Abstract

A coupled dielectric-metal metasurface (CDMM) filter consisting of amorphous silicon (a-Si) rings and subwavelength holes in Au layer separated by a SiO2 layer is presented. The design parameters of the CDMM filter is numerically optimized to have a polarization independent peak transmittance of 0.55 at 1540 nm with a Full Width at Half Maximum (FWHM) of 10 nm. The filter also has a 100 nm quiet zone with ∼10−2 transmittance. A radiating two-oscillator model reveals the fundamental resonances in the filter which interfere to produce the electromagnetically induced transparency (EIT) like effect. Multipole expansion of the currents in the structure validates the fundamental resonances predicted by the two-oscillator model. The presented CDMM filter is robust to artifacts in device fabrication and has performances comparable to a conventional Fabry-Pérot filter. However, it is easier to be integrated in image sensors as the transmittance peak can be tuned by only changing the periodicity resulting in a planar structure with a fixed height.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (4)

2018 (7)

Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic Broadband Super-Resolution Imaging by Super-Oscillatory Metasurface,” Laser Photonics Rev. 12(10), 1800064 (2018).
[Crossref]

J. Algorri, D. Zografopoulos, A. Ferraro, B. García-Cámara, R. Vergaz, R. Beccherelli, and J. Sánchez-Pena, “Anapole Modes in Hollow Nanocuboid Dielectric Metasurfaces for Refractometric Sensing,” Nanomaterials 9(1), 30 (2018).
[Crossref]

B. Han, X. Li, C. Sui, J. Diao, X. Jing, and Z. Hong, “Analog of electromagnetically induced transparency in an E-shaped all-dielectric metasurface based on toroidal dipolar response,” Opt. Mater. Express 8(8), 2197 (2018).
[Crossref]

M. Gupta, Y. K. Srivastava, and R. Singh, “A Toroidal Metamaterial Switch,” Adv. Mater. 30(4), 1704845 (2018).
[Crossref]

V. R. Tuz, V. V. Khardikov, and Y. S. Kivshar, “All-Dielectric Resonant Metasurfaces with a Strong Toroidal Response,” ACS Photonics 5(5), 1871–1876 (2018).
[Crossref]

G. Rana, P. Deshmukh, S. Palkhivala, A. Gupta, S. P. Duttagupta, S. S. Prabhu, V. Achanta, and G. S. Agarwal, “Quadrupole-Quadrupole Interactions to Control Plasmon-Induced Transparency,” Phys. Rev. Appl. 9(6), 064015 (2018).
[Crossref]

Y. D. Shah, J. Grant, D. Hao, M. Kenney, V. Pusino, and D. R. S. Cumming, “Ultra-narrow Line Width Polarization-Insensitive Filter Using a Symmetry-Breaking Selective Plasmonic Metasurface,” ACS Photonics 5(2), 663–669 (2018).
[Crossref]

2017 (4)

G. M. Gibson, B. Sun, M. P. Edgar, D. B. Phillips, N. Hempler, G. T. Maker, G. P. A. Malcolm, and M. J. Padgett, “Real-time imaging of methane gas leaks using a single-pixel camera,” Opt. Express 25(4), 2998 (2017).
[Crossref]

Z. Vafapour and H. Alaei, “Achieving a High Q-Factor and Tunable Slow-Light via Classical Electromagnetically Induced Transparency (Cl-EIT) in Metamaterials,” Plasmonics 12(2), 479–488 (2017).
[Crossref]

S.-D. Liu, Z.-X. Wang, W.-J. Wang, J.-D. Chen, and Z.-H. Chen, “High Q-factor with the excitation of anapole modes in dielectric split nanodisk arrays,” Opt. Express 25(19), 22375 (2017).
[Crossref]

X. Hu, S. Yuan, A. Armghan, Y. Liu, Z. Jiao, H. Lv, C. Zeng, Y. Huang, Q. Huang, Y. Wang, and J. Xia, “Plasmon induced transparency and absorption in bright–bright mode coupling metamaterials: a radiating two-oscillator model analysis,” J. Phys. D: Appl. Phys. 50(2), 025301 (2017).
[Crossref]

