Abstract

Existing transmission type optical quarter-wave plates based on metallic sub-wavelength structures can hardly realize transmission efficiency above 60%. And their working bandwidths are still very narrow. In this paper, we demonstrate a transmission type quarter-wave plate design with efficiency above 92% over a broad wavelength range (from 1260 nm to 1560 nm). The device proposed is based on a one-dimensional metal-insulator-metal waveguide array buried in silica. Phase difference between transmitted TE and TM components can be tuned continuously. At the same time, transmission efficiency can be kept above 90% in the same spectral range for both the TE and TM incidences. The broad bandwidth and remarkable efficiency are explained with the combination of low dispersion of waveguide modes and the resonant cavity enhanced transmission effect. To give a better understanding of the structure, we also propose a modified effective medium model. The optical response of the structure can be well reproduced with the semi-analytic effective medium model.

© 2017 Optical Society of America

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References

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2017 (2)

2016 (6)

M. Ishii, K. Iwami, and N. Umeda, “Highly-efficient and angle-independent zero-order half waveplate at broad visible wavelength based on Au nanofin array embedded in dielectric,” Opt. Express 24(8), 7966–7976 (2016).
[PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[PubMed]

H. Jiang, W. Zhao, and Y. Jiang, “All-dielectric circular polarizer with nearly unit transmission efficiency based on cascaded tensor Huygens surface,” Opt. Express 24(16), 17738–17745 (2016).
[PubMed]

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photon. 1, 030801 (2016).

M. Lorente-Crespo, G. C. Ballesteros, and C. Mateo-Segura, “Transparent all-dielectric gradient index waveplates with compact profiles,” Appl. Phys. Lett. 109, 111105 (2016).

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. U.S.A. 113(38), 10473–10478 (2016).
[PubMed]

2015 (4)

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[PubMed]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

L. Kang, S. Lan, Y. Cui, S. P. Rodrigues, Y. Liu, D. H. Werner, and W. Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383 (2015).
[PubMed]

M. Ishii, K. Iwami, and N. Umeda, “An Au nanofin array for high efficiency plasmonic optical retarders at visible wavelengths,” Appl. Phys. Lett. 106, 021115 (2015).

2014 (8)

H. S. Park, T. T. Kim, H. D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5, 5435 (2014).
[PubMed]

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

T. Ribaudo, A. Taylor, B. M. Nguyen, D. Bethke, and E. A. Shaner, “High efficiency reflective waveplates in the midwave infrared,” Opt. Express 22(3), 2821–2829 (2014).
[PubMed]

H. F. Ma, G. Z. Wang, G. S. Kong, and T. J. Cui, “Broadband circular and linear polarization conversions realized by thin birefringent reflective metasurfaces,” Opt. Mater. Express 4(8), 1717–1724 (2014).

Y. Dai, W. Ren, H. Cai, H. Ding, N. Pan, and X. Wang, “Realizing full visible spectrum metamaterial half-wave plates with patterned metal nanoarray/insulator/metal film structure,” Opt. Express 22(7), 7465–7472 (2014).
[PubMed]

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

2013 (12)

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
[PubMed]

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Broadband plasmonic half-wave plates in reflection,” Opt. Lett. 38(4), 513–515 (2013).
[PubMed]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[PubMed]

H. Zhao, Y. Yang, Q. Li, and M. Qiu, “Sub-wavelength quarter-wave plate based on plasmonic patch antennas,” Appl. Phys. Lett. 103, 261108 (2013).

J. Yang and J. Zhang, “Nano-polarization-converter based on magnetic plasmon resonance excitation in an L-shaped slot antenna,” Opt. Express 21(7), 7934–7942 (2013).
[PubMed]

B. Yang, W. M. Ye, X. D. Yuan, Z. H. Zhu, and C. Zeng, “Design of ultrathin plasmonic quarter-wave plate based on period coupling,” Opt. Lett. 38(5), 679–681 (2013).
[PubMed]

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

X. Yin, M. Schäferling, B. Metzger, and H. Giessen, “Interpreting chiral nanophotonic spectra: the plasmonic Born-Kuhn model,” Nano Lett. 13(12), 6238–6243 (2013).
[PubMed]

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013).
[PubMed]

Y. Zhao and A. Alù, “Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates,” Nano Lett. 13(3), 1086–1091 (2013).
[PubMed]

Y. He and G. V. Eleftheriades, “Design of thin infrared quarter-wave and half-wave plates using antenna-array sheets,” Opt. Express 21(21), 24468–24474 (2013).
[PubMed]

2012 (3)

K. Iwami, M. Ishii, Y. Kuramochi, K. Ida, and N. Umeda, “Ultrasmall radial polarizer array based on patterned plasmonic nanoslits,” Appl. Phys. Lett. 101, 161119 (2012).

