Abstract

Wave retarders, including quarter- and half-wave plates, are used in many optical systems for polarization conversion. They are usually realized with anisotropic crystalline materials. However, much thinner and possibly also less expensive wave plates can be made of micro- and nanostructures. We present a new way to create thin-film optical retarders based on a highly birefringent metamaterial. The wave plate is capable of low-loss, broadband operation, which we verify both numerically and experimentally. Owing to the remarkable simplicity of our design, the wave plates operating on the proposed principle can meet the requirements of large-scale production and find widespread application in optics and photonics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (3)

2015 (7)

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, Nat. Nanotechnol. 10, 308 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

M. Khorasaninejad and F. Capasso, Nano Lett. 15, 6709 (2015).
[Crossref]

I. Yamada, T. Ishihara, and J. Yanagisawa, Jpn. J. Appl. Phys. 54, 092203 (2015).
[Crossref]

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, ACS Nano 9, 4111 (2015).
[Crossref]

Y. Dai, H. Cai, H. Ding, Z. Ning, N. Pan, H. Zhu, Q. Shi, and X. Wang, Opt. Express 23, 8929 (2015).
[Crossref]

J. M. Herrera-Fernandez, J. L. Vilas, L. M. Sanchez-Brea, and E. Bernabeu, Appl. Opt. 54, 9758 (2015).
[Crossref]

2013 (2)

A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, Appl. Phys. Lett. 103, 033111 (2013).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

2012 (4)

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, Nano Lett. 12, 6328 (2012).
[Crossref]

Y. J. Shin, C. Pina-Hernandez, Y.-K. Wu, J. G. Ok, and L. J. Guo, Nanotechnology 23, 344018 (2012).
[Crossref]

A. Roberts and L. Lin, Opt. Lett. 37, 1820 (2012).
[Crossref]

T. Peters, S. S. Ivanov, D. Englisch, A. A. Rangelov, N. V. Vitanov, and T. Halfmann, Appl. Opt. 51, 7466 (2012).
[Crossref]

2011 (2)

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, Adv. Mater. 23, 147 (2011).
[Crossref]

Y. Zhao and A. Alù, Phys. Rev. B 84, 205428 (2011).
[Crossref]

2009 (1)

2008 (2)

1997 (1)

1995 (2)

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Aieta, F.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, Nano Lett. 12, 6328 (2012).
[Crossref]

Alù, A.

Y. Zhao and A. Alù, Phys. Rev. B 84, 205428 (2011).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Bai, B.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Balthasar Mueller, J. P.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

Bernabeu, E.

Brueck, S. R. J.

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, Adv. Mater. 23, 147 (2011).
[Crossref]

Cai, H.

Campbell, G.

Cao, B.

Capasso, F.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

M. Khorasaninejad and F. Capasso, Nano Lett. 15, 6709 (2015).
[Crossref]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, Nano Lett. 12, 6328 (2012).
[Crossref]

Cheah, K.-W.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Chen, S.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Chen, X.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Cheng, C.-C.

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Clarke, I. G.

Dai, Y.

Day, G. W.

Devlin, R. C.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

Ding, F.

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, ACS Nano 9, 4111 (2015).
[Crossref]

Ding, H.

Englisch, D.

Fainman, Y.

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Gaburro, Z.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, Nano Lett. 12, 6328 (2012).
[Crossref]

García-Martínez, P.

Genevet, P.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, Nano Lett. 12, 6328 (2012).
[Crossref]

Gordon, R.

Grahn, P.

A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, Appl. Phys. Lett. 103, 033111 (2013).
[Crossref]

Groever, B.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

Guo, L. J.

Y. J. Shin, C. Pina-Hernandez, Y.-K. Wu, J. G. Ok, and L. J. Guo, Nanotechnology 23, 344018 (2012).
[Crossref]

Guo, P.

Hale, P. D.

Halfmann, T.

He, S.

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, ACS Nano 9, 4111 (2015).
[Crossref]

Herrera-Fernandez, J. M.

Horie, Y.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

Hu, J.

Huang, L.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Ishihara, T.

I. Yamada, T. Ishihara, and J. Yanagisawa, Jpn. J. Appl. Phys. 54, 092203 (2015).
[Crossref]

Ivanov, S. S.

Jin, G.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Kaivola, M.

A. Shevchenko, M. Nyman, V. Kivijärvi, and M. Kaivola, Opt. Express 25, 8550 (2017).
[Crossref]

A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, Appl. Phys. Lett. 103, 033111 (2013).
[Crossref]

Kats, M. A.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, Nano Lett. 12, 6328 (2012).
[Crossref]

Kenney, M.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, Nat. Nanotechnol. 10, 308 (2015).
[Crossref]

Khorasaninejad, M.