2016 (4)

C. Menzel, J. Sperrhake, and T. Pertsch, “Efficient treatment of stacked metasurfaces for optimizing and enhancing the range of accessible optical functionalities,” Phys. Rev. A 93(6), 063832 (2016).
[Crossref]

M. A. van de Haar, J. van de Groep, B. J. Brenny, and A. Polman, “Controlling magnetic and electric dipole modes in hollow silicon nanocylinders,” Opt. Express 24(3), 2047–2064 (2016).
[Crossref]

M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp Toroidal Resonances in Planar Terahertz Metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref]

A. C. Tasolamprou, O. Tsilipakos, M. Kafesaki, C. M. Soukoulis, and E. N. Economou, “Toroidal eigenmodes in all-dielectric metamolecules,” Phys. Rev. B 94(20), 205433 (2016).
[Crossref]

2015 (5)

M.-L. Wan, J.-N. He, Y.-L. Song, and F.-Q. Zhou, “Electromagnetically induced transparency and absorption in plasmonic metasurfaces based on near-field coupling,” Phys. Lett. A 379(30-31), 1791–1795 (2015).
[Crossref]

M. Manjappa, S.-Y. Chiam, L. Cong, A. A. Bettiol, W. Zhang, and R. Singh, “Tailoring the slow light behavior in terahertz metasurfaces,” Appl. Phys. Lett. 106(18), 181101 (2015).
[Crossref]

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric Metamaterials with Toroidal Dipolar Response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

L. Zhu, F.-Y. Meng, L. Dong, Q. Wu, B.-J. Che, J. Gao, J.-H. Fu, K. Zhang, and G.-H. Yang, “Magnetic metamaterial analog of electromagnetically induced transparency and absorption,” J. Appl. Phys. 117(17), 17D146 (2015).
[Crossref]

S. A. Tretyakov, “Metasurfaces for general transformations of electromagnetic fields,” Philos. Trans. R. Soc., A 373(2049), 20140362 (2015).
[Crossref]

2014 (4)

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

J. Zhang, W. Liu, X. Yuan, and S. Qin, “Electromagnetically induced transparency-like optical responses in all-dielectric metamaterials,” J. Opt. 16(12), 125102 (2014).
[Crossref]

P.-J. Lapray, X. Wang, J.-B. Thomas, and P. Gouton, “Multispectral Filter Arrays: Recent Advances and Practical Implementation,” Sensors 14(11), 21626–21659 (2014).
[Crossref]

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[Crossref]

2013 (1)

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
[Crossref]

2012 (2)

R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical Analog of Electromagnetically Induced Absorption in Plasmonics,” Nano Lett. 12(3), 1367–1371 (2012).
[Crossref]

P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, “Electromagnetically Induced Transparency and Absorption in Metamaterials: The Radiating Two-Oscillator Model and Its Experimental Confirmation,” Phys. Rev. Lett. 109(18), 187401 (2012).
[Crossref]

2011 (1)

R. Singh, I. A. I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

2010 (2)

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal Dipolar Response in a Metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref]

B. Schwarz, “LIDAR: Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010).
[Crossref]

2009 (3)

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Planar designs for electromagnetically induced transparency in metamaterials,” Opt. Express 17(7), 5595 (2009).
[Crossref]

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).
[Crossref]

R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “Coupling between a dark and a bright eigenmode in a terahertz metamaterial,” Phys. Rev. B 79(8), 085111 (2009).
[Crossref]

2008 (1)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-Induced Transparency in Metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref]

2006 (1)

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

1988 (1)

1972 (2)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

D. T. Pierce and W. E. Spicer, “Electronic Structure of Amorphous Si from Photoemission and Optical Studies,” Phys. Rev. B 5(8), 3017–3029 (1972).
[Crossref]

1965 (1)

1938 (1)

J. K. Knipp, “Quadrupole-Quadrupole Interatomic Forces,” Phys. Rev. 53(9), 734–745 (1938).
[Crossref]

Achanta, V.