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett. 37(11), 1820–1822 (2012).
[PubMed]

2011 (5)

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).

J. Yang and J. Zhang, “Subwavelength Quarter-Waveplate Composed of L-Shaped Metal Nanoparticles,” Plasmonics 6, 251–254 (2011).

P. F. Chimento, N. V. Kuzmin, J. Bosman, P. F. A. Alkemade, G. W’t Hooft, and E. R. Eliel, “A subwavelength slit as a quarter-wave retarder,” Opt. Express 19(24), 24219–24227 (2011).
[PubMed]

A. Pors, M. G. Nielsen, G. Della Valle, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles,” Opt. Lett. 36(9), 1626–1628 (2011).
[PubMed]

2010 (1)

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).

2009 (1)

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[PubMed]

2008 (1)

T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008).

2007 (1)

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 1188–1190 (2007).

1998 (1)

Abbott, D.

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

Aieta, F.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

Albrektsen, O.

Alkemade, P. F. A.

Alrasheed, S.

Alù, A.

Y. Zhao and A. Alù, “Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates,” Nano Lett. 13(3), 1086–1091 (2013).
[PubMed]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[PubMed]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).

Azad, A. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

Bai, B.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 1188–1190 (2007).

Baida, F. I.

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).

Ballesteros, G. C.

M. Lorente-Crespo, G. C. Ballesteros, and C. Mateo-Segura, “Transparent all-dielectric gradient index waveplates with compact profiles,” Appl. Phys. Lett. 109, 111105 (2016).

Bardou, N.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

Bethke, D.

Bhaskaran, M.

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

Bosman, J.

Bouchon, P.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

Boutria, M.

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).

Bozhevolnyi, S. I.

Brener, I.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Briggs, D. P.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

Cai, H.

Cai, W.

L. Kang, S. Lan, Y. Cui, S. P. Rodrigues, Y. Liu, D. H. Werner, and W. Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383 (2015).
[PubMed]

Campione, S.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Cao, J. X.

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).

Capasso, F.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[PubMed]

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. U.S.A. 113(38), 10473–10478 (2016).
[PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

Chen, H. T.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

Chen, W. T.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[PubMed]

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. U.S.A. 113(38), 10473–10478 (2016).
[PubMed]

Chen, Y.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[PubMed]

Cheng, Y. Z.

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

Chimento, P. F.

Chong, K. E.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Chowdhury, D. R.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

Cui, T. J.

Cui, Y.

L. Kang, S. Lan, Y. Cui, S. P. Rodrigues, Y. Liu, D. H. Werner, and W. Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383 (2015).
[PubMed]

Dai, Y.

Dalvit, D. A.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

Decker, M.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Della Valle, G.

Devlin, R. C.

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. U.S.A. 113(38), 10473–10478 (2016).
[PubMed]

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[PubMed]

Ding, H.

Djurisic, A. B.

Dominguez, J.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Dupuis, C.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

Elazar, J. M.

Eleftheriades, G. V.

Eliel, E. R.

Estakhri, N. M.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[PubMed]

Fabrizio, E. D.

Fedotov, V. A.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[PubMed]

Gaburro, Z.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

Genevet, P.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

Giessen, H.

X. Yin, M. Schäferling, B. Metzger, and H. Giessen, “Interpreting chiral nanophotonic spectra: the plasmonic Born-Kuhn model,” Nano Lett. 13(12), 6238–6243 (2013).
[PubMed]

Gong, R. Z.

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

Grady, N. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

Haïdar, R.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

He, Y.

Headland, D.

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

Heyes, J. E.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

Hillenbrand, R.

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Hopkins, B.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photon. 1, 030801 (2016).

Hu, X.

Hu, Y.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

Ida, K.

