Abstract

We have previously shown through simulation that an optical beam deflector based on the Pancharatnam (geometric) phase can provide high efficiency with up to 80° deflection using a dual-twist structure for polarization-state control [Appl. Opt. 54, 10035 (2015)]. In this report, we demonstrate that its optical performance is as predicted and far beyond what could be expected for a conventional diffractive optical device. We provide details about construction and characterization of a ± 40° beam-steering device with 90% diffraction efficiency based on our dual-twist design at a 633nm wavelength.

© 2017 Optical Society of America

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References

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  1. M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
    [Crossref]
  2. T. Todorov, L. Nikolova, and N. Tomova, “Polarization holography. 2: Polarization holographic gratings in photoanisotropic materials with and without intrinsic birefringence,” Appl. Opt. 23(24), 4588–4591 (1984).
    [Crossref] [PubMed]
  3. Y. Weng, D. Xu, Y. Zhang, X. Li, and S. T. Wu, “Polarization volume grating with high efficiency and large diffraction angle,” Opt. Express 24(16), 17746–17759 (2016).
    [Crossref] [PubMed]
  4. P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
    [Crossref]
  5. G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
    [Crossref]
  6. M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
    [Crossref]
  7. J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015).
    [Crossref]
  8. K. Gao, H. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Thin-film Pancharatnam lens with low f-number and high quality,” Opt. Express 23(20), 26086–26094 (2015).
    [Crossref] [PubMed]
  9. 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(12), 121105 (2006).
    [Crossref]
  10. U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
    [Crossref]
  11. 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(6), 7505–7510 (2013).
    [Crossref] [PubMed]
  12. N. Tabirian, S. Nersisyan, B. Kimball, and D. Steeves, “Broadband optics for manipulating light beams and images,” U.S. Patent Application No. 12/697,083, August 4, 2011.
  13. J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50(17), 2636–2639 (2011).
    [Crossref] [PubMed]
  14. H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,” SID Symp. Dig. Tech. Papers 45, 739–742 (2014).
    [Crossref]
  15. H. Chen, Y. Weng, D. Xu, N. V. Tabiryan, and S. T. Wu, “Beam steering for virtual/augmented reality displays with a cycloidal diffractive waveplate,” Opt. Express 24(7), 7287–7298 (2016).
    [Crossref] [PubMed]
  16. T. Li, Liquid crystal polarization gratings and their applications (Ph. D. Thesis, Hong Kong University of Science and Technology, 2013).
  17. C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006).
    [Crossref] [PubMed]
  18. C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008).
    [Crossref] [PubMed]
  19. C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
    [Crossref]
  20. M. J. Escuti, C. Oh, and R. Komanduri, “Low-twist chiral liquid crystal polarization gratings and related fabrication methods,” U.S. Patent Application No. 12/596,189, September 9, 2010.
  21. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
    [Crossref]
  22. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).
  23. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE, 2000).
  24. C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
    [Crossref]
  25. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Analysis of a dual-twist Pancharatnam phase device with ultrahigh-efficiency large-angle optical beam steering,” Appl. Opt. 54(34), 10035–10043 (2015).
    [Crossref] [PubMed]
  26. H. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Concept for a transmissive, large angle, light steering device with high efficiency,” Opt. Lett. 40(9), 2080–2083 (2015).
    [Crossref] [PubMed]

2016 (2)

2015 (4)

2013 (2)

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (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(6), 7505–7510 (2013).
[Crossref] [PubMed]

2011 (1)

2009 (1)

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

2008 (1)

2007 (2)

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

2006 (3)

M. J. Escuti, C. Oh, C. Sánchez, 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(12), 121105 (2006).
[Crossref]

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006).
[Crossref] [PubMed]

2005 (1)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

1990 (1)

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

1984 (1)

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Bastiaansen, C. W. M.

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

Bhowmik, A. K.

Bos, P. J.

Broer, D. J.

M. J. Escuti, C. Oh, C. Sánchez, 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. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Chen, H.

Cheng, H.

Cheng, H. H.

Cipparrone, G.

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(6), 7505–7510 (2013).
[Crossref] [PubMed]

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
[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(12), 121105 (2006).
[Crossref]

Crawford, G. P.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Eakin, J. N.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Escuti, M. J.

J. Kim, Y. Li, M. N. Miskiewicz, C. Oh, M. W. Kudenov, and M. J. Escuti, “Fabrication of ideal geometric-phase holograms with arbitrary wavefronts,” Optica 2(11), 958–964 (2015).
[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(17), 2636–2639 (2011).
[Crossref] [PubMed]

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008).
[Crossref] [PubMed]

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

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

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006).
[Crossref] [PubMed]

Gao, K.

Heikenfeld, J.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Kim, J.

Kudenov, M. W.

Li, X.

Li, Y.

Martinelli, M.

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

McManamon, P. F.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Miskiewicz, M. N.

Nikolova, L.

Oh, C.

Pagliusi, P.

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (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(6), 7505–7510 (2013).
[Crossref] [PubMed]

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(12), 121105 (2006).
[Crossref]

Pelcovits, R. A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Provenzano, C.

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (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(6), 7505–7510 (2013).
[Crossref] [PubMed]

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(12), 121105 (2006).
[Crossref]

Radcliffe, M. D.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Ruiz, U.

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (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(6), 7505–7510 (2013).
[Crossref] [PubMed]

Sánchez, C.

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

Serati, S.

J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50(17), 2636–2639 (2011).
[Crossref] [PubMed]

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Tabiryan, N. V.

Todorov, T.

Tomova, N.

Vavassori, P.

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

Volke-Sepúlveda, K.