G. Rana, P. Deshmukh, S. Palkhivala, A. Gupta, S. P. Duttagupta, S. S. Prabhu, V. Achanta, and G. S. Agarwal, “Quadrupole-Quadrupole Interactions to Control Plasmon-Induced Transparency,” Phys. Rev. Appl. 9(6), 064015 (2018).
[Crossref]

Agarwal, G. S.

G. Rana, P. Deshmukh, S. Palkhivala, A. Gupta, S. P. Duttagupta, S. S. Prabhu, V. Achanta, and G. S. Agarwal, “Quadrupole-Quadrupole Interactions to Control Plasmon-Induced Transparency,” Phys. Rev. Appl. 9(6), 064015 (2018).
[Crossref]

Alaei, H.

Z. Vafapour and H. Alaei, “Achieving a High Q-Factor and Tunable Slow-Light via Classical Electromagnetically Induced Transparency (Cl-EIT) in Metamaterials,” Plasmonics 12(2), 479–488 (2017).
[Crossref]

Algorri, J.

J. Algorri, D. Zografopoulos, A. Ferraro, B. García-Cámara, R. Vergaz, R. Beccherelli, and J. Sánchez-Pena, “Anapole Modes in Hollow Nanocuboid Dielectric Metasurfaces for Refractometric Sensing,” Nanomaterials 9(1), 30 (2018).
[Crossref]

Algorri, J. F.

Al-Naib, I. A. I.

R. Singh, I. A. I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Armghan, A.

X. Hu, S. Yuan, A. Armghan, Y. Liu, Z. Jiao, H. Lv, C. Zeng, Y. Huang, Q. Huang, Y. Wang, and J. Xia, “Plasmon induced transparency and absorption in bright–bright mode coupling metamaterials: a radiating two-oscillator model analysis,” J. Phys. D: Appl. Phys. 50(2), 025301 (2017).
[Crossref]

Basharin, A. A.

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric Metamaterials with Toroidal Dipolar Response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

Beccherelli, R.

J. F. Algorri, D. C. Zografopoulos, A. Ferraro, B. García-Cámara, R. Beccherelli, and J. M. Sánchez-Pena, “Ultrahigh-quality factor resonant dielectric metasurfaces based on hollow nanocuboids,” Opt. Express 27(5), 6320 (2019).
[Crossref]

J. Algorri, D. Zografopoulos, A. Ferraro, B. García-Cámara, R. Vergaz, R. Beccherelli, and J. Sánchez-Pena, “Anapole Modes in Hollow Nanocuboid Dielectric Metasurfaces for Refractometric Sensing,” Nanomaterials 9(1), 30 (2018).
[Crossref]

Bettiol, A. A.

M. Manjappa, S.-Y. Chiam, L. Cong, A. A. Bettiol, W. Zhang, and R. Singh, “Tailoring the slow light behavior in terahertz metasurfaces,” Appl. Phys. Lett. 106(18), 181101 (2015).
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R. Singh, I. A. I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
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P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Planar designs for electromagnetically induced transparency in metamaterials,” Opt. Express 17(7), 5595 (2009).
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Wei, Z.

Y. Fan, Z. Wei, H. Li, H. Chen, and C. M. Soukoulis, “Low-loss and high-Q planar metamaterial with toroidal moment,” Phys. Rev. B 87(11), 115417 (2013).
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Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

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[Crossref]

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J. Zhang, W. Liu, X. Yuan, and S. Qin, “Electromagnetically induced transparency-like optical responses in all-dielectric metamaterials,” J. Opt. 16(12), 125102 (2014).
[Crossref]

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[Crossref]

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[Crossref]

J. Zhang, W. Liu, X. Yuan, and S. Qin, “Electromagnetically induced transparency-like optical responses in all-dielectric metamaterials,” J. Opt. 16(12), 125102 (2014).
[Crossref]

Zhang, K.

