Digital Stokes polarimetry and its application to structured light: tutorial

Keshaan Singh; Najmeh Tabebordbar; Andrew Forbes; Angela Dudley

doi:10.1364/JOSAA.397912

Journal of the Optical Society of America A
Vol. 37,
Issue 11,
pp. C33-C44
(2020)
•https://doi.org/10.1364/JOSAA.397912

Digital Stokes polarimetry and its application to structured light: tutorial

Keshaan Singh, Najmeh Tabebordbar, Andrew Forbes, and Angela Dudley

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Keshaan Singh, Najmeh Tabebordbar, Andrew Forbes, and Angela Dudley, "Digital Stokes polarimetry and its application to structured light: tutorial," J. Opt. Soc. Am. A 37, C33-C44 (2020)

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Abstract

Stokes polarimetry is a mature topic in optics, most commonly performed to extract the polarization structure of optical fields for a range of diverse applications. For historical reasons, most Stokes polarimetry approaches are based on static optical polarization components that must be manually adjusted, prohibiting automated, real-time analysis of fast changing fields. Here we provide a tutorial on performing Stokes polarimetry in an all-digital approach, exploiting a modern optical toolkit based on liquid-crystal-on-silicon spatial light modulators and digital micromirror devices. We explain in a tutorial fashion how to implement two digital approaches, based on these two devices, for extracting Stokes parameters in a fast, cheap, and dynamic manner. After outlining the core concepts, we demonstrate their applicability to the modern topic of structured light, and highlight some common experimental issues. In particular, we illustrate how digital Stokes polarimetry can be used to measure key optical parameters such as the state of polarization, degree of vectorness, and intra-modal phase of complex light fields.

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References

View by:
Article Order
Year
Author
Publication

J. D. Pye, Polarised Light in Science and Nature (CRC Press, 2015).
S. Cloude, Polarisation: Applications in Remote Sensing (Oxford University, 2010).
E. Collett, “The description of polarization in classical physics,” Am. J. Phys. 36, 713–725 (1968).
[Crossref]
E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekkar, 1993).
E. Wolf, “Optics in terms of observable quantities,” Nuovo. Cim. 12, 884–888 (1954).
[Crossref]
G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399 (1851).
W. A. Shurcliff, Polarized Light; Production and Use (Harvard University, 1962).
D. Clarke and J. Grainger, “Polarized light and optical measurement,” Am. J. Phys. 40, 1055–1056 (1971).
[Crossref]
M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (1997).
D. H. Goldstein, Polarized Light (CRC Press, 2016).
W. H. McMaster, “Polarization and the Stokes parameters,” Am. J. Phys. 22, 351–362 (1954).
[Crossref]
H. Berry, L. Curtis, D. Ellis, and R. Schectman, “Anisotropy in the beam-foil light source,” Phys. Rev. Lett. 32, 751 (1974).
[Crossref]
B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]
E. Collett, “Determination of the ellipsometric characteristics of optical surfaces using nanosecond laser pulses,” Surf. Sci. 96, 156–167 (1980).
[Crossref]
R. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[Crossref]
M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of space-variant polarizations,” Opt. Express 18, 10805–10812 (2010).
[Crossref]
P. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[Crossref]
R. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
[Crossref]
H. G. Berry, G. Gabrielse, and A. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. 16, 3200–3205 (1977).
[Crossref]
J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216 (2000).
[Crossref]
E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455, 120–123 (2004).
[Crossref]
G. Myhre, W.-L. Hsu, A. Peinado, C. LaCasse, N. Brock, R. A. Chipman, and S. Pau, “Liquid crystal polymer full-stokes division of focal plane polarimeter,” Opt. Express 20, 27393–27409 (2012).
[Crossref]
J. B. Mueller, K. Leosson, and F. Capasso, “Ultracompact metasurface in-line polarimeter,” Optica 3, 42–47 (2016).
[Crossref]
E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes imaging polarimetry using dielectric metasurfaces,” ACS Photon. 5, 3132–3140 (2018).
[Crossref]
S. Shibata, N. Hagen, S. Kawabata, and Y. Otani, “Compact and high-speed Stokes polarimeter using three-way polarization-preserving beam splitters,” Appl. Opt. 58, 5644–5649 (2019).
[Crossref]
C. Rosales-Guzmán and A. Forbes, How to Shape Light with Spatial Light Modulators (SPIE, 2017).
A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200–227 (2016).
[Crossref]
G. Lazarev, P.-J. Chen, J. Strauss, N. Fontaine, and A. Forbes, “Beyond the display: phase-only liquid crystal on silicon devices and their applications in photonics,” Opt. Express 27, 16206–16249 (2019).
[Crossref]
L. J. Hornbeck, “Digital light processing and MEMS: an overview,” in Digest IEEE/Leos 1996 Summer Topical Meeting. Advanced Applications of Lasers in Materials and Processing (IEEE, 1996), pp. 7–8.
Y.-X. Ren, R.-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]
S. Scholes, R. Kara, J. Pinnell, V. Rodríguez-Fajardo, and A. Forbes, “Structured light with digital micromirror devices: a guide to best practice,” Opt. Eng. 59, 1–12 (2019).
[Crossref]
A. Peña and M. F. Andersen, “Complete polarization and phase control with a single spatial light modulator for the generation of complex light fields,” Laser Phys. 28, 076201 (2018).
[Crossref]
Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light Sci. Appl. 8, 90 (2019).
[Crossref]
H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]
A. Forbes and I. Nape, “Quantum mechanics with patterns of light: progress in high dimensional and multidimensional entanglement with structured light,” AVS Quantum Sci. 1, 011701 (2019).
[Crossref]
Q. Hu, Y. Dai, C. He, and M. J. Booth, “Arbitrary vectorial state conversion using liquid crystal spatial light modulators,” Opt. Commun. 459, 125028 (2020).
[Crossref]
C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20, 123001 (2018).
[Crossref]
E. Otte, C. Alpmann, and C. Denz, “Polarization singularity explosions in tailored light fields,” Laser Photon. Rev. 12, 1700200 (2018).
[Crossref]
E. Otte and C. Denz, “Sculpting complex polarization singularity networks,” Opt. Lett. 43, 5821–5824 (2018).
[Crossref]
E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularitites in tailored vector beams,” J. Opt. 18, 074012 (2016).
[Crossref]
J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]
Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[Crossref]
S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photon. Res. 6, 228–233 (2018).
[Crossref]
B. Perez-Garcia, C. López-Mariscal, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “On-demand tailored vector beams,” Appl. Opt. 56, 6967–6972 (2017).
[Crossref]
W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21, 20692–20706 (2013).
[Crossref]
T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347, 964–966 (2015).
[Crossref]
E. J. Galvez, I. Dutta, K. Beach, J. J. Zeosky, J. A. Jones, and B. Khajavi, “Multitwist Möbius strips and twisted ribbons in the polarization of paraxial light beams,” Sci. Rep. 7, 13653 (2017).
[Crossref]
E. J. Galvez, S. Khadka, W. H. Schubert, and S. Nomoto, “Poincaré-beam patterns produced by nonseparable superpositions of Laguerre–Gauss and polarization modes of light,” Appl. Opt. 51, 2925–2934 (2012).
[Crossref]
H. Larocque, D. Sugic, D. Mortimer, A. J. Taylor, R. Fickler, R. W. Boyd, M. R. Dennis, and E. Karimi, “Reconstructing the topology of optical polarization knots,” Nat. Phys. 14, 1079–1082 (2018).
[Crossref]
A. Dudley, G. Milione, R. R. Alfano, and A. Forbes, “All-digital wavefront sensing for structured light beams,” Opt. Express 22, 14031–14040 (2014).
[Crossref]
B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett. 41, 3407–3410 (2016).
[Crossref]
M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]
V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]
E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photon. 11, 67–134 (2019).
[Crossref]
X.-B. Hu, B. Zhao, Z.-H. Zhu, W. Gao, and C. Rosales-Guzmán, “In situ detection of a cooperative target’s longitudinal and angular speed using structured light,” Opt. Lett. 44, 3070–3073 (2019).
[Crossref]
B. Zhao, X.-B. Hu, V. Rodrguez-Fajardo, Z.-H. Zhu, W. Gao, A. Forbes, and C. Rosales-Guzmán, “Real-time Stokes polarimetry using a digital micromirror device,” Opt. Express 27, 31087–31093 (2019).
[Crossref]
A. Manthalkar, I. Nape, N. T. Bordbar, C. Rosales-Guzmán, S. Bhattacharya, A. Forbes, and A. Dudley, “All-digital Stokes polarimetry with a digital micromirror device,” Opt. Lett. 45, 2319–2322 (2020).
[Crossref]
A. Selyem, C. Rosales-Guzmán, S. Croke, A. Forbes, and S. Franke-Arnold, “Basis-independent tomography and nonseparability witnesses of pure complex vectorial light fields by Stokes projections,” Phys. Rev. A 100, 063842 (2019).
[Crossref]
B. Zhao, X.-B. Hu, V. Rodrguez-Fajardo, A. Forbes, W. Gao, Z.-H. Zhu, and C. Rosales-Guzmán, “Determining the non-separability of vector modes with digital micromirror devices,” Appl. Phys. Lett. 116, 091101 (2020).
[Crossref]
K. J. Mitchell, S. Turtaev, M. J. Padgett, T. Čižmár, and D. B. Phillips, “High-speed spatial control of the intensity, phase and polarisation of vector beams using a digital micro-mirror device,” Opt. Express 24, 29269–29282 (2016).
[Crossref]
M. A. Cox, E. Toninelli, L. Cheng, M. J. Padgett, and A. Forbes, “A high-speed, wavelength invariant, single-pixel wavefront sensor with a digital micromirror device,” IEEE Access 7, 85860–85866 (2019).
[Crossref]
S. Shin, K. Lee, Z. Yaqoob, P. T. So, and Y. Park, “Reference-free polarization-sensitive quantitative phase imaging using single-point optical phase conjugation,” Opt. Express 26, 26858–26865 (2018).
[Crossref]
S. Turtaev, I. T. Leite, K. J. Mitchell, M. J. Padgett, D. B. Phillips, and T. Čižmár, “Comparison of nematic liquid-crystal and DMD based spatial light modulation in complex photonics,” Opt. Express 25, 29874–29884 (2017).
[Crossref]
L. J. Hornbeck, “Deformable mirror light modulator,” U.S. patent4,441,791 (April10, 1984).
L. J. Hornbeck, “Current status of the digital micromirror device (DMD) for projection television applications,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 1993), pp. 381–384.
J. B. Sampsell, “Digital micromirror device and its application to projection displays,” J. Vac. Sci. Technol. B 12, 3242–3246 (1994).
[Crossref]
T. M. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]
Y. Li, J. Kim, and M. J. Escuti, “Orbital angular momentum generation and mode transformation with high efficiency using forked polarization gratings,” Appl. Opt. 51, 8236–8245 (2012).
[Crossref]
R. Komanduri and M. Escuti, “High efficiency reflective liquid crystal polarization gratings,” Appl. Phys. Lett. 95, 091106 (2009).
[Crossref]
E. Nicolescu and M. J. Escuti, “Polarization-independent tunable optical filters using bilayer polarization gratings,” Appl. Opt. 49, 3900–3904 (2010).
[Crossref]
A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
[Crossref]
W.-H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
[Crossref]
L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]
A. Vaziri, G. Weihs, and A. Zeilinger, “Superpositions of the orbital angular momentum for applications in quantum experiments,” J. Opt. B 4, S47 (2002).
[Crossref]
https://github.com/angeladudley1983/DigitalStokesCalc .
C. Schulze, D. Flamm, M. Duparré, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
[Crossref]
W. K. Wootters, “Entanglement of formation and concurrence,” Quantum Inf. Comput. 1, 27–44 (2001).

