Abstract

We present a novel optical element that efficiently generates orbital angular momentum (OAM) of light and transforms light between OAM modes based on a polarization grating with a fork-shaped singularity. This forked polarization grating (FPG) is composed of liquid crystalline materials, and can be made either static or switchable with high diffraction efficiency (i.e., 100% theoretically) into a single order. By spatially varying the Pancharatnam–Berry phase, FPGs shape the wavefront and thus control the OAM mode. We demonstrate theoretically and empirically that a charge lg FPG creates helical modes with OAM charge ±lg when a Gaussian beam is input, and more generally, transforms the incident helical mode with OAM charge lin into output modes with OAM charge lin±lg. We also show for the first time that this conversion into a single mode can be very efficient (i.e., 95% experimentally) at visible wavelengths, and the relative power between the two possible output modes is polarization-controllable from 0% to 100%. We developed a fabrication method that substantially improves FPG quality and efficiency over prior work. We also successfully fabricated switchable FPGs, which can be electrically switched between an OAM generating/transforming state and a transmissive state. Our experimental results showed >92% conversion efficiency for both configurations at 633 nm. These holographically fabricated elements are compact (i.e., thin glass plates), lightweight, and easily optimized for nearly any wavelength from ultraviolet to infrared, for a wide range of OAM charge, and for large or small clear apertures. They are ideal elements for enhanced control of OAM, e.g., in optical trapping and high-capacity information.

© 2012 Optical Society of America

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  1. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef]
  2. V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
    [CrossRef]
  3. J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18, 2144–2151 (2010).
    [CrossRef]
  4. G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Lett. 12, 5448–5456 (2004).
    [CrossRef]
  5. J. García-Escartín and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A 78, 1–10 (2008).
    [CrossRef]
  6. T. Todorov, L. Nikolova, and N. Tomova, “Polarization holography. 2. Polarization holographic gratings in photoanisotropic materials with and without intrinsic birefringence,” Appl. Opt. 23, 4588–4591 (1984).
    [CrossRef]
  7. C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
    [CrossRef]
  8. 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]
  9. M. J. Escuti, C. Oh, S. Carlos, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
    [CrossRef]
  10. 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]
  11. S. Nersisyan, N. Tabiryan, D. Steeves, and B. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
    [CrossRef]
  12. J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
    [CrossRef]
  13. E. Nicolescu and M. J. Escuti, “Polarization-independent tunable optical filters using bilayer polarization gratings,” Appl. Opt. 49, 3900–3904 (2010).
    [CrossRef]
  14. E. Nicolescu, C. Mao, and A. Fardad, “Polarization-insensitive variable optical attenuator and wavelength blocker using liquid crystal polarization gratings,” J. Lightwave Technol. 28, 3121–3127 (2009).
    [CrossRef]
  15. M. Kudenov, M. J. Escuti, E. Dereniak, and K. Oka, “White-light channeled imaging polarimeter using broadband polarization gratings,” Appl. Opt. 50, 2283–2293(2011).
    [CrossRef]
  16. R. Komanduri, W. Jones, C. Oh, and M. J. Escuti, “Polarization-independent modulation for projection displays using small-period LC polarization,” J. Soc. Inf. Disp. 15, 589–594 (2007).
    [CrossRef]
  17. J. Kim, R. K. Komanduri, K. F. Lawler, D. J. Kekas, and M. J. Escuti, “Efficient and monolithic polarization conversion system based on a polarization grating,” Appl. Opt. 51, 4852–4857 (2012).
    [CrossRef]
  18. H. Choi, J. H. Woo, J. W. Wu, D.-W. Kim, T.-K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
    [CrossRef]
  19. Y. Li, J. Kim, and M. J. Escuti, “Controlling orbital angular momentum using forked polarization gratings,” Proc. SPIE 7789, 77890F (2010).
    [CrossRef]
  20. Y. Li, J. Kim, and M. J. Escuti, “Experimental realization of high-efficiency switchable optical OAM state generator and transformer,” Proc. SPIE 8130, 81300F (2011).
    [CrossRef]
  21. 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]
  22. S. McEldowney, D. Shemo, R. Chipman, and P. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33, 134–136 (2008).
    [CrossRef]
  23. M. Schadt, H. Seiberle, and A. Schuster, “Optical patterning of multi-domain liquid-crystal displays with wide viewing angles,” Nature 381, 212–215 (1996).
    [CrossRef]
  24. I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).
    [CrossRef]