L. Zhu, F.-Y. Meng, L. Dong, Q. Wu, B.-J. Che, J. Gao, J.-H. Fu, K. Zhang, and G.-H. Yang, “Magnetic metamaterial analog of electromagnetically induced transparency and absorption,” J. Appl. Phys. 117(17), 17D146 (2015).
[Crossref]

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P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, “Electromagnetically Induced Transparency and Absorption in Metamaterials: The Radiating Two-Oscillator Model and Its Experimental Confirmation,” Phys. Rev. Lett. 109(18), 187401 (2012).
[Crossref]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Planar designs for electromagnetically induced transparency in metamaterials,” Opt. Express 17(7), 5595 (2009).
[Crossref]

Zhang, S.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-Induced Transparency in Metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
[Crossref]

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Z. Li, T. Zhang, Y. Wang, W. Kong, J. Zhang, Y. Huang, C. Wang, X. Li, M. Pu, and X. Luo, “Achromatic Broadband Super-Resolution Imaging by Super-Oscillatory Metasurface,” Laser Photonics Rev. 12(10), 1800064 (2018).
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M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp Toroidal Resonances in Planar Terahertz Metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref]

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[Crossref]

R. Singh, I. A. I. Al-Naib, Y. Yang, D. Roy Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

R. Singh, C. Rockstuhl, F. Lederer, and W. Zhang, “Coupling between a dark and a bright eigenmode in a terahertz metamaterial,” Phys. Rev. B 79(8), 085111 (2009).
[Crossref]

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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-Induced Transparency in Metamaterials,” Phys. Rev. Lett. 101(4), 047401 (2008).
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Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).
[Crossref]

Zhao, R.

P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, “Electromagnetically Induced Transparency and Absorption in Metamaterials: The Radiating Two-Oscillator Model and Its Experimental Confirmation,” Phys. Rev. Lett. 109(18), 187401 (2012).
[Crossref]

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M. Gupta, V. Savinov, N. Xu, L. Cong, G. Dayal, S. Wang, W. Zhang, N. I. Zheludev, and R. Singh, “Sharp Toroidal Resonances in Planar Terahertz Metasurfaces,” Adv. Mater. 28(37), 8206–8211 (2016).
[Crossref]

A. A. Basharin, M. Kafesaki, E. N. Economou, C. M. Soukoulis, V. A. Fedotov, V. Savinov, and N. I. Zheludev, “Dielectric Metamaterials with Toroidal Dipolar Response,” Phys. Rev. X 5(1), 011036 (2015).
[Crossref]

V. Savinov, V. A. Fedotov, and N. I. Zheludev, “Toroidal dipolar excitation and macroscopic electromagnetic properties of metamaterials,” Phys. Rev. B 89(20), 205112 (2014).
[Crossref]

T. Kaelberer, V. A. Fedotov, N. Papasimakis, D. P. Tsai, and N. I. Zheludev, “Toroidal Dipolar Response in a Metamaterial,” Science 330(6010), 1510–1512 (2010).
[Crossref]

Zhou, F.-Q.

M.-L. Wan, J.-N. He, Y.-L. Song, and F.-Q. Zhou, “Electromagnetically induced transparency and absorption in plasmonic metasurfaces based on near-field coupling,” Phys. Lett. A 379(30-31), 1791–1795 (2015).
[Crossref]

Zhou, J.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).
[Crossref]

Zhu, L.

L. Zhu, F.-Y. Meng, L. Dong, Q. Wu, B.-J. Che, J. Gao, J.-H. Fu, K. Zhang, and G.-H. Yang, “Magnetic metamaterial analog of electromagnetically induced transparency and absorption,” J. Appl. Phys. 117(17), 17D146 (2015).
[Crossref]

Zografopoulos, D.