2020 (3)

Q. Hu, Y. Dai, C. He, and M. J. Booth, “Arbitrary vectorial state conversion using liquid crystal spatial light modulators,” Opt. Commun. 459, 125028 (2020).
[Crossref]

A. Manthalkar, I. Nape, N. T. Bordbar, C. Rosales-Guzmán, S. Bhattacharya, A. Forbes, and A. Dudley, “All-digital Stokes polarimetry with a digital micromirror device,” Opt. Lett. 45, 2319–2322 (2020).
[Crossref]

B. Zhao, X.-B. Hu, V. Rodrguez-Fajardo, A. Forbes, W. Gao, Z.-H. Zhu, and C. Rosales-Guzmán, “Determining the non-separability of vector modes with digital micromirror devices,” Appl. Phys. Lett. 116, 091101 (2020).
[Crossref]

2019 (10)

A. Selyem, C. Rosales-Guzmán, S. Croke, A. Forbes, and S. Franke-Arnold, “Basis-independent tomography and nonseparability witnesses of pure complex vectorial light fields by Stokes projections,” Phys. Rev. A 100, 063842 (2019).
[Crossref]

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photon. 11, 67–134 (2019).
[Crossref]

X.-B. Hu, B. Zhao, Z.-H. Zhu, W. Gao, and C. Rosales-Guzmán, “In situ detection of a cooperative target’s longitudinal and angular speed using structured light,” Opt. Lett. 44, 3070–3073 (2019).
[Crossref]

B. Zhao, X.-B. Hu, V. Rodrguez-Fajardo, Z.-H. Zhu, W. Gao, A. Forbes, and C. Rosales-Guzmán, “Real-time Stokes polarimetry using a digital micromirror device,” Opt. Express 27, 31087–31093 (2019).
[Crossref]

M. A. Cox, E. Toninelli, L. Cheng, M. J. Padgett, and A. Forbes, “A high-speed, wavelength invariant, single-pixel wavefront sensor with a digital micromirror device,” IEEE Access 7, 85860–85866 (2019).
[Crossref]

A. Forbes and I. Nape, “Quantum mechanics with patterns of light: progress in high dimensional and multidimensional entanglement with structured light,” AVS Quantum Sci. 1, 011701 (2019).
[Crossref]

S. Shibata, N. Hagen, S. Kawabata, and Y. Otani, “Compact and high-speed Stokes polarimeter using three-way polarization-preserving beam splitters,” Appl. Opt. 58, 5644–5649 (2019).
[Crossref]

G. Lazarev, P.-J. Chen, J. Strauss, N. Fontaine, and A. Forbes, “Beyond the display: phase-only liquid crystal on silicon devices and their applications in photonics,” Opt. Express 27, 16206–16249 (2019).
[Crossref]

S. Scholes, R. Kara, J. Pinnell, V. Rodríguez-Fajardo, and A. Forbes, “Structured light with digital micromirror devices: a guide to best practice,” Opt. Eng. 59, 1–12 (2019).
[Crossref]

Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, and X. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light Sci. Appl. 8, 90 (2019).
[Crossref]

2018 (9)

A. Peña and M. F. Andersen, “Complete polarization and phase control with a single spatial light modulator for the generation of complex light fields,” Laser Phys. 28, 076201 (2018).
[Crossref]

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes imaging polarimetry using dielectric metasurfaces,” ACS Photon. 5, 3132–3140 (2018).
[Crossref]

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20, 123001 (2018).
[Crossref]

E. Otte, C. Alpmann, and C. Denz, “Polarization singularity explosions in tailored light fields,” Laser Photon. Rev. 12, 1700200 (2018).
[Crossref]

E. Otte and C. Denz, “Sculpting complex polarization singularity networks,” Opt. Lett. 43, 5821–5824 (2018).
[Crossref]

S. Shin, K. Lee, Z. Yaqoob, P. T. So, and Y. Park, “Reference-free polarization-sensitive quantitative phase imaging using single-point optical phase conjugation,” Opt. Express 26, 26858–26865 (2018).
[Crossref]

S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, and J. Zhao, “Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude,” Photon. Res. 6, 228–233 (2018).
[Crossref]