2012 (1)

2011 (3)

2010 (3)

2009 (2)

E. Nicolescu, C. Mao, and A. Fardad, “Polarization-insensitive variable optical attenuator and wavelength blocker using liquid crystal polarization gratings,” J. Lightwave Technol. 28, 3121–3127 (2009).
[CrossRef]

S. Nersisyan, N. Tabiryan, D. Steeves, and B. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

2008 (2)

S. McEldowney, D. Shemo, R. Chipman, and P. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33, 134–136 (2008).
[CrossRef]

J. García-Escartín and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A 78, 1–10 (2008).
[CrossRef]

2007 (3)

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

R. Komanduri, W. Jones, C. Oh, and M. J. Escuti, “Polarization-independent modulation for projection displays using small-period LC polarization,” J. Soc. Inf. Disp. 15, 589–594 (2007).
[CrossRef]

H. Choi, J. H. Woo, J. W. Wu, D.-W. Kim, T.-K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[CrossRef]

2006 (3)

M. J. Escuti, C. Oh, S. Carlos, C. W. M. Bastiaansen, and D. J. 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]

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]

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 (1)

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Lett. 12, 5448–5456 (2004).
[CrossRef]

2003 (1)

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

1999 (1)

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).
[CrossRef]

1996 (1)

M. Schadt, H. Seiberle, and A. Schuster, “Optical patterning of multi-domain liquid-crystal displays with wide viewing angles,” Nature 381, 212–215 (1996).
[CrossRef]

1992 (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

1984 (1)

Allen, L.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Barnett, S.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Lett. 12, 5448–5456 (2004).
[CrossRef]

Bastiaansen, C. W. M.

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

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Broer, D. J.

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

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]

Carlos, S.

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

Chamorro-Posada, P.

J. García-Escartín and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A 78, 1–10 (2008).
[CrossRef]

Chipman, R.

Choi, H.

H. Choi, J. H. Woo, J. W. Wu, D.-W. Kim, T.-K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[CrossRef]

Chujo, K.

Cipparrone, G.

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]

Courtial, J.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Lett. 12, 5448–5456 (2004).
[CrossRef]

Crawford, G.

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]

Dereniak, E.

Dholakia, K.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Dultz, W.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Eakin, J.

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]

Escuti, M. J.

J. Kim, R. K. Komanduri, K. F. Lawler, D. J. Kekas, and M. J. Escuti, “Efficient and monolithic polarization conversion system based on a polarization grating,” Appl. Opt. 51, 4852–4857 (2012).
[CrossRef]

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
[CrossRef]

M. Kudenov, M. J. Escuti, E. Dereniak, and K. Oka, “White-light channeled imaging polarimeter using broadband polarization gratings,” Appl. Opt. 50, 2283–2293(2011).
[CrossRef]

Y. Li, J. Kim, and M. J. Escuti, “Experimental realization of high-efficiency switchable optical OAM state generator and transformer,” Proc. SPIE 8130, 81300F (2011).
[CrossRef]

Y. Li, J. Kim, and M. J. Escuti, “Controlling orbital angular momentum using forked polarization gratings,” Proc. SPIE 7789, 77890F (2010).
[CrossRef]

E. Nicolescu and M. J. Escuti, “Polarization-independent tunable optical filters using bilayer polarization gratings,” Appl. Opt. 49, 3900–3904 (2010).
[CrossRef]

R. Komanduri, W. Jones, C. Oh, and M. J. Escuti, “Polarization-independent modulation for projection displays using small-period LC polarization,” J. Soc. Inf. Disp. 15, 589–594 (2007).
[CrossRef]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

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

Fardad, A.

Franke-Arnold, S.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Lett. 12, 5448–5456 (2004).
[CrossRef]

Freund, I.

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).
[CrossRef]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

García-Escartín, J.

J. García-Escartín and P. Chamorro-Posada, “Quantum multiplexing with the orbital angular momentum of light,” Phys. Rev. A 78, 1–10 (2008).
[CrossRef]

Gibson, G.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Lett. 12, 5448–5456 (2004).
[CrossRef]

Hamazaki, J.

Jones, W.

R. Komanduri, W. Jones, C. Oh, and M. J. Escuti, “Polarization-independent modulation for projection displays using small-period LC polarization,” J. Soc. Inf. Disp. 15, 589–594 (2007).
[CrossRef]

Kekas, D. J.

