Abstract

The constituent elements of metasurfaces may be designed with explicit polarization dependence, making metasurfaces a fascinating platform for new polarization optics. In this work we show that a metasurface grating can be designed to produce arbitrarily specified polarization states on a set of defined diffraction orders given that the polarization of the incident beam is known. We also demonstrate that, when used in a reverse configuration, the same grating may be used as a parallel snapshot polarimeter, requiring a minimum of bulk polarization optics. We demonstrate its use in measuring partially polarized light, and show that it performs favorably in comparison to a commercial polarimeter. This work is of consequence in any application requiring lightweight, compact, and low-cost polarization optics, polarimetry, or polarization imaging.

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

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2018 (1)

Z. Lin, B. Groever, F. Capasso, A. W. Rodriguez, and M. Lončar, “Topology-optimized multilayered metaoptics,” Phys. Rev. Appl. 9, 044030 (2018).
[Crossref]

2017 (8)

A. Cofré, A. Vargas, F. A. Torres-Ruiz, J. Campos, A. Lizana, M. del Mar Sánchez-López, and Moreno Isa, “Quantitative performance of a polarization diffraction grating polarimeter encoded onto two liquid-crystal-on-silicon displays,” Opt. Laser Technol. 96, 219–226 (2017).
[Crossref]

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

F. Ding, A. Pors, Y. Chen, V. A. Zenin, and S. I. Bozhevolnyi, “Beam-size-invariant spectropolarimeters using gap-plasmon metasurfaces,” ACS Photonics 4, 943–949 (2017).
[Crossref]

D. Sell, J. Yang, S. Doshay, R. Yang, and J. A. Fan, “Large-angle, multifunctional metagratings based on freeform multimode geometries,” Nano Lett. 17, 3752–3757 (2017).
[Crossref] [PubMed]

S. Wei, Z. Yang, and M. Zhao, “Design of ultracompact polarimeters based on dielectric metasurfaces,” Opt. Lett. 42, 1580–1583 (2017).
[Crossref] [PubMed]

I. J. Vaughn, A. S. Alenin, and J. Scott Tyo, “Focal plane filter array engineering I: rectangular lattices,” Opt. Express 25, 11954–11968 (2017).
[Crossref] [PubMed]

J. Yang and J. A. Fan, “Topology-optimized metasurfaces: impact of initial geometric layout,” Opt. Lett. 42, 3161–3164 (2017).
[Crossref] [PubMed]

M. Juhl, C. Mendoza, J. P. B. Mueller, F. Capasso, and K. Leosson, “Performance characteristics of 4-port in-plane and out-of-plane in-line metasurface polarimeters,” Opt. Express 25, 28697–28709 (2017).
[Crossref]

2016 (7)

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

J. A. Davis, I. Moreno, M. M. Sánchez-López, K. Badham, J. Albero, and D. M. Cottrell, “Diffraction gratings generating orders with selective states of polarization,” Opt. Express 24, 907–917 (2016).
[Crossref] [PubMed]

R. M. A. Azzam, “Stokes-vector and Mueller-matrix polarimetry,” J. Opt. Soc. Am. A 33, 1396–1408 (2016).
[Crossref]

R. C. Devlin, M. Khorasaninejad, W.-T. Chen, J. Oh, and F. Capasso, “Broadband high-efficiency dielectric metasurfaces for the visible spectrum,” Proc. Natl. Acad. Sci. 113, 10473–10478 (2016).
[Crossref] [PubMed]

A. Pors and S. I. Bozhevolnyi, “Waveguide metacouplers for in-plane polarimetry,” Phys. Rev. Appl. 5, 1–9 (2016).
[Crossref]

W. T. Chen, P. Török, M. R. Foreman, C. Y. Liao, W.-Y. Tsai, P. R. Wu, and D. P. Tsai, “Integrated plasmonic metasurfaces for spectropolarimetry,” Nanotechnology 27, 224002 (2016).
[Crossref] [PubMed]

C. F. LaCasse, B. J. Redman, M. W. Kudenov, and J. M. Craven, “Maximum bandwidth snapshot channeled imaging polarimeter with polarization gratings,” Proc. SPIE 9853, 98530U (2016).
[Crossref]

2015 (4)

2014 (4)

W.-L. Hsu, G. Myhre, K. Balakrishnan, N. Brock, M. Ibn-Elhaj, S. Pau, K. M. Twietmeyer, R. A. Chipman, A. E. Elsner, Y. Zhao, and D. VanNasdale, “Full-Stokes imaging polarimeter using an array of elliptical polarizer,” Opt. Express 22, 3063–3074 (2014).
[Crossref] [PubMed]

D. A. LeMaster and K. Hirakawa, “Improved microgrid arrangement for integrated imaging polarimeters,” Opt. Lett. 39, 1811–1814 (2014).
[Crossref] [PubMed]

F. Snik, J. Craven-Jones, M. Escuti, S. Fineschi, D. Harrington, A. De Martino, D. Mawet, J. Riedi, and J. S. Tyo, “An overview of polarimetric sensing techniques and technology with applications to different research fields,” Proc. SPIE 9099, 90990B (2014).