H. Larocque, D. Sugic, D. Mortimer, A. J. Taylor, R. Fickler, R. W. Boyd, M. R. Dennis, and E. Karimi, “Reconstructing the topology of optical polarization knots,” Nat. Phys. 14, 1079–1082 (2018).
[Crossref]

2017 (4)

B. Perez-Garcia, C. López-Mariscal, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “On-demand tailored vector beams,” Appl. Opt. 56, 6967–6972 (2017).
[Crossref]

E. J. Galvez, I. Dutta, K. Beach, J. J. Zeosky, J. A. Jones, and B. Khajavi, “Multitwist Möbius strips and twisted ribbons in the polarization of paraxial light beams,” Sci. Rep. 7, 13653 (2017).
[Crossref]

S. Turtaev, I. T. Leite, K. J. Mitchell, M. J. Padgett, D. B. Phillips, and T. Čižmár, “Comparison of nematic liquid-crystal and DMD based spatial light modulation in complex photonics,” Opt. Express 25, 29874–29884 (2017).
[Crossref]

H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

2016 (6)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200–227 (2016).
[Crossref]

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularitites in tailored vector beams,” J. Opt. 18, 074012 (2016).
[Crossref]

J. B. Mueller, K. Leosson, and F. Capasso, “Ultracompact metasurface in-line polarimeter,” Optica 3, 42–47 (2016).
[Crossref]

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett. 41, 3407–3410 (2016).
[Crossref]

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]

K. J. Mitchell, S. Turtaev, M. J. Padgett, T. Čižmár, and D. B. Phillips, “High-speed spatial control of the intensity, phase and polarisation of vector beams using a digital micro-mirror device,” Opt. Express 24, 29269–29282 (2016).
[Crossref]

2015 (3)

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347, 964–966 (2015).
[Crossref]

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

Y.-X. Ren, R.-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

2009 (2)

R. Komanduri and M. Escuti, “High efficiency reflective liquid crystal polarization gratings,” Appl. Phys. Lett. 95, 091106 (2009).
[Crossref]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[Crossref]

2007 (1)

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

2004 (1)

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455, 120–123 (2004).
[Crossref]

2002 (1)

A. Vaziri, G. Weihs, and A. Zeilinger, “Superpositions of the orbital angular momentum for applications in quantum experiments,” J. Opt. B 4, S47 (2002).
[Crossref]

2001 (2)

W. K. Wootters, “Entanglement of formation and concurrence,” Quantum Inf. Comput. 1, 27–44 (2001).

T. M. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

2000 (1)

J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216 (2000).
[Crossref]

1994 (1)

J. B. Sampsell, “Digital micromirror device and its application to projection displays,” J. Vac. Sci. Technol. B 12, 3242–3246 (1994).
[Crossref]

1985 (1)

R. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
[Crossref]

1982 (1)

R. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[Crossref]

1980 (2)

E. Collett, “Determination of the ellipsometric characteristics of optical surfaces using nanosecond laser pulses,” Surf. Sci. 96, 156–167 (1980).
[Crossref]

P. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[Crossref]

1977 (1)

H. G. Berry, G. Gabrielse, and A. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. 16, 3200–3205 (1977).
[Crossref]

1974 (2)

H. Berry, L. Curtis, D. Ellis, and R. Schectman, “Anisotropy in the beam-foil light source,” Phys. Rev. Lett. 32, 751 (1974).
[Crossref]

W.-H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
[Crossref]

1971 (1)

D. Clarke and J. Grainger, “Polarized light and optical measurement,” Am. J. Phys. 40, 1055–1056 (1971).
[Crossref]

1968 (1)

E. Collett, “The description of polarization in classical physics,” Am. J. Phys. 36, 713–725 (1968).
[Crossref]

1954 (2)

E. Wolf, “Optics in terms of observable quantities,” Nuovo. Cim. 12, 884–888 (1954).
[Crossref]

W. H. McMaster, “Polarization and the Stokes parameters,” Am. J. Phys. 22, 351–362 (1954).
[Crossref]

1851 (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399 (1851).

Alfano, R. R.

A. Dudley, G. Milione, R. R. Alfano, and A. Forbes, “All-digital wavefront sensing for structured light beams,” Opt. Express 22, 14031–14040 (2014).
[Crossref]

Alpmann, C.

E. Otte, C. Alpmann, and C. Denz, “Polarization singularity explosions in tailored light fields,” Laser Photon. Rev. 12, 1700200 (2018).
[Crossref]

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularitites in tailored vector beams,” J. Opt. 18, 074012 (2016).
[Crossref]

Ambrosio, A.

Andersen, M. F.

A. Peña and M. F. Andersen, “Complete polarization and phase control with a single spatial light modulator for the generation of complex light fields,” Laser Phys. 28, 076201 (2018).
[Crossref]

Andrews, D. L.

Arbabi, A.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes imaging polarimetry using dielectric metasurfaces,” ACS Photon. 5, 3132–3140 (2018).
[Crossref]

Arbabi, E.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes imaging polarimetry using dielectric metasurfaces,” ACS Photon. 5, 3132–3140 (2018).
[Crossref]

Aswendt, P.

T. M. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

Azzam, R.

R. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
[Crossref]

R. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[Crossref]

Baker, M.

Banzer, P.

Barrett, D.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Bauer, T.

Beach, K.

Belmonte, A.

Berry, H.

H. Berry, L. Curtis, D. Ellis, and R. Schectman, “Anisotropy in the beam-foil light source,” Phys. Rev. Lett. 32, 751 (1974).
[Crossref]

Berry, H. G.

H. G. Berry, G. Gabrielse, and A. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. 16, 3200–3205 (1977).
[Crossref]

Berry, M. V.

Bhattacharya, S.

Bigelow, N. P.

Booth, M. J.

Q. Hu, Y. Dai, C. He, and M. J. Booth, “Arbitrary vectorial state conversion using liquid crystal spatial light modulators,” Opt. Commun. 459, 125028 (2020).
[Crossref]

Bordbar, N. T.

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (1997).

Boyd, R. W.

Brock, N.

Bueno, J. M.

J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216 (2000).
[Crossref]

Capasso, F.

J. B. Mueller, K. Leosson, and F. Capasso, “Ultracompact metasurface in-line polarimeter,” Optica 3, 42–47 (2016).
[Crossref]

Carvacho, G.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]

Chen, J.

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

Chen, P.-J.

Cheng, L.

Cheng, W.

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21, 20692–20706 (2013).
[Crossref]

Chipman, R. A.

Cižmár, T.

Clarke, D.

D. Clarke and J. Grainger, “Polarized light and optical measurement,” Am. J. Phys. 40, 1055–1056 (1971).
[Crossref]

Cloude, S.

S. Cloude, Polarisation: Applications in Remote Sensing (Oxford University, 2010).

Collett, E.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

E. Collett, “Determination of the ellipsometric characteristics of optical surfaces using nanosecond laser pulses,” Surf. Sci. 96, 156–167 (1980).
[Crossref]

E. Collett, “The description of polarization in classical physics,” Am. J. Phys. 36, 713–725 (1968).
[Crossref]

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekkar, 1993).

Cox, M. A.

Croke, S.

Curtis, L.

H. Berry, L. Curtis, D. Ellis, and R. Schectman, “Anisotropy in the beam-foil light source,” Phys. Rev. Lett. 32, 751 (1974).
[Crossref]

D’Ambrosio, V.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]

Dai, Y.

Q. Hu, Y. Dai, C. He, and M. J. Booth, “Arbitrary vectorial state conversion using liquid crystal spatial light modulators,” Opt. Commun. 459, 125028 (2020).
[Crossref]

Davidson, N.

M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of space-variant polarizations,” Opt. Express 18, 10805–10812 (2010).
[Crossref]

De Martino, A.

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455, 120–123 (2004).
[Crossref]

Dennis, M. R.

Denz, C.