Kim, D.-W.

H. Choi, J. H. Woo, J. W. Wu, D.-W. Kim, T.-K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[CrossRef]

Kim, J.

J. Kim, R. K. Komanduri, K. F. Lawler, D. J. Kekas, and M. J. Escuti, “Efficient and monolithic polarization conversion system based on a polarization grating,” Appl. Opt. 51, 4852–4857 (2012).
[CrossRef]

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
[CrossRef]

Y. Li, J. Kim, and M. J. Escuti, “Experimental realization of high-efficiency switchable optical OAM state generator and transformer,” Proc. SPIE 8130, 81300F (2011).
[CrossRef]

Y. Li, J. Kim, and M. J. Escuti, “Controlling orbital angular momentum using forked polarization gratings,” Proc. SPIE 7789, 77890F (2010).
[CrossRef]

Kimball, B.

S. Nersisyan, N. Tabiryan, D. Steeves, and B. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

Kobayashi, Y.

Komanduri, R.

R. Komanduri, W. Jones, C. Oh, and M. J. Escuti, “Polarization-independent modulation for projection displays using small-period LC polarization,” J. Soc. Inf. Disp. 15, 589–594 (2007).
[CrossRef]

Komanduri, R. K.

Kudenov, M.

Lawler, K. F.

Li, Y.

Y. Li, J. Kim, and M. J. Escuti, “Experimental realization of high-efficiency switchable optical OAM state generator and transformer,” Proc. SPIE 8130, 81300F (2011).
[CrossRef]

Y. Li, J. Kim, and M. J. Escuti, “Controlling orbital angular momentum using forked polarization gratings,” Proc. SPIE 7789, 77890F (2010).
[CrossRef]

Lim, T.-K.

H. Choi, J. H. Woo, J. W. Wu, D.-W. Kim, T.-K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[CrossRef]

Manzo, C.

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]

Mao, C.

Marrucci, L.

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]

McEldowney, S.

McGloin, D.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Morita, R.

Nersisyan, S.

S. Nersisyan, N. Tabiryan, D. Steeves, and B. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

Nicolescu, E.

Nikolova, L.

Oh, C.

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50, 2636–2639 (2011).
[CrossRef]

R. Komanduri, W. Jones, C. Oh, and M. J. Escuti, “Polarization-independent modulation for projection displays using small-period LC polarization,” J. Soc. Inf. Disp. 15, 589–594 (2007).
[CrossRef]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76, 043815 (2007).
[CrossRef]

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

Oka, K.

Omatsu, T.

Padgett, M.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Lett. 12, 5448–5456 (2004).
[CrossRef]

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Pagliusi, P.

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]

Paparo, D.

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]

Pas’ko, V.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Lett. 12, 5448–5456 (2004).
[CrossRef]

Pelcovits, R.

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]

Provenzano, C.

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]

Radcliffe, M.

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]

Schadt, M.

M. Schadt, H. Seiberle, and A. Schuster, “Optical patterning of multi-domain liquid-crystal displays with wide viewing angles,” Nature 381, 212–215 (1996).
[CrossRef]

Schmitzer, H.

V. Garcés-Chávez, D. McGloin, M. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, “Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle,” Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Schuster, A.

M. Schadt, H. Seiberle, and A. Schuster, “Optical patterning of multi-domain liquid-crystal displays with wide viewing angles,” Nature 381, 212–215 (1996).
[CrossRef]

Seiberle, H.

M. Schadt, H. Seiberle, and A. Schuster, “Optical patterning of multi-domain liquid-crystal displays with wide viewing angles,” Nature 381, 212–215 (1996).
[CrossRef]

Serati, S.

Shemo, D.

Smith, P.

Song, S. H.

H. Choi, J. H. Woo, J. W. Wu, D.-W. Kim, T.-K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[CrossRef]

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Steeves, D.

S. Nersisyan, N. Tabiryan, D. Steeves, and B. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

Tabiryan, N.

S. Nersisyan, N. Tabiryan, D. Steeves, and B. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

Tanda, S.

Todorov, T.

Tomova, N.

Vasnetsov, M.

G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Lett. 12, 5448–5456 (2004).
[CrossRef]

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef]

Woo, J. H.

H. Choi, J. H. Woo, J. W. Wu, D.-W. Kim, T.-K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[CrossRef]

Wu, J. W.