K. Iwami, M. Ishii, Y. Kuramochi, K. Ida, and N. Umeda, “Ultrasmall radial polarizer array based on patterned plasmonic nanoslits,” Appl. Phys. Lett. 101, 161119 (2012).

Ishii, M.

M. Ishii, K. Iwami, and N. Umeda, “Highly-efficient and angle-independent zero-order half waveplate at broad visible wavelength based on Au nanofin array embedded in dielectric,” Opt. Express 24(8), 7966–7976 (2016).
[PubMed]

M. Ishii, K. Iwami, and N. Umeda, “An Au nanofin array for high efficiency plasmonic optical retarders at visible wavelengths,” Appl. Phys. Lett. 106, 021115 (2015).

K. Iwami, M. Ishii, Y. Kuramochi, K. Ida, and N. Umeda, “Ultrasmall radial polarizer array based on patterned plasmonic nanoslits,” Appl. Phys. Lett. 101, 161119 (2012).

Iwami, K.

M. Ishii, K. Iwami, and N. Umeda, “Highly-efficient and angle-independent zero-order half waveplate at broad visible wavelength based on Au nanofin array embedded in dielectric,” Opt. Express 24(8), 7966–7976 (2016).
[PubMed]

M. Ishii, K. Iwami, and N. Umeda, “An Au nanofin array for high efficiency plasmonic optical retarders at visible wavelengths,” Appl. Phys. Lett. 106, 021115 (2015).

K. Iwami, M. Ishii, Y. Kuramochi, K. Ida, and N. Umeda, “Ultrasmall radial polarizer array based on patterned plasmonic nanoslits,” Appl. Phys. Lett. 101, 161119 (2012).

Jaeck, J.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

James, A.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Jiang, H.

Jiang, S.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Jiang, Y.

Kang, L.

L. Kang, S. Lan, Y. Cui, S. P. Rodrigues, Y. Liu, D. H. Werner, and W. Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383 (2015).
[PubMed]

Kats, M. A.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

Khorasaninejad, M.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[PubMed]

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. U.S.A. 113(38), 10473–10478 (2016).
[PubMed]

Kim, H. D.

H. S. Park, T. T. Kim, H. D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5, 5435 (2014).
[PubMed]

Kim, K.

H. S. Park, T. T. Kim, H. D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5, 5435 (2014).
[PubMed]

Kim, T. T.

H. S. Park, T. T. Kim, H. D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5, 5435 (2014).
[PubMed]

Kivshar, Y. S.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photon. 1, 030801 (2016).

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Kong, G. S.

Kravchenko, I. I.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photon. 1, 030801 (2016).

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

Kruk, S.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photon. 1, 030801 (2016).

Kuramochi, Y.

K. Iwami, M. Ishii, Y. Kuramochi, K. Ida, and N. Umeda, “Ultrasmall radial polarizer array based on patterned plasmonic nanoslits,” Appl. Phys. Lett. 101, 161119 (2012).

Kuzmin, N. V.

Lan, S.

L. Kang, S. Lan, Y. Cui, S. P. Rodrigues, Y. Liu, D. H. Werner, and W. Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383 (2015).
[PubMed]

Lévesque, Q.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

Li, Q.

H. Zhao, Y. Yang, Q. Li, and M. Qiu, “Sub-wavelength quarter-wave plate based on plasmonic patch antennas,” Appl. Phys. Lett. 103, 261108 (2013).

Li, T.

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).

T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008).

Lin, L.

Litchinitser, N. M.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[PubMed]

Liu, H.

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).

T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008).

Liu, S.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Liu, X. X.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[PubMed]

Liu, Y.

L. Kang, S. Lan, Y. Cui, S. P. Rodrigues, Y. Liu, D. H. Werner, and W. Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383 (2015).
[PubMed]

Lorente-Crespo, M.

M. Lorente-Crespo, G. C. Ballesteros, and C. Mateo-Segura, “Transparent all-dielectric gradient index waveplates with compact profiles,” Appl. Phys. Lett. 109, 111105 (2016).

Luk, T. S.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Ma, G.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

Ma, H. F.

Majewski, M. L.

Makhsiyan, M.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

Mateo-Segura, C.

