F / # ; dot indicates the GP lens reported here. (d) Imaging through the GP lens with | χ + polarization, showing positive focal length. (e) Same as (d), but with | χ polarization, showing negative focal length.
Fig. 4.
Fig. 4. Direct-Write GPH. (a) Vortex phase plate. (b) Fourier hologram fan-out grid. Columns: i, Simulated phase. ii, Theoretical optical axis profile with simulated crossed polarizer texture. iii, Measured polarizing optical micrograph under crossed polarizers. iv, Far-field result. Scale bars in column iii indicate 20 μm. The approximate writing beam size and scan pattern is shown in column i. The insets of (b.i), (b.ii), and (b.iii) show a magnified view of the 8 × 8 pixels of the top left corner.

Equations (1)

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e i δ in | χ in GPH η + e i ( δ in + 2 Φ ) | χ + + η e i ( δ in 2 Φ ) | χ + η 0 e i δ in | χ in .

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