E. Otte and C. Denz, “Sculpting complex polarization singularity networks,” Opt. Lett. 43, 5821–5824 (2018).
[Crossref]

E. Otte, C. Alpmann, and C. Denz, “Polarization singularity explosions in tailored light fields,” Laser Photon. Rev. 12, 1700200 (2018).
[Crossref]

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularitites in tailored vector beams,” J. Opt. 18, 074012 (2016).
[Crossref]

Drevillon, B.

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455, 120–123 (2004).
[Crossref]

Dudley, A.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200–227 (2016).
[Crossref]

A. Dudley, G. Milione, R. R. Alfano, and A. Forbes, “All-digital wavefront sensing for structured light beams,” Opt. Express 22, 14031–14040 (2014).
[Crossref]

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
[Crossref]

Duparré, M.

C. Schulze, D. Flamm, M. Duparré, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
[Crossref]

Dutta, I.

Ellis, D.

H. Berry, L. Curtis, D. Ellis, and R. Schectman, “Anisotropy in the beam-foil light source,” Phys. Rev. Lett. 32, 751 (1974).
[Crossref]

Escuti, M.

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
[Crossref]

R. Komanduri and M. Escuti, “High efficiency reflective liquid crystal polarization gratings,” Appl. Phys. Lett. 95, 091106 (2009).
[Crossref]

Escuti, M. J.

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

Faraon, A.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes imaging polarimetry using dielectric metasurfaces,” ACS Photon. 5, 3132–3140 (2018).
[Crossref]

Fickler, R.

Flamm, D.

C. Schulze, D. Flamm, M. Duparré, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
[Crossref]

Fontaine, N.

Forbes, A.

S. Scholes, R. Kara, J. Pinnell, V. Rodríguez-Fajardo, and A. Forbes, “Structured light with digital micromirror devices: a guide to best practice,” Opt. Eng. 59, 1–12 (2019).
[Crossref]

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20, 123001 (2018).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200–227 (2016).
[Crossref]

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett. 41, 3407–3410 (2016).
[Crossref]

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

A. Dudley, G. Milione, R. R. Alfano, and A. Forbes, “All-digital wavefront sensing for structured light beams,” Opt. Express 22, 14031–14040 (2014).
[Crossref]

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
[Crossref]

C. Schulze, D. Flamm, M. Duparré, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
[Crossref]

C. Rosales-Guzmán and A. Forbes, How to Shape Light with Spatial Light Modulators (SPIE, 2017).

Fraher, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Franke-Arnold, S.

Fridman, M.

M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of space-variant polarizations,” Opt. Express 18, 10805–10812 (2010).
[Crossref]

Friesem, A. A.

M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of space-variant polarizations,” Opt. Express 18, 10805–10812 (2010).
[Crossref]

Fu, X.

Gabrielse, G.

H. G. Berry, G. Gabrielse, and A. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. 16, 3200–3205 (1977).
[Crossref]

Galvez, E. J.

Gao, W.

Garcia-Caurel, E.

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455, 120–123 (2004).
[Crossref]

Goldstein, D. H.

D. H. Goldstein, Polarized Light (CRC Press, 2016).

Gong, L.

Y.-X. Ren, R.-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

Gong, M.

Gordon, R.

Graffitti, F.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]

Grainger, J.

D. Clarke and J. Grainger, “Polarized light and optical measurement,” Am. J. Phys. 40, 1055–1056 (1971).
[Crossref]

Grinvald, E.

M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of space-variant polarizations,” Opt. Express 18, 10805–10812 (2010).
[Crossref]

Gutiérrez-Vega, J. C.

B. Perez-Garcia, C. López-Mariscal, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “On-demand tailored vector beams,” Appl. Opt. 56, 6967–6972 (2017).
[Crossref]

Hagen, N.

S. Shibata, N. Hagen, S. Kawabata, and Y. Otani, “Compact and high-speed Stokes polarimeter using three-way polarization-preserving beam splitters,” Appl. Opt. 58, 5644–5649 (2019).
[Crossref]

Han, L.

Han, W.

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21, 20692–20706 (2013).
[Crossref]

Hauge, P.

P. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[Crossref]

He, C.

Q. Hu, Y. Dai, C. He, and M. J. Booth, “Arbitrary vectorial state conversion using liquid crystal spatial light modulators,” Opt. Commun. 459, 125028 (2020).
[Crossref]

Hernandez-Aranda, R. I.

B. Perez-Garcia, C. López-Mariscal, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “On-demand tailored vector beams,” Appl. Opt. 56, 6967–6972 (2017).
[Crossref]

Höfling, R.

T. M. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

Hornbeck, L. J.

L. J. Hornbeck, “Deformable mirror light modulator,” U.S. patent4,441,791 (April10, 1984).

L. J. Hornbeck, “Current status of the digital micromirror device (DMD) for projection television applications,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 1993), pp. 381–384.

L. J. Hornbeck, “Digital light processing and MEMS: an overview,” in Digest IEEE/Leos 1996 Summer Topical Meeting. Advanced Applications of Lasers in Materials and Processing (IEEE, 1996), pp. 7–8.

Hsu, W.-L.

Hu, Q.

Q. Hu, Y. Dai, C. He, and M. J. Booth, “Arbitrary vectorial state conversion using liquid crystal spatial light modulators,” Opt. Commun. 459, 125028 (2020).
[Crossref]

Hu, X.-B.

Jones, J. A.

Kamali, S. M.

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes imaging polarimetry using dielectric metasurfaces,” ACS Photon. 5, 3132–3140 (2018).
[Crossref]

Kara, R.

S. Scholes, R. Kara, J. Pinnell, V. Rodríguez-Fajardo, and A. Forbes, “Structured light with digital micromirror devices: a guide to best practice,” Opt. Eng. 59, 1–12 (2019).
[Crossref]

Karimi, E.

Kawabata, S.

S. Shibata, N. Hagen, S. Kawabata, and Y. Otani, “Compact and high-speed Stokes polarimeter using three-way polarization-preserving beam splitters,” Appl. Opt. 58, 5644–5649 (2019).
[Crossref]

Khadka, S.

Khajavi, B.

Kim, J.

Komanduri, R.

R. Komanduri and M. Escuti, “High efficiency reflective liquid crystal polarization gratings,” Appl. Phys. Lett. 95, 091106 (2009).
[Crossref]

Konrad, T.

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

Kreis, T. M.

T. M. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

LaCasse, C.

Larocque, H.

Lazarev, G.

Lee, K.

Lee, W.-H.

W.-H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
[Crossref]

Leite, I. T.

Leosson, K.

J. B. Mueller, K. Leosson, and F. Capasso, “Ultracompact metasurface in-line polarimeter,” Optica 3, 42–47 (2016).
[Crossref]

Leuchs, G.

Li, P.

Li, Y.

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
[Crossref]

Litchinitser, N. M.

Liu, Q.

Liu, S.

Livingston, A.

H. G. Berry, G. Gabrielse, and A. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. 16, 3200–3205 (1977).
[Crossref]

López-Mariscal, C.

B. Perez-Garcia, C. López-Mariscal, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “On-demand tailored vector beams,” Appl. Opt. 56, 6967–6972 (2017).
[Crossref]

Lu, R.-D.

Y.-X. Ren, R.-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

Mansuripur, M.

Manthalkar, A.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Marrucci, L.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

McLaren, M.

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett. 41, 3407–3410 (2016).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200–227 (2016).
[Crossref]

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

McMaster, W. H.

W. H. McMaster, “Polarization and the Stokes parameters,” Am. J. Phys. 22, 351–362 (1954).
[Crossref]

McMorran, B.

Mhlanga, T.

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
[Crossref]

Milione, G.

A. Dudley, G. Milione, R. R. Alfano, and A. Forbes, “All-digital wavefront sensing for structured light beams,” Opt. Express 22, 14031–14040 (2014).
[Crossref]

Min, C.

Mitchell, K. J.

Mortimer, D.

Mueller, J. B.

J. B. Mueller, K. Leosson, and F. Capasso, “Ultracompact metasurface in-line polarimeter,” Optica 3, 42–47 (2016).
[Crossref]

Myhre, G.

Nape, I.

Ndagano, B.