J. Algorri, D. Zografopoulos, A. Ferraro, B. García-Cámara, R. Vergaz, R. Beccherelli, and J. Sánchez-Pena, “Anapole Modes in Hollow Nanocuboid Dielectric Metasurfaces for Refractometric Sensing,” Nanomaterials 9(1), 30 (2018).
[Crossref]

Zografopoulos, D. C.

ACS Photonics (2)

Y. D. Shah, J. Grant, D. Hao, M. Kenney, V. Pusino, and D. R. S. Cumming, “Ultra-narrow Line Width Polarization-Insensitive Filter Using a Symmetry-Breaking Selective Plasmonic Metasurface,” ACS Photonics 5(2), 663–669 (2018).
[Crossref]

V. R. Tuz, V. V. Khardikov, and Y. S. Kivshar, “All-Dielectric Resonant Metasurfaces with a Strong Toroidal Response,” ACS Photonics 5(5), 1871–1876 (2018).
[Crossref]

Adv. Mater. (2)

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Figures (12)

Fig. 1.
Fig. 1. Schematic of the proposed CDMM filter highlighting the key design parameters.
Fig. 2.
Fig. 2. Numerically simulated normal incidence transmittance of the designed CDMM filter under planewave illumination. The black curve represents $0^{\textrm {th}}$ order transmittance, while the red curve represents total transmittance including all diffraction orders present.
Fig. 3.
Fig. 3. Numerically simulated normal incidence absorbance of the designed CDMM filter for a normal incident plane wave illumination.
Fig. 4.
Fig. 4. Moduli of electric fields of the CDMM filter under a $y$-polarized planewave illumination of 1540 nm wavelength. The white arrows, with lengths proportional to the magnitude, indicate the field components. (a) vertical cut in the center of the CDMM filter along $xz$ plane. Horizontal cuts along the (b) center of a-Si ring and (c) top of Au layer.
Fig. 5.
Fig. 5. Fitting the numerically obtained transmittance (black curve) with radiative coupled-oscillator model (red dots). The fit parameters are shown in the insert.
Fig. 6.
Fig. 6. Scattering efficiency of the CDMM filter. Modal decomposition of the currents in (a) the a-Si ring, (b) the Au layer. The black star locates the origin. a-Si has a sharp scattering at 1500 nm, Au layer has two scattering peaks, one at 1540 nm and one at 1629 nm.
Fig. 7.
Fig. 7. Scattering efficiency of the two constituents of the CDMM filter. Modal decomposition of the currents in (a) the a-Si ring , (b) the Au layer. The $\textrm {SiO}_{2}$ substrate is included in both cases as shown in the inserts. a-Si has two sharp scattering peaks at 1581 nm and 1609 nm, Au layer has a sharp scattering peak at 1514 nm and a broad scattering peak centered at 1671 nm.
Fig. 8.
Fig. 8. Moduli of electric fields of the CDMM filter at 1500 nm along (a) $xz$ plane and (b) $xy$ plane along the center of the a-Si ring. (c) The corresponding magnetic field moduli at the $xy$ plane. Moduli of electric fields of the CDMM filter at 1629 nm along (d) $xy$ plane along the center of the a-Si ring, (e) $xy$ plane along the center of the Au layer, and (f) $xz$ plane. The white arrows, with lengths proportional to the magnitude, indicate the field components. The normally incident planewave is polarized along $y$-axis.
Fig. 9.
Fig. 9. Simulated Effects of (a) $Y$ offset and (b) $X$ offset between the a-Si ring and the Au layer of the CDMM filter on the transmittance. The normal incident planewave illumination is polarized along $y$ axis as shown in the insets.
Fig. 10.
Fig. 10. Robustness of the CDMM filter. Simulated effects of changes in the diameter of (a) a-Si ring and (b) subwavelength holes in Au layer of the CDMM filter on the transmittance. The normal incident planewave illumination is polarized along $y$ axis. The ideal diameters are represented by $D_1$ and $D_2$ respectively, while the values in red denote positive/negative changes in nm in the diameter.
Fig. 11.
Fig. 11. Simulated dependence of the CDMM filter transmittance on the angle of incidence for a TE polarized planewave illumination.
Fig. 12.
Fig. 12. Simulated dependence of the peak transmittance on the periodicity ($\Lambda$) of the unit cell for a normal incidence y-polarized illumination. All other design parameters are fixed.