M. Lorente-Crespo, G. C. Ballesteros, and C. Mateo-Segura, “Transparent all-dielectric gradient index waveplates with compact profiles,” Appl. Phys. Lett. 109, 111105 (2016).

Metzger, B.

X. Yin, M. Schäferling, B. Metzger, and H. Giessen, “Interpreting chiral nanophotonic spectra: the plasmonic Born-Kuhn model,” Nano Lett. 13(12), 6238–6243 (2013).
[PubMed]

Min, B.

H. S. Park, T. T. Kim, H. D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5, 5435 (2014).
[PubMed]

Miroshnichenko, A.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photon. 1, 030801 (2016).

Moitra, P.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

Monticone, F.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[PubMed]

Neshev, D. N.

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photon. 1, 030801 (2016).

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Nguyen, B. M.

Nie, Y.

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

Nielsen, M. G.

Nikolskiy, K.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[PubMed]

Oh, J.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[PubMed]

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. U.S.A. 113(38), 10473–10478 (2016).
[PubMed]

Oussaid, R.

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).

Pan, N.

Pandey, A.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[PubMed]

Pardo, F.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

Park, H. S.

H. S. Park, T. T. Kim, H. D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5, 5435 (2014).
[PubMed]

Pelouard, J.-L.

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

Peng, R.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Plum, E.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[PubMed]

Pors, A.

Qiu, M.

H. Zhao, Y. Yang, Q. Li, and M. Qiu, “Sub-wavelength quarter-wave plate based on plasmonic patch antennas,” Appl. Phys. Lett. 103, 261108 (2013).

Radko, I. P.

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
[PubMed]

Rakic, A. D.

Reiten, M. T.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

Ren, W.

Ribaudo, T.

Roberts, A.

Rodrigues, S. P.

L. Kang, S. Lan, Y. Cui, S. P. Rodrigues, Y. Liu, D. H. Werner, and W. Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383 (2015).
[PubMed]

Sarriugarte, P.

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Schäferling, M.

X. Yin, M. Schäferling, B. Metzger, and H. Giessen, “Interpreting chiral nanophotonic spectra: the plasmonic Born-Kuhn model,” Nano Lett. 13(12), 6238–6243 (2013).
[PubMed]

Shalaev, M. I.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[PubMed]

Shaner, E. A.

Sriram, S.

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

Staude, I.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Subramania, G. S.

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Sun, C.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

Sun, J.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[PubMed]

Svirko, Y.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 1188–1190 (2007).

Taylor, A.

Taylor, A. J.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

Tsai, D. P.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[PubMed]

Tsukernik, A.

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[PubMed]

Turunen, J.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 1188–1190 (2007).

Umeda, N.

M. Ishii, K. Iwami, and N. Umeda, “Highly-efficient and angle-independent zero-order half waveplate at broad visible wavelength based on Au nanofin array embedded in dielectric,” Opt. Express 24(8), 7966–7976 (2016).
[PubMed]

M. Ishii, K. Iwami, and N. Umeda, “An Au nanofin array for high efficiency plasmonic optical retarders at visible wavelengths,” Appl. Phys. Lett. 106, 021115 (2015).

K. Iwami, M. Ishii, Y. Kuramochi, K. Ida, and N. Umeda, “Ultrasmall radial polarizer array based on patterned plasmonic nanoslits,” Appl. Phys. Lett. 101, 161119 (2012).

Upadhyay, A.

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

Valentine, J.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

Vallius, T.

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 1188–1190 (2007).

Van Labeke, D.

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).

W’t Hooft, G.

Wang, F.-M.

T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008).

Wang, G. Z.

Wang, M.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Wang, S. M.

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).

Wang, S.-M.

T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008).

Wang, W.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

Wang, X.

Wang, Y.

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Wei, X.

Werner, D. H.

L. Kang, S. Lan, Y. Cui, S. P. Rodrigues, Y. Liu, D. H. Werner, and W. Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383 (2015).
[PubMed]

Willatzen, M.

Withayachumnankul, W.

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

Wu, D.

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Wu, S.

S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013).
[PubMed]

Xiong, X.

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Yang, B.

Yang, J.

J. Yang and J. Zhang, “Nano-polarization-converter based on magnetic plasmon resonance excitation in an L-shaped slot antenna,” Opt. Express 21(7), 7934–7942 (2013).
[PubMed]

J. Yang and J. Zhang, “Subwavelength Quarter-Waveplate Composed of L-Shaped Metal Nanoparticles,” Plasmonics 6, 251–254 (2011).