S. J. Wiktorowicz and G. P. Laughlin, “Toward the detection of exoplanet transits with polarimetry,” Astrophys. J. 795, 12 (2014).
[Crossref]

2013 (1)

2012 (3)

M. W. Kudenov, M. J. Escuti, N. Hagen, E. L. Dereniak, and K. Oka, “Snapshot imaging Mueller matrix polarimeter using polarization gratings,” Opt. Lett. 37, 1367–1369 (2012).
[Crossref] [PubMed]

T. Novikova, A. Pierangelo, and A. De Martino, “Polarimetric imaging for cancer diagnosis and staging,” Opt. Photonics News 23, 26–33 (2012).
[Crossref]

F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
[Crossref]

2011 (3)

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photonics Rev. 5, 308–321 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

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

2010 (1)

C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced Jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82, 053811 (2010).
[Crossref]

2009 (1)

L. A. Romero and F. M. Dickey, “The mathematical theory of laser beam-splitting gratings,” Prog. Opt. 54, 319–386 (2009).
[Crossref]

2008 (2)

2007 (1)

2006 (1)

2005 (1)

E. Hasman, G. Biener, A. Niv, and V. Kleiner, “Space-variant polarization manipulation,” Prog. Opt. 47, 215–289 (2005).
[Crossref]

2003 (1)

G. Cincotti, “Polarization gratings: design and applications,” IEEE J. Quantum Electron. 39, 1645–1652 (2003).
[Crossref]

2002 (4)

A. G. Andreou and Z. K. Kalayjian, “Polarization imaging: Principles and integrated polarimeters,” IEEE Sens. J. 2, 566–576 (2002).
[Crossref]

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

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating,” Opt. Lett. 27, 188–190 (2002).
[Crossref]

J. S. Tyo, “Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41, 619–630 (2002).
[Crossref] [PubMed]

2001 (3)

2000 (2)

1999 (2)

1996 (1)

1995 (1)

1994 (1)

P. Y. Deschamps, J. C. Buriez, F. M. Bréon, M. Leroy, A. Podaire, A. Bricaud, and G. Sèze, “The POLDER mission: instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Remote Sens. 32, 598–615 (1994).
[Crossref]

1993 (1)

1992 (1)

1989 (1)

1985 (1)

1984 (1)

1982 (1)

R. M. A. Azzam, “Division-of-amplitude photopolarimeter (DOAP) for the simultaneous measurement of all four Stokes parameters of light,” J. Mod. Opt. 29, 685–689 (1982).

1977 (1)

Adachi, J.

Afshinmanesh, F.

F. Afshinmanesh, J. S. White, W. Cai, and M. L. Brongersma, “Measurement of the polarization state of light using an integrated plasmonic polarimeter,” Nanophotonics 1, 125–129 (2012).
[Crossref]

Agol, E.

J. Trujillo-Bueno, F. Moreno-Insertis, F. Sanchez, E. Landi Degl’Innocenti, J. O. Stenflo, G. Mathys, R. Antonucci, R. Blandford, E. Agol, A. Broderick, J. Heyl, L. Koopmans, H.-W. Lee, M. Elitzur, R. H. Hildebrand, and C. U. Keller, Astrophysical Spectropolarimetry(Cambridge University, 2002).

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Albero, J.

Alenin, A. S.

Andreou, A. G.

A. G. Andreou and Z. K. Kalayjian, “Polarization imaging: Principles and integrated polarimeters,” IEEE Sens. J. 2, 566–576 (2002).
[Crossref]

Antonelli, M.-R.

Antonucci, R.

J. Trujillo-Bueno, F. Moreno-Insertis, F. Sanchez, E. Landi Degl’Innocenti, J. O. Stenflo, G. Mathys, R. Antonucci, R. Blandford, E. Agol, A. Broderick, J. Heyl, L. Koopmans, H.-W. Lee, M. Elitzur, R. H. Hildebrand, and C. U. Keller, Astrophysical Spectropolarimetry(Cambridge University, 2002).