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20, 123001 (2018).
[Crossref]

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett. 41, 3407–3410 (2016).
[Crossref]

Neely, T. W.

Nicolescu, E.

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

Nixon, M.

M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of space-variant polarizations,” Opt. Express 18, 10805–10812 (2010).
[Crossref]

Nomoto, S.

Orlov, S.

Otani, Y.

S. Shibata, N. Hagen, S. Kawabata, and Y. Otani, “Compact and high-speed Stokes polarimeter using three-way polarization-preserving beam splitters,” Appl. Opt. 58, 5644–5649 (2019).
[Crossref]

Otte, E.

E. Otte, C. Alpmann, and C. Denz, “Polarization singularity explosions in tailored light fields,” Laser Photon. Rev. 12, 1700200 (2018).
[Crossref]

E. Otte and C. Denz, “Sculpting complex polarization singularity networks,” Opt. Lett. 43, 5821–5824 (2018).
[Crossref]

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularitites in tailored vector beams,” J. Opt. 18, 074012 (2016).
[Crossref]

Padgett, M.

Padgett, M. J.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

Park, Y.

Pau, S.

Peinado, A.

Peña, A.

A. Peña and M. F. Andersen, “Complete polarization and phase control with a single spatial light modulator for the generation of complex light fields,” Laser Phys. 28, 076201 (2018).
[Crossref]

Perez-Garcia, B.

B. Perez-Garcia, C. López-Mariscal, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “On-demand tailored vector beams,” Appl. Opt. 56, 6967–6972 (2017).
[Crossref]

Phillips, D. B.

Piccirillo, B.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]

Pinnell, J.

S. Scholes, R. Kara, J. Pinnell, V. Rodríguez-Fajardo, and A. Forbes, “Structured light with digital micromirror devices: a guide to best practice,” Opt. Eng. 59, 1–12 (2019).
[Crossref]

Pye, J. D.

J. D. Pye, Polarised Light in Science and Nature (CRC Press, 2015).

Qi, S.

Ren, Y.-X.

Y.-X. Ren, R.-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

Ritsch-Marte, M.

Rodrguez-Fajardo, V.

Rodríguez-Fajardo, V.

S. Scholes, R. Kara, J. Pinnell, V. Rodríguez-Fajardo, and A. Forbes, “Structured light with digital micromirror devices: a guide to best practice,” Opt. Eng. 59, 1–12 (2019).
[Crossref]

Romero, J.

Rosales-Guzmán, C.

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20, 123001 (2018).
[Crossref]

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett. 41, 3407–3410 (2016).
[Crossref]

C. Rosales-Guzmán and A. Forbes, How to Shape Light with Spatial Light Modulators (SPIE, 2017).

Rubano, A.

Rubinsztein-Dunlop, H.

Sampsell, J. B.

J. B. Sampsell, “Digital micromirror device and its application to projection displays,” J. Vac. Sci. Technol. B 12, 3242–3246 (1994).
[Crossref]

Santamato, E.

Schaefer, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Schectman, R.

H. Berry, L. Curtis, D. Ellis, and R. Schectman, “Anisotropy in the beam-foil light source,” Phys. Rev. Lett. 32, 751 (1974).
[Crossref]

Scholes, S.

S. Scholes, R. Kara, J. Pinnell, V. Rodríguez-Fajardo, and A. Forbes, “Structured light with digital micromirror devices: a guide to best practice,” Opt. Eng. 59, 1–12 (2019).
[Crossref]

Schubert, W. H.

Schulze, C.

C. Schulze, D. Flamm, M. Duparré, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
[Crossref]

Sciarrino, F.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]

Selyem, A.

Sephton, B.

Shen, Y.

Shibata, S.

S. Shibata, N. Hagen, S. Kawabata, and Y. Otani, “Compact and high-speed Stokes polarimeter using three-way polarization-preserving beam splitters,” Appl. Opt. 58, 5644–5649 (2019).
[Crossref]

Shin, S.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light; Production and Use (Harvard University, 1962).

Smyth, R.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

So, P. T.

Sroor, H.

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett. 41, 3407–3410 (2016).
[Crossref]

Stilgoe, A. B.

Stokes, G. G.

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399 (1851).

Strauss, J.

Sugic, D.

Taylor, A. J.

Toninelli, E.

Torres, J. P.

Turtaev, S.

Vallés, A.

Vaziri, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Superpositions of the orbital angular momentum for applications in quantum experiments,” J. Opt. B 4, S47 (2002).
[Crossref]

Vitelli, C.

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]

Wan, C.

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

Wang, X.

Weihs, G.

A. Vaziri, G. Weihs, and A. Zeilinger, “Superpositions of the orbital angular momentum for applications in quantum experiments,” J. Opt. B 4, S47 (2002).
[Crossref]

Weiner, A. M.

White, A. G.

Willner, A. E.

Wolf, E.

E. Wolf, “Optics in terms of observable quantities,” Nuovo. Cim. 12, 884–888 (1954).
[Crossref]

M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (1997).

Wootters, W. K.

W. K. Wootters, “Entanglement of formation and concurrence,” Quantum Inf. Comput. 1, 27–44 (2001).

Wu, D.

Xie, G.

Xie, Z.

Yang, Y.

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21, 20692–20706 (2013).
[Crossref]

Yaqoob, Z.

Yuan, X.

Zeilinger, A.

A. Vaziri, G. Weihs, and A. Zeilinger, “Superpositions of the orbital angular momentum for applications in quantum experiments,” J. Opt. B 4, S47 (2002).
[Crossref]

Zeosky, J. J.

Zhan, Q.

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21, 20692–20706 (2013).
[Crossref]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[Crossref]

Zhang, Y.

Zhao, B.

Zhao, J.

Zhu, Z.-H.

ACS Photon. (1)

E. Arbabi, S. M. Kamali, A. Arbabi, and A. Faraon, “Full-Stokes imaging polarimetry using dielectric metasurfaces,” ACS Photon. 5, 3132–3140 (2018).
[Crossref]

Adv. Opt. Photon. (3)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200–227 (2016).
[Crossref]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[Crossref]

Am. J. Phys. (4)

E. Collett, “The description of polarization in classical physics,” Am. J. Phys. 36, 713–725 (1968).
[Crossref]

D. Clarke and J. Grainger, “Polarized light and optical measurement,” Am. J. Phys. 40, 1055–1056 (1971).
[Crossref]

W. H. McMaster, “Polarization and the Stokes parameters,” Am. J. Phys. 22, 351–362 (1954).
[Crossref]

B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[Crossref]

Ann. Phys. (1)

Y.-X. Ren, R.-D. Lu, and L. Gong, “Tailoring light with a digital micromirror device,” Ann. Phys. 527, 447–470 (2015).
[Crossref]

Appl. Opt. (7)

S. Shibata, N. Hagen, S. Kawabata, and Y. Otani, “Compact and high-speed Stokes polarimeter using three-way polarization-preserving beam splitters,” Appl. Opt. 58, 5644–5649 (2019).
[Crossref]

H. G. Berry, G. Gabrielse, and A. Livingston, “Measurement of the Stokes parameters of light,” Appl. Opt. 16, 3200–3205 (1977).
[Crossref]

B. Perez-Garcia, C. López-Mariscal, R. I. Hernandez-Aranda, and J. C. Gutiérrez-Vega, “On-demand tailored vector beams,” Appl. Opt. 56, 6967–6972 (2017).
[Crossref]

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

W.-H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
[Crossref]

Appl. Phys. Lett. (2)

R. Komanduri and M. Escuti, “High efficiency reflective liquid crystal polarization gratings,” Appl. Phys. Lett. 95, 091106 (2009).
[Crossref]

AVS Quantum Sci. (1)

IEEE Access (1)

J. Opt. (3)

E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularitites in tailored vector beams,” J. Opt. 18, 074012 (2016).
[Crossref]

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20, 123001 (2018).
[Crossref]

J. Opt. A (1)

J. M. Bueno, “Polarimetry using liquid-crystal variable retarders: theory and calibration,” J. Opt. A 2, 216 (2000).
[Crossref]