Yang, Y.

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

H. Zhao, Y. Yang, Q. Li, and M. Qiu, “Sub-wavelength quarter-wave plate based on plasmonic patch antennas,” Appl. Phys. Lett. 103, 261108 (2013).

Ye, W. M.

Yin, X.

X. Yin, M. Schäferling, B. Metzger, and H. Giessen, “Interpreting chiral nanophotonic spectra: the plasmonic Born-Kuhn model,” Nano Lett. 13(12), 6238–6243 (2013).
[PubMed]

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Yin, X.-G.

T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008).

Yu, N.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

Yuan, X. D.

Zeng, C.

Zeng, Y.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

Zhang, J.

J. Yang and J. Zhang, “Nano-polarization-converter based on magnetic plasmon resonance excitation in an L-shaped slot antenna,” Opt. Express 21(7), 7934–7942 (2013).
[PubMed]

J. Yang and J. Zhang, “Subwavelength Quarter-Waveplate Composed of L-Shaped Metal Nanoparticles,” Plasmonics 6, 251–254 (2011).

Zhang, K.

S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013).
[PubMed]

Zhang, X.

S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013).
[PubMed]

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008).

Zhang, Y.

S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013).
[PubMed]

Zhang, Z.

S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013).
[PubMed]

Zhao, H.

H. Zhao, Y. Yang, Q. Li, and M. Qiu, “Sub-wavelength quarter-wave plate based on plasmonic patch antennas,” Appl. Phys. Lett. 103, 261108 (2013).

Zhao, W.

Zhao, Y.

Y. Zhao and A. Alù, “Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates,” Nano Lett. 13(3), 1086–1091 (2013).
[PubMed]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).

Zheludev, N. I.

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[PubMed]

Zhou, L.

S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013).
[PubMed]

Zhu, A. Y.

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[PubMed]

Zhu, S. N.

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).

Zhu, S.-N.

T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008).

Zhu, Y.

S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013).
[PubMed]

Zhu, Z. H.

Adv. Mater. (1)

L. Kang, S. Lan, Y. Cui, S. P. Rodrigues, Y. Liu, D. H. Werner, and W. Cai, “An Active Metamaterial Platform for Chiral Responsive Optoelectronics,” Adv. Mater. 27(29), 4377–4383 (2015).
[PubMed]

APL Photon. (1)

S. Kruk, B. Hopkins, I. I. Kravchenko, A. Miroshnichenko, D. N. Neshev, and Y. S. Kivshar, “Invited Article: Broadband highly efficient dielectric metadevices for polarization control,” APL Photon. 1, 030801 (2016).

Appl. Opt. (2)

Appl. Phys. Lett. (8)

Q. Lévesque, M. Makhsiyan, P. Bouchon, F. Pardo, J. Jaeck, N. Bardou, C. Dupuis, R. Haïdar, and J.-L. Pelouard, “Plasmonic planar antenna for wideband and efficient linear polarization conversion,” Appl. Phys. Lett. 104, 111105 (2014).

K. Iwami, M. Ishii, Y. Kuramochi, K. Ida, and N. Umeda, “Ultrasmall radial polarizer array based on patterned plasmonic nanoslits,” Appl. Phys. Lett. 101, 161119 (2012).

M. Ishii, K. Iwami, and N. Umeda, “An Au nanofin array for high efficiency plasmonic optical retarders at visible wavelengths,” Appl. Phys. Lett. 106, 021115 (2015).

M. Lorente-Crespo, G. C. Ballesteros, and C. Mateo-Segura, “Transparent all-dielectric gradient index waveplates with compact profiles,” Appl. Phys. Lett. 109, 111105 (2016).

Y. Z. Cheng, W. Withayachumnankul, A. Upadhyay, D. Headland, Y. Nie, R. Z. Gong, M. Bhaskaran, S. Sriram, and D. Abbott, “Ultrabroadband reflective polarization convertor for terahertz waves,” Appl. Phys. Lett. 105, 181111 (2014).

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 261113 (2010).

T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008).