M. Khorasaninejad and F. Capasso, Nano Lett. 15, 6709 (2015).
[Crossref]

Kildishev, A. V.

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, ACS Nano 9, 4111 (2015).
[Crossref]

Kim, T. J.

Kivijärvi, V.

Kostuk, R. K.

Kravchenko, A.

A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, Appl. Phys. Lett. 103, 033111 (2013).
[Crossref]

Ku, Z.

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, Adv. Mater. 23, 147 (2011).
[Crossref]

Kuittinen, M.

Laakkonen, P.

Lee, S. C.

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, Adv. Mater. 23, 147 (2011).
[Crossref]

Li, G.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, Nat. Nanotechnol. 10, 308 (2015).
[Crossref]

Li, J.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Lin, L.

Lin, Y.

Messaadi, A.

Moreno, I.

Mühlenbernd, H.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, Nat. Nanotechnol. 10, 308 (2015).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Ning, Z.

Nyman, M.

Ok, J. G.

Y. J. Shin, C. Pina-Hernandez, Y.-K. Wu, J. G. Ok, and L. J. Guo, Nanotechnology 23, 344018 (2012).
[Crossref]

Ovchinnikov, V.

A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, Appl. Phys. Lett. 103, 033111 (2013).
[Crossref]

Päivänranta, B.

Pan, N.

Pang, Y.

Passilly, N.

Peters, T.

Pietarinen, J.

Pina-Hernandez, C.

Y. J. Shin, C. Pina-Hernandez, Y.-K. Wu, J. G. Ok, and L. J. Guo, Nanotechnology 23, 344018 (2012).
[Crossref]

Qiu, C.-W.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Rangelov, A. A.

Roberts, A.

Rochford, K. B.

Rose, A. H.

Rubin, N. A.

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Sanchez-Brea, L. M.

Sánchez-López, M. M.

Scherer, A.

Schift, H.

H. Schift, J. Vac. Sci. Technol. B 26, 458 (2008).
[Crossref]

Shalaev, V. M.

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, ACS Nano 9, 4111 (2015).
[Crossref]

Shevchenko, A.

A. Shevchenko, M. Nyman, V. Kivijärvi, and M. Kaivola, Opt. Express 25, 8550 (2017).
[Crossref]

A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, Appl. Phys. Lett. 103, 033111 (2013).
[Crossref]

Shi, Q.

Shin, Y. J.

Y. J. Shin, C. Pina-Hernandez, Y.-K. Wu, J. G. Ok, and L. J. Guo, Nanotechnology 23, 344018 (2012).
[Crossref]

Sun, P.-C.

Tan, Q.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Tervo, J.

Tyan, R.-C.

Vargas, A.

Vilas, J. L.

Vitanov, N. V.

Wang, C.

Wang, C. M.

Wang, X.

Wang, Z.

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, ACS Nano 9, 4111 (2015).
[Crossref]

Williams, P. A.

Wu, Y.-K.

Y. J. Shin, C. Pina-Hernandez, Y.-K. Wu, J. G. Ok, and L. J. Guo, Nanotechnology 23, 344018 (2012).
[Crossref]

Xia, D.

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, Adv. Mater. 23, 147 (2011).
[Crossref]

Xu, C.

Xu, F.

Yamada, I.

I. Yamada, T. Ishihara, and J. Yanagisawa, Jpn. J. Appl. Phys. 54, 092203 (2015).
[Crossref]

Yanagisawa, J.

I. Yamada, T. Ishihara, and J. Yanagisawa, Jpn. J. Appl. Phys. 54, 092203 (2015).
[Crossref]

Yu, N.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, Nano Lett. 12, 6328 (2012).
[Crossref]

Zentgraf, T.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, Nat. Nanotechnol. 10, 308 (2015).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Zhang, H.

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Zhang, S.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, Nat. Nanotechnol. 10, 308 (2015).
[Crossref]

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Zhao, X.

Zhao, Y.

Y. Zhao and A. Alù, Phys. Rev. B 84, 205428 (2011).
[Crossref]

Zheng, G.

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, Nat. Nanotechnol. 10, 308 (2015).
[Crossref]

Zhu, A.

Zhu, H.

Zhu, X.