H. Choi, J. H. Woo, J. W. Wu, D.-W. Kim, T.-K. Lim, and S. H. Song, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (2007).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Operation of our FPG concept as an OAM mode generator and transformer. The input beam has OAM charge l0, which is diffracted by the FPG (with charge lg) into (a) and (b) circularly polarized beam with charge l0lg or l0+lg for a right or left circularly polarized input. (c) If the input beam is linearly polarized or unpolarized, both outputs exist. In a more general case, there is a zero-order leakage that has the same polarization and OAM charge as the input.

Fig. 2.
Fig. 2.

FPG structure. (a) Two periods in x dimension, (b) top view, (c), and (d) anisotropic in-plane structure of charge lg=+1 and charge lg=+2 FPGs. Arrows illustrate the local optical axis at each spacial point. Background color is an indication of the optical axis orientation that helps show the “fork” singularity, where purple (red) corresponds to the optical axis parallel to the x(y) axis. LPP, linear polymerizable polymer.

Fig. 3.
Fig. 3.

Numerical simulation of two cases of FPG diffraction, showing far-field intensity (a)–(c) and phase at diffracted beam cross sections (d), (e). The FPG charge lg and input l0 for each simulation is shown at the top of each column. Diffraction order m is shown at the bottom of each column. The input polarization is (a) linear, (b) right circular, and (c) left circular. The phase distributions of diffracted beams are calculated at (a) the on-axis cross section and (e) the off-axis cross section of each beam.

Fig. 4.
Fig. 4.

Fabrication of FPG: (a) polarized holography setup, (b) detailed view of the interference, where the q-plate singularity is projected twice onto the sample plane (yellow arrows), and (c) equivalent holographic interference for each singularity in (b). M, mirror; BS, beam splitter; QWP, quarter-wave plate; HWP, half-wave plate.

Fig. 5.
Fig. 5.

Polarizing optical microscope pictures of FPGs between crossed polarizers: (a) at the singularity of a polymer FPG (lg=+1), (b) at the singularity of another polymer FPG (lg=+2), (c) a view well away from the singularity of the FPG in (a), (d) low-mag view of both singularities of the FPG in part (a); a switchable FPG (lg=+1) at (e) 0 V, and (f) 15 V. In (a)–(d), a fullwave retarder was inserted in the microscope to emphasize the forked alignment pattern, in (e) and (f) this was removed.

Fig. 6.
Fig. 6.

Diffraction efficiency spectra of a polymer FPG (lg=+1), optimized for visible wavelength at 633 nm. Square data points are measured directly by an HeNe laser.

Fig. 7.
Fig. 7.

Interference pattern of input light and each diffraction order from a lg=+1 FPG. (a)–(d) Gaussian input and (e)–(h) OAM charge l=2 input. (a), (e) Input beam; (b), (f) m=+1 diffraction; (c), (g) m=0 diffraction; (d), (h) m=1 diffraction.

Fig. 8.
Fig. 8.

Output OAM chart of switchable FPG for three modes. Upper row, far-field intensity; bottom row, interference with tilted plane wave. Input is a Gaussian beam. FPG has charge lg=+1.

Fig. 9.
Fig. 9.

Zero-order (m=0) and first-order (Σm=±1) diffraction-efficiency responses to applied voltage. Solid curves are measured using 633 nm laser. Dashed curves are measured using 532 nm laser.

Tables (2)

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Table 1. Measured FPG Diffraction Efficiency (%)

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Table 2. Measured Switchable FPG Diffraction Efficiency (%)

Equations (7)

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Φ(x,y)=12lgϕ(x,y)πx/Λ+Φ0,
T(x,y)=cosζI+isinζ[cos2Φ(x,y)sin2Φ(x,y)sin2Φ(x,y)cos2Φ(x,y)],
T(x,y)=cosζI+isinζ12(ei2Φ(x,y)S++ei2Φ(x,y)S),
D(x,y)=T(x,y)Ein(x,y)=cosζeilinϕ(x,y)χ(±)+sinζei(lin±lg)ϕ(x,y)i2πx/Λχ().
Dm=cosζδmeilinϕ(x,y)χ(±)+sinζδm±1ei(lin±lg)ϕ(x,y)χ().
η0=cos2ζ,
η±1=|χ()Ψ|2sin2ζ,

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