H. Zhao, Y. Yang, Q. Li, and M. Qiu, “Sub-wavelength quarter-wave plate based on plasmonic patch antennas,” Appl. Phys. Lett. 103, 261108 (2013).

Nano Lett. (6)

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[PubMed]

Y. Zhao and A. Alù, “Tailoring the dispersion of plasmonic nanorods to realize broadband optical meta-waveplates,” Nano Lett. 13(3), 1086–1091 (2013).
[PubMed]

X. Yin, M. Schäferling, B. Metzger, and H. Giessen, “Interpreting chiral nanophotonic spectra: the plasmonic Born-Kuhn model,” Nano Lett. 13(12), 6238–6243 (2013).
[PubMed]

Y. Yang, W. Wang, P. Moitra, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Dielectric meta-reflectarray for broadband linear polarization conversion and optical vortex generation,” Nano Lett. 14(3), 1394–1399 (2014).
[PubMed]

M. I. Shalaev, J. Sun, A. Tsukernik, A. Pandey, K. Nikolskiy, and N. M. Litchinitser, “High-efficiency all-dielectric metasurfaces for ultracompact beam manipulation in transmission mode,” Nano Lett. 15(9), 6261–6266 (2015).
[PubMed]

K. E. Chong, I. Staude, A. James, J. Dominguez, S. Liu, S. Campione, G. S. Subramania, T. S. Luk, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control,” Nano Lett. 15(8), 5369–5374 (2015).
[PubMed]

Nat. Commun. (1)

H. S. Park, T. T. Kim, H. D. Kim, K. Kim, and B. Min, “Nondispersive optical activity of meshed helical metamaterials,” Nat. Commun. 5, 5435 (2014).
[PubMed]

Opt. Express (8)

P. F. Chimento, N. V. Kuzmin, J. Bosman, P. F. A. Alkemade, G. W’t Hooft, and E. R. Eliel, “A subwavelength slit as a quarter-wave retarder,” Opt. Express 19(24), 24219–24227 (2011).
[PubMed]

Y. He and G. V. Eleftheriades, “Design of thin infrared quarter-wave and half-wave plates using antenna-array sheets,” Opt. Express 21(21), 24468–24474 (2013).
[PubMed]

T. Ribaudo, A. Taylor, B. M. Nguyen, D. Bethke, and E. A. Shaner, “High efficiency reflective waveplates in the midwave infrared,” Opt. Express 22(3), 2821–2829 (2014).
[PubMed]

J. Yang and J. Zhang, “Nano-polarization-converter based on magnetic plasmon resonance excitation in an L-shaped slot antenna,” Opt. Express 21(7), 7934–7942 (2013).
[PubMed]

Y. Dai, W. Ren, H. Cai, H. Ding, N. Pan, and X. Wang, “Realizing full visible spectrum metamaterial half-wave plates with patterned metal nanoarray/insulator/metal film structure,” Opt. Express 22(7), 7465–7472 (2014).
[PubMed]

H. Jiang, W. Zhao, and Y. Jiang, “All-dielectric circular polarizer with nearly unit transmission efficiency based on cascaded tensor Huygens surface,” Opt. Express 24(16), 17738–17745 (2016).
[PubMed]

M. Ishii, K. Iwami, and N. Umeda, “Highly-efficient and angle-independent zero-order half waveplate at broad visible wavelength based on Au nanofin array embedded in dielectric,” Opt. Express 24(8), 7966–7976 (2016).
[PubMed]

X. Hu and X. Wei, “Metallic metasurface for high efficiency optical phase control in transmission mode,” Opt. Express 25(13), 15208–15215 (2017).
[PubMed]

Opt. Lett. (4)

Opt. Mater. Express (1)

Phys. Rev. A (1)

B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 1188–1190 (2007).

Phys. Rev. B (3)

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84, 205428 (2011).

F. I. Baida, M. Boutria, R. Oussaid, and D. Van Labeke, “Enhanced-transmission metamaterials as anisotropic plates,” Phys. Rev. B 84, 035107 (2011).

S. Jiang, X. Xiong, P. Sarriugarte, S. Jiang, X. Yin, Y. Wang, R. Peng, D. Wu, R. Hillenbrand, X. Zhang, and M. Wang, “Tuning the polarization state of light via time retardation with a microstructured surface,” Phys. Rev. B 88, 161104 (2013).