ACS Nano (1)

F. Ding, Z. Wang, S. He, V. M. Shalaev, and A. V. Kildishev, ACS Nano 9, 4111 (2015).
[Crossref]

Adv. Mater. (1)

D. Xia, Z. Ku, S. C. Lee, and S. R. J. Brueck, Adv. Mater. 23, 147 (2011).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

A. Kravchenko, A. Shevchenko, V. Ovchinnikov, P. Grahn, and M. Kaivola, Appl. Phys. Lett. 103, 033111 (2013).
[Crossref]

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

H. Schift, J. Vac. Sci. Technol. B 26, 458 (2008).
[Crossref]

Jpn. J. Appl. Phys. (1)

I. Yamada, T. Ishihara, and J. Yanagisawa, Jpn. J. Appl. Phys. 54, 092203 (2015).
[Crossref]

Nano Lett. (2)

M. Khorasaninejad and F. Capasso, Nano Lett. 15, 6709 (2015).
[Crossref]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, Nano Lett. 12, 6328 (2012).
[Crossref]

Nanotechnology (1)

Y. J. Shin, C. Pina-Hernandez, Y.-K. Wu, J. G. Ok, and L. J. Guo, Nanotechnology 23, 344018 (2012).
[Crossref]

Nat. Commun. (1)

L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, Nat. Commun. 4, 2808 (2013).
[Crossref]

Nat. Nanotechnol. (2)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, Nat. Nanotechnol. 10, 937 (2015).
[Crossref]

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, Nat. Nanotechnol. 10, 308 (2015).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Phys. Rev. B (2)

Y. Zhao and A. Alù, Phys. Rev. B 84, 205428 (2011).
[Crossref]

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[Crossref]

Phys. Rev. Lett. (1)

J. P. Balthasar Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

Other (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

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Figures (5)

Fig. 1.
Fig. 1. Structure of a metal–dielectric wave plate consisting of vertical metal stripes embedded in a dielectric medium. The plates are effectively infinite in the y direction.
Fig. 2.
Fig. 2. Optical properties of the silver–glass quarter-wave plate at λ 0 = 790 nm for a range of values of d d and d m . The birefringence n TM n TE is shown in (a), while (b) shows the average transmittance, T avg = ( T TM + T TE ) / 2 , of the device. In both plots, the dashed line denotes the points at which the TE mode is at the Fabry–Perot resonance.
Fig. 3.
Fig. 3. (a) Spectrum of the magnitude of the transmission coefficient of the designed quarter-wave plate. The blue and red lines correspond to TE and TM polarizations, respectively. The dashed line denotes analytical results, and the solid lines are obtained from numerical calculations. (b) Spectrum of the phase retardation between TM and TE polarizations Δ ϕ = arg ( t TM ) arg ( t TE ) . The shaded region contains values limited by π / 2 ± 0.2 rad . (c) Ellipses of the polarization states that appear after 45° linearly polarized light passes through the wave plate at four different wavelengths. (d) Intensity distribution of a TE-polarized plane wave transmitted through the wave plate at λ 0 = 790 nm . The silver stripes are outlined with gray contours. (e) Intensity distribution of a TM-polarized wave.
Fig. 4.
Fig. 4. Schematic and analysis of the fabrication process. Fabrication steps: (a) spin coating of PMMA resist, (b) e-beam patterning, (c) development of the exposed resist to obtain a PMMA grating and deposition of aluminium, (d) deposition of silver on the sidewalls of PMMA, (e) plasma etch using Ar ions followed by chemical etching of Al, and (f) covering the structure by spin coating a 630 nm layer of PMMA on top of the grating. (g) Scanning electron microscope (SEM) image of sample surface after step (d). (h) SEM image of the sample after step (d) milled with a focused ion beam. Inset: schematic of the imaging.
Fig. 5.
Fig. 5. Measured spectra of (a)  | t | and (b)  Δ ϕ = arg ( t TM ) arg ( t TE ) of the fabricated quarter-wave plate. The shaded region in (b) contains the phase retardations limited by π / 2 ± 0.2 rad . The four polarization ellipses in (c) show the polarization states that result from passing 45° linearly polarized light (denoted by the dashed lines) through the wave plate at different wavelengths.

Equations (3)

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tan ( ϵ d n TE 2 k 0 d d / 2 ) tan ( ϵ m n TE 2 k 0 d m / 2 ) = ϵ m n TE 2 ϵ d n TE 2 ,
tan ( ϵ d n TM 2 k 0 d d / 2 ) tan ( ϵ m n TM 2 k 0 d m / 2 ) = ϵ m n TM 2 ϵ d n TM 2 ϵ d ϵ m ,
η eff = η 0 n eff ,

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