J. Opt. B (1)

A. Vaziri, G. Weihs, and A. Zeilinger, “Superpositions of the orbital angular momentum for applications in quantum experiments,” J. Opt. B 4, S47 (2002).
[Crossref]

J. Vac. Sci. Technol. B (1)

J. B. Sampsell, “Digital micromirror device and its application to projection displays,” J. Vac. Sci. Technol. B 12, 3242–3246 (1994).
[Crossref]

Laser Photon. Rev. (1)

E. Otte, C. Alpmann, and C. Denz, “Polarization singularity explosions in tailored light fields,” Laser Photon. Rev. 12, 1700200 (2018).
[Crossref]

Laser Phys. (1)

A. Peña and M. F. Andersen, “Complete polarization and phase control with a single spatial light modulator for the generation of complex light fields,” Laser Phys. 28, 076201 (2018).
[Crossref]

Light Sci. Appl. (1)

Nat. Phys. (1)

Nuovo. Cim. (1)

E. Wolf, “Optics in terms of observable quantities,” Nuovo. Cim. 12, 884–888 (1954).
[Crossref]

Opt. Acta (1)

R. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four stokes parameters of light,” Opt. Acta 29, 685–689 (1982).
[Crossref]

Opt. Commun. (1)

Q. Hu, Y. Dai, C. He, and M. J. Booth, “Arbitrary vectorial state conversion using liquid crystal spatial light modulators,” Opt. Commun. 459, 125028 (2020).
[Crossref]

Opt. Eng. (2)

S. Scholes, R. Kara, J. Pinnell, V. Rodríguez-Fajardo, and A. Forbes, “Structured light with digital micromirror devices: a guide to best practice,” Opt. Eng. 59, 1–12 (2019).
[Crossref]

T. M. Kreis, P. Aswendt, and R. Höfling, “Hologram reconstruction using a digital micromirror device,” Opt. Eng. 40, 926–933 (2001).
[Crossref]

Opt. Express (9)

A. Dudley, G. Milione, R. R. Alfano, and A. Forbes, “All-digital wavefront sensing for structured light beams,” Opt. Express 22, 14031–14040 (2014).
[Crossref]

W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21, 20692–20706 (2013).
[Crossref]

M. Fridman, M. Nixon, E. Grinvald, N. Davidson, and A. A. Friesem, “Real-time measurement of space-variant polarizations,” Opt. Express 18, 10805–10812 (2010).
[Crossref]

Opt. Lett. (7)

E. Otte and C. Denz, “Sculpting complex polarization singularity networks,” Opt. Lett. 43, 5821–5824 (2018).
[Crossref]

R. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985).
[Crossref]

B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett. 41, 3407–3410 (2016).
[Crossref]

C. Schulze, D. Flamm, M. Duparré, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
[Crossref]

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
[Crossref]

Optica (1)

J. B. Mueller, K. Leosson, and F. Capasso, “Ultracompact metasurface in-line polarimeter,” Optica 3, 42–47 (2016).
[Crossref]

Photon. Res. (1)

Phys. Rev. A (3)

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

V. D’Ambrosio, G. Carvacho, F. Graffitti, C. Vitelli, B. Piccirillo, L. Marrucci, and F. Sciarrino, “Entangled vector vortex beams,” Phys. Rev. A 94, 030304 (2016).
[Crossref]

Phys. Rev. Lett. (2)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96, 163905 (2006).
[Crossref]

H. Berry, L. Curtis, D. Ellis, and R. Schectman, “Anisotropy in the beam-foil light source,” Phys. Rev. Lett. 32, 751 (1974).
[Crossref]

Quantum Inf. Comput. (1)

W. K. Wootters, “Entanglement of formation and concurrence,” Quantum Inf. Comput. 1, 27–44 (2001).

Sci. Bull. (1)

J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63(1), 54–74 (2018).
[Crossref]

Sci. Rep. (1)

Science (1)

Surf. Sci. (2)

E. Collett, “Determination of the ellipsometric characteristics of optical surfaces using nanosecond laser pulses,” Surf. Sci. 96, 156–167 (1980).
[Crossref]

P. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci. 96, 108–140 (1980).
[Crossref]

Thin Solid Films (1)

E. Garcia-Caurel, A. De Martino, and B. Drevillon, “Spectroscopic Mueller polarimeter based on liquid crystal devices,” Thin Solid Films 455, 120–123 (2004).
[Crossref]

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, “On the composition and resolution of streams of polarized light from different sources,” Trans. Cambridge Philos. Soc. 9, 399 (1851).

Other (11)

W. A. Shurcliff, Polarized Light; Production and Use (Harvard University, 1962).

M. Born and E. Wolf, Principles of Optics, 6th (corrected) ed. (1997).

D. H. Goldstein, Polarized Light (CRC Press, 2016).

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekkar, 1993).

J. D. Pye, Polarised Light in Science and Nature (CRC Press, 2015).

S. Cloude, Polarisation: Applications in Remote Sensing (Oxford University, 2010).

C. Rosales-Guzmán and A. Forbes, How to Shape Light with Spatial Light Modulators (SPIE, 2017).

https://github.com/angeladudley1983/DigitalStokesCalc .

L. J. Hornbeck, “Deformable mirror light modulator,” U.S. patent4,441,791 (April10, 1984).

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Fig. 1. Conceptual schematics of (a) the conventional Stokes polarimetry measurements, together with the digital adaptations, implementing (b) a LCoS-SLM and (c) a DMD. QWP, quarter-wave plate; LP, linear polarizer; SLM, liquid-crystal-on-silicon (LCoS) spatial light modulator; PG, polarization grating; DMD, digital micromirror device; BS, 50:50 beam splitter.

Download Full Size | PPT Slide | PDF

Fig. 2. Experimental diagrams illustrating the arrangement of the optical components used to acquire Stokes parameters for (a) conventional Stokes polarimetry and the digital approaches, implementing (b) a LCoS-SLM and (c) a DMD. The representative holograms encoded onto the LCoS-SLM and DMD screens are provided as insets. HeNe, helium neon laser; QP,

${q}$

-plate; M, mirror.

Download Full Size | PPT Slide | PDF

Fig. 3. Conventional Stokes polarimetry. Left: the generated field of interest, on which the Stokes polarimetry is performed [in this case described by Eq. (32)]. Middle: measured intensity profiles of the Stokes projections. Right: the corresponding calculated Stokes parameters (min = 0 and max = 1 for

${S_0}$

${S_3}$

, while min = −1 and max = 1 for

${S_1}$

${S_2}$

). Theoretical simulations are given as insets.

Download Full Size | PPT Slide | PDF

Fig. 4. Digital LCoS-SLM Stokes polarimetry. Left: the generated field of interest, on which the Stokes polarimetry is performed [in this case described by a superposition of the two equations in Eq. (34)]. Middle: measured intensity profiles of the Stokes projections. Right: the corresponding calculated Stokes parameters (min = 0 and max = 1 for

${S_0}$

${S_1}$

, while min = −1 and max = 1 for

${S_2}$

${S_3}$

). Theoretical simulations are given as insets.

Download Full Size | PPT Slide | PDF

Fig. 5. Diagram depicting the alignment of orthogonally polarized components through a 50:50 BS. As the misalignment in the beam paths improves (left to right), so the number of fringes decreases.

Download Full Size | PPT Slide | PDF

Fig. 6. Diagram showing the independent phase modulation of orthogonal polarization components (top two rows for DMD transmission functions,

${T_A}$

and

${T_B}$

) and simulated interference of the components through a 50:50 BS (bottom row).

Download Full Size | PPT Slide | PDF

Fig. 7. Digital DMD Stokes polarimetry. Left: the generated field of interest, on which the Stokes polarimetry is performed [in this case described by Eq. (34)]. Middle: measured intensity profiles of the Stokes projections. Right: the corresponding calculated Stokes parameters (min = 0 and max = 1 for

${S_0}$

${S_3}$

, while min = −1 and max = 1 for

${S_1}$

${S_2}$

). Theoretical simulations are given as insets.