Phys. Rev. Lett. (3)

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[PubMed]

S. Wu, Z. Zhang, Y. Zhang, K. Zhang, L. Zhou, X. Zhang, and Y. Zhu, “Enhanced rotation of the polarization of a light beam transmitted through a silver film with an array of perforated S-shaped holes,” Phys. Rev. Lett. 110(20), 207401 (2013).
[PubMed]

E. Plum, X. X. Liu, V. A. Fedotov, Y. Chen, D. P. Tsai, and N. I. Zheludev, “Metamaterials: optical activity without chirality,” Phys. Rev. Lett. 102(11), 113902 (2009).
[PubMed]

Phys. Rev. X (1)

S. Jiang, X. Xiong, Y. Hu, Y. Hu, G. Ma, R. Peng, C. Sun, and M. Wang, “Controlling the Polarization State of Light with a Dispersion-Free Metastructure,” Phys. Rev. X 4(2), 021026 (2014).

Plasmonics (1)

J. Yang and J. Zhang, “Subwavelength Quarter-Waveplate Composed of L-Shaped Metal Nanoparticles,” Plasmonics 6, 251–254 (2011).

Proc. Natl. Acad. Sci. U.S.A. (1)

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. U.S.A. 113(38), 10473–10478 (2016).
[PubMed]

Sci. Rep. (1)

A. Pors, O. Albrektsen, I. P. Radko, and S. I. Bozhevolnyi, “Gap plasmon-based metasurfaces for total control of reflected light,” Sci. Rep. 3, 2155 (2013).
[PubMed]

Science (2)

M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016).
[PubMed]

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[PubMed]

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Figures (7)

Fig. 1
Fig. 1 Schematic illustration of the quarter-wave plate’s structure. (a) 3D sketch of the structure. The periodicity of the structure in x-direction is P = 800 nm, the gap between neighboring silver strips is g = 650 nm, the width of the silver strip is w = 150 nm, and the height of the silver strip is t = 600 nm. (b) Profile of the structure in x-z plane.
Fig. 2
Fig. 2 (a) Transmittance spectra of the structure in Fig. 1 under TE incidence and TM incidence. (b) The phase difference between transmitted TE light and transmitted TM light, the shadowed region indicates the spectral range in which the phase difference is within 90° ± 10°.
Fig. 3
Fig. 3 Real part (a) and imaginary part (b) of the effective refractive index for TE and TM modes.
Fig. 4
Fig. 4 Field distribution at the FP resonance peak under TE (a) and TM (b) incidence. Transmittance spectra in dependence of metallic strip thickness t under TE (c) and TM (d) incidence. The transmittance spectra (e) and phase difference spectrum (f) with metallic strip thickness equal to 1500 nm.
Fig. 5
Fig. 5 (a) Three-layer dielectric material model for the structure in Fig. 1. Transmittance spectra (b) and phase difference spectrum (c) calculated with the transfer matrix with effective layer thickness set to be equal to the metallic strip thickness t = 600 nm.
Fig. 6
Fig. 6 Extra cavity length Δd estimated from Eq. (5) for TE incidence (a) and TM incidence (d), respectively. Transmittance (c) and phase difference (d) calculated with the semi-analytic model in comparison with the results from FEM simulations.
Fig. 7
Fig. 7 Spectral response for devices built with different metallic materials. (a) Transmittance under TE and TM incidence. (b) Phase difference between transmitted TE and TM field.

Equations (5)

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tan( g 2 k 0 2 ε d β TE 2 )= β TE 2 k 0 2 ε m k 0 2 ε d β TE 2
tanh( g 2 β TM 2 k 0 2 ε d )= ε d ε m β TM 2 k 0 2 ε m β TM 2 k 0 2 ε d .
n TE(TM) = β TE(TM) / k 0 .
M=( n 1 + n 2 2 n 1 n 1 n 2 2 n 1 n 1 n 2 2 n 1 n 1 + n 2 2 n 1 )*( e i 2π λ n 2 d 0 0 e i 2π λ n 2 d )*( n 2 + n 3 2 n 2 n 2 n 3 2 n 2 n 2 n 3 2 n 2 n 2 + n 3 2 n 2 )
Δd(λ)= λ 2 n 2 (λ) t FP (λ)

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