Watson, E. A.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Weng, Y.

Wu, S. T.

Xie, H.

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Xu, D.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Zhang, Y.

Appl. Opt. (3)

Appl. Phys. Lett. (2)

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(12), 121105 (2006).
[Crossref]

U. Ruiz, P. Pagliusi, C. Provenzano, and G. Cipparrone, “Highly efficient generation of vector beams through polarization holograms,” Appl. Phys. Lett. 102(16), 161104 (2013).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

J. Appl. Phys. (1)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Opt. Commun. (1)

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Optica (1)

Phys. Rev. A (1)

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

Proc. IEEE (1)

P. F. McManamon, P. J. Bos, M. J. Escuti, J. Heikenfeld, S. Serati, H. Xie, and E. A. Watson, “A review of phased array steering for narrow-band electrooptical systems,” Proc. IEEE 97(6), 1078–1096 (2009).
[Crossref]

Proc. SPIE (2)

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

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

Other (6)

M. J. Escuti, C. Oh, and R. Komanduri, “Low-twist chiral liquid crystal polarization gratings and related fabrication methods,” U.S. Patent Application No. 12/596,189, September 9, 2010.

H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,” SID Symp. Dig. Tech. Papers 45, 739–742 (2014).
[Crossref]

N. Tabirian, S. Nersisyan, B. Kimball, and D. Steeves, “Broadband optics for manipulating light beams and images,” U.S. Patent Application No. 12/697,083, August 4, 2011.

T. Li, Liquid crystal polarization gratings and their applications (Ph. D. Thesis, Hong Kong University of Science and Technology, 2013).

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 2000).

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley-IEEE, 2000).

Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (1088 KB)      +40 beam steering
» Visualization 2: MP4 (1117 KB)      -40 beam steering

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Figures (12)

Fig. 1
Fig. 1 Concept of Pancharatnam phase deflector. (a) A c-PPD in its side-view and top-view. The inset shows a molecular alignment of reactive mesogen (RM). (b) A revolutionary dual-twist design in its side view with two combined DTPPDs, in which the twist angle is mirror symmetric. S/M/E correspond to the position of simulation in Fig. 11.
Fig. 2
Fig. 2 Simulation of the 1st-order intrinsic diffraction efficiency vs. diffraction angle for c-PPD with different birefringent media at normal incidence.
Fig. 3
Fig. 3 Schematics of the procedure for fabricating a Pancharatnam phase deflector.
Fig. 4
Fig. 4 Experimental setup for holographic exposure. (a) The blue laser (457 nm) with 200 mW power is used to expose the photo-alignment layer, and two coherent laser beams with the same intensity interfere at the place of the sample. (b) Observation of the interference pattern using a camera. (c) The appearance of written BY immediately after the exposure.
Fig. 5
Fig. 5 Schematics of optical setup for diffraction efficiency test.
Fig. 6
Fig. 6 Diffraction efficiency for a c-PPD. (a) A c-PPD with 20° deflection angle can achieve up to 97% efficiency upon the increased retardation, which is realized by coating RM257 layers and tested using a 633 nm wavelength of laser. (b) A c-PPD with 40° deflection angle can only achieve up to ~50% efficiency, experimentally tested using a 633 nm wavelength of laser.
Fig. 7
Fig. 7 Diffraction efficiency for a single DTPPD. (a) The efficiency of the 1st DTPPD upon the increased retardation is measured with input of LCP. Insets show photograph of the light intensity of each diffraction order with input of LCP/RCP after the 10th layer of RM257 is coated (photograph taken in a darkened room). (b) The schematic of optical performance observed in experiments when LCP/RCP is input to the 1st DTPPD, as shown in Fig. 1(b).
Fig. 8
Fig. 8 (a) The efficiency of a DTPPD as retardation increases with RCP input. (b) The schematic of optical performance observed in experiments when LCP/RCP is input to the 2nd DTPPD, as shown in Fig. 1(b).
Fig. 9
Fig. 9 The x component of the instantaneous E field in FDTD simulation for the 1st DTPPD with input of (a) LCP light and (b) RCP light. The black and white lines represent the wave front; red arrows represent the direction of light propagation.
Fig. 10
Fig. 10 The diffraction efficiency of the 1st DTPPD with input of (a) LCP light and (b) RCP light.
Fig. 11
Fig. 11 The y component of the instantaneous E field in FDTD simulation for this ± 40° beam steering device as (a) a positive deflector and (b) a negative deflector. S/M/E correspond to the position as shown in Fig. 1(b). The black and white lines represent the wave front; red arrows represent the direction of light propagation.
Fig. 12
Fig. 12 Realization of a ± 40° beam steering from two combined DTPPDs. (a) By using the input of RCP, the red laser beam is diffracted to its + 1st-order with + 40° deflection angle (see Visualization 1). (b) By using the input of LCP, the red laser beam is diffracted to its −1st- order with −40° deflection angle (see Visualization 2). Insets show the simulation result of far field intensity in both cases with the same unit and coordinate as shown in Fig. 10.

Tables (1)

Tables Icon

Table 1 Transmission and reflection of ± 40° steered beam

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

[ E out ]=[M(Γ,φ)][ E in ], with [M(Γ,φ)]=[R(φ)][ e iΓ/2 0 0 e iΓ/2 ][R(φ)].
[ E zout E xout ]=cos Γ 2 [ 1 ±i ]isin Γ 2 e i(2φ(x)) [ 1 i ],
[ E zout E xout ]=i e i(2φ(x)) [ 1 i ].
η mth i = I mth I Totaldiff , with I Totaldiff = m I mth .

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