Download Full Size | PPT Slide | PDF

Fig. 8. Digital DMD Stokes polarimetry with curvature. Left: the generated field of interest, on which the Stokes polarimetry is performed [in this case described by Eq. (32)]. Middle: measured intensity profiles of the Stokes projections. Right: the corresponding calculated Stokes parameters (min = 0 and max = 1 for

${S_0}$

${S_3}$

, while min = −1 and max = 1 for

${S_1}$

${S_2}$

). Theoretical simulations are given as insets. Note the spiral lobes in

${I_D},{I_H},{S_1}$

, and

${S_2}$

Download Full Size | PPT Slide | PDF

Fig. 9. Diagram showing the relationship between the Cartesian co-ordinates of the Poincaré sphere and the ellipticity and orientation angles of the polarization ellipse.

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Fig. 10. Reconstructed polarization structures (top row) for the conventional and digital DMD techniques, together with their reconstructed intra-modal phases (bottom row); the DMD results labeled as “imaged” were acquired by implementing the

${4f}$

imaging system discussed in Section 4.C. The ellipses are colored according to the intensity value of the optical field.

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Fig. 11. Diagram showing the curvature developed in the SoP and intra-modal phase,

$\delta$

, of a TE vector vortex beam due to propagation over a distance

$z = [0,(1.8 \times {10^{- 3}}){z_R}]$

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Fig. 12. Experimentally extracted intermodal phase profiles of a propagating vector vortex beam (

$\ell = 1$

), described by Eq. (34), illustrating the spiraling nature of the phase distribution.

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Fig. 13. Plot of the measured vectorness (black data points) versus the QWP angle [positioned before the

$q$

-plate in Figs. 2(a) and 2(c)]. The blue, dashed curve denotes the theoretical prediction.

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Tables (1)

Table 1. Jones Matrix Parameters Imparted by the DMD to Acquire Stokes Intensity Measurements

View Table

Equations (51)

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E_{x} (t) = E_{0 x} \cos (ω t + δ_{x}),

E_{y} (t) = E_{0 y} \cos (ω t + δ_{y}),

\frac{E_{x}^{2} (t)}{E_{0 x}^{2}} + \frac{E_{y}^{2} (t)}{E_{0 y}^{2}} - \frac{2 E_{x} (t) E_{y} (t)}{E_{0 x} E_{0 y}} \cos (δ) = \sin^{2} (δ),

\begin{aligned} \frac{E_{0 x}^{2} ⟨ \cos^{2} (ω t - δ_{x}) ⟩}{E_{0 x}^{2}} + \frac{E_{0 y}^{2} ⟨ \cos^{2} (ω t - δ_{y}) ⟩}{E_{0 y}^{2}} \\ - \frac{2 E_{0 x} E_{0 y} ⟨ \cos (ω t - δ_{x}) \cos (ω t - δ_{y}) ⟩}{E_{0 x} E_{0 y}} \cos (δ) = \sin^{2} (δ), \end{aligned}

⟨ E_{i} (t) E_{j} (t) ⟩ = lim_{T \to \infty} \frac{1}{T} \int_{0}^{T} E_{i} (t) E_{j} (t) d t i, j = x, y .

⟨ \cos^{2} (ω t - δ_{x}) ⟩ = ⟨ \cos^{2} (ω t - δ_{y}) ⟩ = \frac{1}{2},

⟨ \cos (ω t - δ_{x}) \cos (ω t - δ_{y}) ⟩ = \frac{1}{2} \cos (δ),

\begin{aligned} (E_{0 x}^{2} + E_{0 y}^{2})^{2} & - (E_{0 x}^{2} - E_{0 y}^{2})^{2} - (2 E_{0 x} E_{0 y} \cos (δ))^{2} \\ = (2 E_{0 x} E_{0 y} \sin (δ))^{2} . \end{aligned}

\begin{aligned} S_{0} & = E_{0 x}^{2} + E_{0 y}^{2}, \\ S_{1} & = E_{0 x}^{2} - E_{0 y}^{2}, \\ S_{2} & = 2 E_{0 x} E_{0 y} \cos (δ), \\ S_{3} & = 2 E_{0 x} E_{0 y} \sin (δ) . \end{aligned}

S_{0}^{2} = S_{1}^{2} + S_{2}^{2} + S_{3}^{2} .

S_{0}^{2} \geq S_{1}^{2} + S_{2}^{2} + S_{3}^{2} .

E_{x} (t) = E_{0 x} e^{i (ω t + δ_{x})} = E_{x} e^{i ω t},

E_{y} (t) = E_{0 y} e^{i (ω t + δ_{y})} = E_{y} e^{i ω t} .

\begin{aligned} S_{0} & = E_{x} E_{x}^{*} + E_{y} E_{y}^{*}, \\ S_{1} & = E_{x} E_{x}^{*} - E_{y} E_{y}^{*}, \\ S_{2} & = E_{x} E_{y}^{*} + E_{y} E_{x}^{*}, \\ S_{3} & = i (E_{x} E_{y}^{*} - E_{y} E_{x}^{*}) . \end{aligned}

S_{0} = I_{H} + I_{V}, S_{1} = I_{H} - I_{V}, S_{2} = I_{D} - I_{A}, S_{3} = I_{R} - I_{L},

\begin{aligned} E_{D, A} (t) & = \frac{1}{\sqrt{2}} (E_{H} (t) \pm E_{V} (t)), \\ E_{L, R} (t) & = \frac{1}{\sqrt{2}} (E_{H} (t) \pm i E_{V} (t)) . \end{aligned}

E_{x} \cos (θ) + E_{y} \sin (θ),

\begin{aligned} I (θ) & = E_{x} E_{x}^{*} \cos^{2} (θ) + E_{y} E_{y}^{*} \sin^{2} (θ) \\ + E_{x}^{*} E_{y} \cos (θ) \sin (θ) + E_{x} E_{y}^{*} \cos (θ) \sin (θ) . \end{aligned}

I (0^{\circ}) = I_{H}, I (90^{\circ}) = I_{V}, I (45^{\circ}) = I_{D}, I (135^{\circ}) = I_{A} .

E_{x} e^{i \frac{ϕ}{2}} \cos (θ) + E_{y} e^{- i \frac{ϕ}{2}} \sin (θ),

\begin{aligned} I (θ, ϕ) & = E_{x} E_{x}^{*} \cos^{2} (θ) + E_{y} E_{y}^{*} \sin^{2} (θ) \\ + E_{x}^{*} E_{y} e^{- i ϕ} \cos (θ) \sin (θ) \\ + E_{x} E_{y}^{*} e^{i ϕ} \cos (θ) \sin (θ) . \end{aligned}

I (45^{\circ}, 90^{\circ}) = I_{R}, I (135^{\circ}, 90^{\circ}) = I_{L} .

\begin{aligned} \cos^{2} (θ) & = \frac{1 + \cos (2 θ)}{2}, \\ \sin^{2} (θ) & = \frac{1 - \cos (2 θ)}{2}, \\ \cos (θ) \sin (θ) & = \frac{\sin (2 θ)}{2} . \end{aligned}

\begin{aligned} I (θ, ϕ) & = \frac{1}{2} [S_{0} + S_{1} \cos (2 θ) \\ + S_{2} \cos (ϕ) \sin (2 θ) + S_{3} \sin (ϕ) \sin (2 θ)] . \end{aligned}

S_{0} = I_{R} + I_{L}, S_{1} = 2 I_{H} - S_{0}, S_{2} = 2 I_{D} - S_{0}, S_{3} = I_{R} - I_{L},

\begin{aligned} U (\vec{r}) & = U_{A} (\vec{r}) | R ⟩ + U_{B} (\vec{r}) | L ⟩ \to \\ PG & \to | U_{A} (\vec{r}) | e^{i δ_{A}} | R ⟩ & | U_{B} (\vec{r}) | e^{i δ_{B}} | L ⟩, \end{aligned}

\begin{aligned} H_{A} (\vec{r}) & = \frac{1}{2} + \frac{1}{2} s i g n (\cos (2 π (G_{x} x + G_{y} y) + π Φ_{A} (\vec{r})) \\ - \cos (π A_{A} (\vec{r}))), \end{aligned}

\begin{aligned} H_{B} (\vec{r}) & = \frac{1}{2} + \frac{1}{2} s i g n (\cos (2 π (G_{x} x + G_{y} y) + π Φ_{B} (\vec{r})) \\ - \cos (π A_{B} (\vec{r}))) . \end{aligned}