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Asensio Ramos, A.

Azzam, R. M. A.

Badham, K.

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Figures (9)

Fig. 1
Fig. 1 a, Conceptual schematic: A metasurface diffraction grating can be designed to produce arbitrarily specified polarization states on its diffraction orders. The same device can also act as a parallel polarimeter. b, Such a metasurface is composed of pillar-like phase-shifting elements with two perpendicular mirror symmetry axes (e.g., rectangles) whose orthogonal dimensions wx and wy may be adjusted to allow for independent and tailorable phase delays ϕx and ϕy on x- and y-polarized light. c, If Q such elements of varying dimensions are arranged into a periodic unit cell along the x ˜ direction, we form a 1D diffraction grating. At each point in the unit cell, constant phases are imparted on x- and y-polarized light. We may then describe the phase profiles experienced by these polarizations in the form of Q-vectors Φ x and Φ y. d, The action of each diffraction order is equivalent to a bulk optic cascade of a diattenuator and a phase retarder, each oriented along x/y. e, The Poincaré sphere aids in understanding the behavior of the diffraction order for general input polarization. A standard Poincaré sphere (left) represents the set of all possible incident polarizations. After the beam passes through the diattenuator, the sphere is distorted along the S1 axis according to the extinction ratio of the diattenuator (center). Finally, the phase retarder enacts a precession of the sphere along the S1 axis by an angle equal to its retardance δ(m) (right). The red arrows depict the corresponding polarization states in (d). Note also that the power of the output beam is polarization-dependent (not shown). f, The functionality contained in a single metasurface (c) would require, most generally, a two birefringent plates on each order in addition to a grating. g, Conceptually, polarimetry amounts to several projective measurements of an incident Stokes vector, S inc, onto a number of analysis Stokes vectors { S n }. If the analysis vectors are known and linearly independent, S inc can be recovered.
Fig. 2
Fig. 2 a, Schematic of optimization routine used to design metasurface polarization gratings. A random initial guess for the phase profiles Φ x and Φ y is optimized to direct as much light as possible into the diffraction orders of interest using gradient descent under the constraints of the desired polarization states. This result is improved by a gradient-free method that accounts for simulated properties of the phase shifters used, and a final geometry is generated. These geometries are realized in TiO2 for operation at λ = 532 nm. b, The scheme in (a) is used to generate two gratings, one for four polarizations of general interest (top) and one for a tetrahedron configuration of polarization states (bottom). Each grating generates four polarization states, and the target ellipse, expected result from FDTD simulation, and experimentally observed polarization ellipse on each grating order are shown. c, Design (black) and electron micrographs as-fabricated of the “four polarization” (top) and “tetrahedron” (bottom) gratings. In the tetrahedron grating, the small rightmost pillar has not survived fabrication.
Fig. 3
Fig. 3 a, As each diffraction order may be thought of as a cascade of a diattenuator and a retarder (Fig. 1d), when light from a source of known polarization (in this case, linearly polarized at 45°) is incident, a characteristic polarization S c is produced. If light of unknown polarization S inc is incident in the reverse direction and the source is replaced with a detector, the measured intensity I S inc S c , with S c identical to S c with a change in the sign of the last component. b, This allows the meta-grating to function as a parallel polarimeter. Each of the four diffraction orders of the tetrahedron grating may be used as an analyzer. Light incident on the metasurface passes through a linear polarizer at 45° and diffracts onto four photodiodes whose photocurrents are amplified and digitized through an analog-to-digital converter (ADC). During testing and calibration, light passes through various polarization optics in front of the meta-grating. The role of the boxed components (i) and (ii) are described in the text. c, As the linear polarizer is rotated in front of a polarization Mach-Zehnder interferometer ((i) in (b)) whose path length difference is larger than the laser coherence length Lcoh, the degree of polarization (DOP) varies. Plotted in red is the DOP measured by the meta-grating polarimeter which closely follows the theoretically expected curve (black). At 45° (inset) a DOP of p = 1.2 ± 0.18% is measured.
Fig. 4
Fig. 4 In each column, the metasurface grating polarimeter (metasurface) and the commercial rotating waveplate polarimeter (RWP) are compared using different polarimetric quantities. In the top row of graphs, values measured by each polarimeter are plotted against one another (in the case of perfect correspondence all values would lie along the black 1:1 line). Insets of each plot are shown. Error bars are given only for the metasurface values since precision is not well-known for the commercial RWP. In the bottom row of plots, the differences between the values reported by each polarimeter are computed and plotted in a histogram. Each distribution is fitted with a normal distribution and the mean µ and variance σ are given for each. The quantities examined are the degree of polarization (DOP), the azimuth double angle 2θ, and the ellipticity double angle 2ϵ. The latter two are parameters of the polarization ellipse that give the spherical coordinates of the polarization state on the Poincaré sphere.
Fig. 5
Fig. 5 Effect of changing nominal fabrication CAD given to e-beam system on polarization ellipses produced on the m = −2, −1, +1, and +2 on the tetrahedron grating.
Fig. 6
Fig. 6 A schematic of the procedure used to analyze the effect of errors in the angle of incidence, or more generally of any effect that contributes to error in the instrument matrix, on reported Stokes vectors from the polarimeter.
Fig. 7
Fig. 7 Results of angle-dependent polarimetry study. Note that DOP errors are expressed in absolute terms (i.e., not in %). For each quantity of interest (DOP, azimuth, and ellipticity) and each incident angle (5°, 10°, 15°, 20°), a Poincaré sphere populated with dots representing a sample set of Stokes vectors is shown. The color of each dot represents the error in that quantity a user would report at that accidental misalignment, with red representing higher error. Also given are the maximum, minimum, mean, and variance of the error over the sample set for each quantity and angle.
Fig. 8
Fig. 8 On the left, generators (combinations of linear polarizers (LP) and quarter-wave plates (QWP) that generate x, 45°, and RCP (the cardinal directions on the Poincaré sphere) are shown. On the right, analyzers constructed from these generators by three different linear transformations are shown. In each case, one of the three analyzers (marked by a red ’x’) shown passes the orthogonal polarization rather than the one produced by the generator. Intuitively, this demonstrates that the analyzer’s Stokes vector differs from the generator’s Stokes vector in a way that depends on the symmetry of the transformation between the two.
Fig. 9
Fig. 9 Schematic of a prototype laboratory-grade polarimeter utilizing the tetrahedron grating presented in this work, which is mounted in the faceplate at the right of the enclosure.