Equations (23)

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x ¨ Si ( t ) + γ Si x ˙ Si ( t ) + ω Si 2 x Si ( t ) Ω 2 e i φ x Au ( t ) = f 1 ( t )
x ¨ Au ( t ) + γ Au x ˙ Au ( t ) + ω Au 2 x Au ( t ) Ω 2 e i φ x Si ( t ) = f 1 ( t )
X Si = Ω 2 + ( ω Au 2 ω 2 i ω γ Au ) ( ω Si 2 ω 2 i ω γ Si ) ( ω Au 2 ω 2 i ω γ Au ) Ω 4 f ~
X Au = Ω 2 + ( ω Si 2 ω 2 i ω γ Si ) ( ω Si 2 ω 2 i ω γ Si ) ( ω Au 2 ω 2 i ω γ Au ) Ω 4 f ~
σ e = i n s ω [ 2 Ω 2 + ( ω Au 2 ω 2 i ω γ Au ) + ( ω Si 2 ω 2 i ω γ Si ) ( ω Si 2 ω 2 i ω γ Si ) ( ω Au 2 ω 2 i ω γ Au ) Ω 4 ]
T = 2 2 + Z 0 σ e
J ( r ) = i ω ( ε p a r t i c l e ε h o s t ) E ( r )
p j = i ω v J j d v
m j = 1 2 v ( r × J ) j d v
T j ( e ) = 1 10 v [ ( J r ) r j 2 r 2 J j ] d v
T j ( 2 e ) = 1 280 v [ 3 r 4 J j 2 r 2 ( r J ) r j ] d v
T j ( m ) = i ω 20 v r 2 ( r × J ) j d v
Q ¯ ¯ j k ( e ) = i ω v [ r j J k + r k J j 2 3 δ j k ( r J ) ] d v
Q ¯ ¯ j k ( m ) = 1 3 v [ ( r × J ) j r k + ( r × J ) k r j ] d v
T ¯ ¯ j k ( Q e ) = 1 42 v [ 4 ( r J ) r j r k + 2 ( J r ) r 2 δ j k 5 r 2 ( r j J k + r k J j ) ] d v
T ¯ ¯ j k ( Q m ) = i ω 42 v r 2 [ r j ( r × J ) k + ( r × J ) j r k ] d v
P s c a t ( e ) = k 4 ε h o s t 12 π ε 0 2 c μ 0 j = 1 3 | p | j 2
P s c a t ( T e ) = k 4 ε h o s t 12 π ε 0 2 c μ 0 j = 1 3 | i k ε h o s t c T j ( e ) + i k 3 ε h o s t 2 c T j ( 2 e ) | 2
P s c a t ( m ) = k 4 ε h o s t 3 12 π ε 0 c j = 1 3 | m j + i k ε h o s t c T j ( m ) | 2
P s c a t ( Q e ) = k 6 ε h o s t 3 160 π ε 0 2 c μ 0 k = 1 3 j = 1 3 | Q ¯ ¯ j k ( e ) + i k ε h o s t c T ¯ ¯ j k ( Q e ) | 2
P s c a t ( Q m ) = k 6 ε h o s t 5 160 π ε 0 c k = 1 3 j = 1 3 | Q ¯ ¯ j k ( m ) + i k ε h o s t c T ¯ ¯ j k ( Q m ) | 2
σ s c a t = 2 μ 0 ε 0 ε h o s t P s c a t | E i n c | 2
Q s c a t = σ s c a t σ g e o m

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