T_{A} = e^{i c_{A}} a n d T_{B} = e^{i c_{B}},

U^{'} (\vec{r}) = U_{A}^{'} (\vec{r}) + U_{B}^{'} (\vec{r}) = U_{A} (\vec{r}) e^{i φ_{A}} T_{A} + U_{B} (\vec{r}) e^{i φ_{B}} T_{B},

\begin{aligned} \underset{B S M a t r i x}{\underset{⏟}{\frac{1}{\sqrt{2}} (\begin{matrix} 1 & 1 \\ 1 & - 1 \end{matrix})}} \underset{D M D M a t r i x}{\underset{⏟}{(\begin{matrix} A e^{i c_{A}} & 0 \\ 0 & B e^{i c_{B}} \end{matrix})}} \underset{I n p u t F i e l d}{\underset{⏟}{\frac{1}{\sqrt{2}} (\begin{matrix} U_{A} \\ U_{B} \end{matrix})}} = \\ \underset{J o n e s M a t r i x o f S y s t e m}{\underset{⏟}{\frac{1}{2} (\begin{matrix} A e^{i c_{A}} & B e^{i c_{B}} \\ A e^{i c_{A}} & - B e^{i c_{B}} \end{matrix})}} (\begin{matrix} U_{A} \\ U_{B} \end{matrix}) = \underset{B S O u t p u t s}{\underset{⏟}{(\begin{matrix} \frac{1}{2} (A e^{i c_{A}} U_{A} + B e^{i c_{B}} U_{B}) \\ \frac{1}{2} (A e^{i c_{A}} U_{A} - B e^{i c_{B}} U_{B}) \end{matrix})}} . \end{aligned}

T E (\vec{r}) = {L G}_{0}^{1} (\vec{r}) | R ⟩ + {L G}_{0}^{- 1} (\vec{r}) | L ⟩ .

\begin{aligned} {L G}_{p}^{l} (r, ϕ, z) & = \frac{w_{0}}{w (z)} \sqrt{\frac{2 p!}{π (| l | + p)!}} {(\frac{\sqrt{2} r}{w (z)})}^{| l |} L_{p}^{l} (\frac{2 r^{2}}{w {(z)}^{2}}) \\ \times e^{i (2 p + | l | + 1) ξ (z)} e^{- \frac{r^{2}}{w {(z)}^{2}}} e^{- i \frac{k r^{2}}{2 R (z)}} e^{i l ϕ}, \end{aligned}

\begin{aligned} U_{\leftrightarrow} (r, ϕ) & = \exp (- r^{2} / ω_{0}) a n d \\ U_{↕} (r, ϕ) & = \exp (- r^{2} / ω_{0}) \exp (i δ (r, ϕ)) . \end{aligned}

S_{0} = \sqrt{S_{1}^{2} + S_{2}^{2} + S_{3}^{2}},

S_{1} = S_{0} \cos 2 χ \cos 2 ψ,

S_{2} = S_{0} \cos 2 χ \sin 2 ψ,

S_{3} = S_{0} \sin 2 χ .

\begin{aligned} \frac{S_{1}}{S_{0} \cos 2 χ \cos 2 ψ} & = \frac{S_{2}}{S_{0} \cos 2 χ \sin 2 ψ} \\ ψ & = \frac{1}{2} \tan^{- 1} (\frac{S_{2}}{S_{1}}) . \end{aligned}

\begin{aligned} \sqrt{S_{1}^{2} + S_{2}^{2}} & = \sqrt{S_{0}^{2} \cos^{2} 2 χ (\cos^{2} 2 ψ + \sin^{2} 2 ψ)} \\ χ & = \frac{1}{2} \tan^{- 1} (\frac{S_{3}}{\sqrt{S_{1}^{2} + S_{2}^{2}}}) . \end{aligned}

H_{C P} = {\begin{matrix} R f o r & S_{3} > 0, \\ L f o r & S_{3} < 0 . \end{matrix}

δ (r, ϕ) = a r c t a n (\frac{S_{3} (r, ϕ)}{S_{2} (r, ϕ)}) .

| Ψ ⟩ = \sqrt{a} | {\bar{u}}_{R} ⟩ \otimes | R ⟩ + \sqrt{1 - a} | {\bar{u}}_{L} ⟩ \otimes | L ⟩ .

ρ = (\begin{matrix} a | {\bar{u}}_{R} ⟩ ⟨ {\bar{u}}_{R} | & \sqrt{a (1 - a)} | {\bar{u}}_{R} ⟩ ⟨ {\bar{u}}_{L} | \\ \sqrt{a (1 - a)} | {\bar{u}}_{L} ⟩ ⟨ {\bar{u}}_{R} | & (1 - a) | {\bar{u}}_{L} ⟩ ⟨ {\bar{u}}_{L} | \end{matrix}) .

C = m a x {0, \sqrt{λ_{1}}, - \sqrt{λ_{2}}, - \sqrt{λ_{3}}, - \sqrt{λ_{4}}},

ρ (σ_{3} \otimes σ_{3}) ρ^{*} (σ_{3} \otimes σ_{3}),

Ψ = b | u_{+} ⟩ | R ⟩ + c | u_{-} ⟩ | R ⟩ + d | u_{+} ⟩ | L ⟩ + f | u_{-} ⟩ | L ⟩,

C (Ψ) = 2 | b f - c d | .

| {\bar{u}}_{i} ⟩ = \int d x d y | {\bar{u}}_{i} ({\vec{r}}_{⊥}) | e^{i ϕ_{i} ({\vec{r}}_{⊥})} | x, y ⟩,

C (| Ψ ⟩) = 2 \sqrt{⟨ {\bar{u}}_{R} | {\bar{u}}_{R} ⟩ ⟨ {\bar{u}}_{L} | {\bar{u}}_{L} ⟩ - | ⟨ {\bar{u}}_{R} | {\bar{u}}_{L} ⟩ |^{2}} .

C = \sqrt{1 - \frac{S_{1}^{2}}{S_{0}^{2}} - \frac{S_{2}^{2}}{S_{0}^{2}} - \frac{S_{3}^{2}}{S_{0}^{2}}} = \sqrt{1 - \sum_{i = 1}^{3} \frac{S_{i}^{2}}{S_{0}^{2}}} .

Intensity Measurement	$A$	$B$	$c_{B}$
$I_{R}$	0	1	0
$I_{L}$	1	0	0
$I_{H}$	1	1	0
$I_{D}$	1	1	$\frac{π}{2}$

Abstract

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Alfano, R. R.

Alpmann, C.

Ambrosio, A.

Andersen, M. F.

Andrews, D. L.

Arbabi, A.

Arbabi, E.

Aswendt, P.

Azzam, R.

Baker, M.

Banzer, P.

Barrett, D.

Bauer, T.

Beach, K.

Belmonte, A.

Berry, H.

Berry, H. G.

Berry, M. V.

Bhattacharya, S.

Bigelow, N. P.

Booth, M. J.

Bordbar, N. T.

Born, M.

Boyd, R. W.

Brock, N.

Bueno, J. M.

Capasso, F.

Carvacho, G.

Chen, J.

Chen, P.-J.

Cheng, L.

Cheng, W.

Chipman, R. A.

Cižmár, T.

Clarke, D.

Cloude, S.

Collett, E.

Cox, M. A.

Croke, S.

Curtis, L.

D’Ambrosio, V.

Dai, Y.

Davidson, N.

De Martino, A.

Dennis, M. R.

Denz, C.

Drevillon, B.

Dudley, A.

Duparré, M.

Dutta, I.

Ellis, D.