Tables (5)

Tables Icon

Table 1 Extended polarization state data for tetrahedron grating, as presented in Fig. 2(b). The azimuth (θ) and ellipticty (ϵ) angles for each diffraction order (target, FDTD, and measured) are given in radians. Note that the azimuth of the target polarization state for the m = +2 order is not defined since this state was designed to be circular.

Tables Icon

Table 2 Extended polarization state data for the four-state grating, as presented in Fig. 2(b). The azimuth (θ) and ellipticty (ϵ) angles for each diffraction order (target, FDTD, and measured) are given in radians. Note that the azimuth of the target polarization state for the m = −1 and m = +1 orders are not defined since these states were designed to be circular.

Tables Icon

Table 3 Details of the design of the two gratings presented in this work. For each of the two gratings, the x ˜ and y ˜ phase profiles are provided (in radians). Corresponding to each pair {ϕx, ϕy} are the lateral dimensions {wx, wy} of a rectangular pillar of a-TiO2, 600 nm in height best implementing this pair of phases (in nanometers).

Tables Icon

Table 4 Efficiency data for the tetrahedron grating.

Tables Icon

Table 5 Comparison of the two polarimeters.

Equations (11)

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A S inc = I
c x ( m ) = m | e i ϕ x ( x ˜ ) = 1 2 π 0 d e i ϕ x ( x ˜ ) = e i 2 π m x ˜ d d x ˜
c y ( m ) = m | e i ϕ y ( x ˜ ) = 1 2 π 0 d e i ϕ y ( x ˜ ) = e i 2 π m x ˜ d d x ˜
J ( m ) = ( c x ( m ) 0 0 c y ( m ) ) = ( | c x ( m ) | 0 0 | c y ( m ) | ) ( e i δ x ( m ) 0 0 e i δ y ( m ) ) .
E ( m ) = E 0 2 ( c x ( m ) c y ( m ) ) .
j ( m ) = ( cos χ ( m ) sin χ ( m ) e i ϕ ( m ) ) .
η ( Φ x , Φ y ) = m { } ( | c x ( m ) | 2 + | c y ( m ) | 2 )
| c y ( m ) | | c x ( m ) | = tan χ ( m )
δ x ( m ) δ y ( m ) = ϕ ( m ) .
p = S 1 2 + S 2 2 + S 3 2 S 0
Δ ( S a ) = ( A p 1 A a 1 ) I meas = ( A p 1 A a 1 ) A a S a = ( A p 1 A a I ) S a .

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