Abstract

In this paper, we provide a theoretical analysis and discussion of the fundamental principles of nonlinear surface wave absorbers, in which ideal diodes are used to rectify surface currents to produce nonlinear harmonic terms including DC, and higher order modes (2f0, and 4f0, …). Interestingly, we find rectification converts most of the power to DC that can be completely absorbed by resistance in the surface, leading to advantages of nonlinear absorbers over conventional linear surface wave absorbers in both bandwidth and attenuation. We demonstrate the full-wave rectification case, and diode-rectifier-based nonlinear absorbing metasurfaces possess obvious advantages and can exceed the performance of linear absorbers, which relates the bandwidth and attenuation rate to the substrate thickness. For nonlinear metasurfaces, even with very thin substrates (for instance 0.35 mm thickness which is λ0/143 for center frequency 6 GHz), we can potentially achieve more than 60% relative bandwidth, three times of that in linear metasurfaces. To visualize the practical working mechanism, the distributed nonlinear network using ideal diode model is presented, and the full-wave simulations are demonstrated with nonlinear advantages. Differences between the theoretical case and practical case are addressed as well.

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

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  11. M. A. Lopez, M. J. Freire, M. J. Algarin, V. C. Behr, P. M. Jakob, and R. Marqués, “Nonlinear split-ring metamaterial slabs for magnetic resonance imaging,” Appl. Phys. Lett. 98(13), 133508 (2011).
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    [Crossref]
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2016 (3)

2014 (3)

S. Kim and D. Sievenpiper, “Theoretical Limitations for TM Surface Wave Attenuation by Lossy Coatings on Conducting Surfaces,” IEEE Trans. Antennas Prop. 62(1), 475–480 (2014).

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

S. Kim and D. Sievenpiper, “Theoretical Limitations for TM Surface Wave Attenuation by Lossy Coatings on Conducting Surfaces,” IEEE Trans. Antennas Prop. 62(1), 475 (2014).

2013 (2)

H. Wakatsuchi, S. Kim, J. J. Rushton, and D. F. Sievenpiper, “Waveform-Dependent Absorbing Metasurfaces,” Phys. Rev. Lett. 111(24), 245501 (2013).
[Crossref] [PubMed]

G. Dayal and S. A. Ramakrishna, “Design of multi-band metamaterial perfect absorbers with stacked metal-dielectric disk,” J. Opt. 15(5), 055106 (2013).
[Crossref]

2012 (1)

D. Sievenpiper, “Nonlinear Grounded Metasurfaces for Suppression of High-Power Pulsed RF Currents,” IEEE Antennas Wirel. Propag. Lett. 11, 1516–1519 (2012).

2011 (5)

A. R. Katko, A. M. Hawkes, J. P. Barrett, and S. A. Cummer, “RF limiter metamaterial using PIN diodes,” IEEE 10, 1571–1574 (2011).
[Crossref]

M. A. Lopez, M. J. Freire, M. J. Algarin, V. C. Behr, P. M. Jakob, and R. Marqués, “Nonlinear split-ring metamaterial slabs for magnetic resonance imaging,” Appl. Phys. Lett. 98(13), 133508 (2011).
[Crossref]

D. Sievenpiper, “Nonlinear grounded metasurfaces for suppression of high-power pulsed RF currents,” IEEE Antennas Wirel. Propag. Lett. 10, 1516–1519 (2011).
[Crossref]

X. Shen, T. J. Cui, J. Zhao, H. F. Ma, W. X. Jiang, and H. Li, “Polarization-independent wide-angle triple-band metamaterial absorber,” Opt. Express 19(10), 9401–9407 (2011).
[Crossref] [PubMed]

A. Rose and D. R. Smith, “Overcoming phase mismatch in nonlinear metamaterials,” Opt. Mater. Express 1(7), 1232 (2011).
[Crossref]

2010 (2)

H. Wakatsuchi, S. Greedy, C. Christopoulos, and J. Paul, “Customised broadband metamaterial absorbers for arbitrary polarisation,” Opt. Express 18(21), 22187–22198 (2010).
[Crossref] [PubMed]

G. Goussetis, A. P. Feresidis, and N. K. Uzunoglu, “Artificial impedance surfaces for reduced dispersion in antenna feeding systems,” IEEE Trans. Antenn. Propag. 58(11), 3629–3636 (2010).
[Crossref]

2008 (2)

2007 (1)

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: Restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40(22), 7146–7151 (2007).
[Crossref]

2006 (1)

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[Crossref] [PubMed]

2000 (1)

K. N. Rozanov, “Ultimate thickness to bandwidth ratio of radar absorbers,” IEEE Trans. Antenn. Propag. 48(8), 1230–1234 (2000).
[Crossref]

1951 (1)

S. Attwood, “Surface-wave propagation over a coated plane conductor,” J. Appl. Phys. 22(4), 504–509 (1951).
[Crossref]

Algarin, M. J.

M. A. Lopez, M. J. Freire, M. J. Algarin, V. C. Behr, P. M. Jakob, and R. Marqués, “Nonlinear split-ring metamaterial slabs for magnetic resonance imaging,” Appl. Phys. Lett. 98(13), 133508 (2011).
[Crossref]

Alù, A.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Amann, M. C.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Argyropoulos, C.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Attwood, S.

S. Attwood, “Surface-wave propagation over a coated plane conductor,” J. Appl. Phys. 22(4), 504–509 (1951).
[Crossref]

Barrett, J. P.

A. R. Katko, A. M. Hawkes, J. P. Barrett, and S. A. Cummer, “RF limiter metamaterial using PIN diodes,” IEEE 10, 1571–1574 (2011).
[Crossref]

Behr, V. C.

M. A. Lopez, M. J. Freire, M. J. Algarin, V. C. Behr, P. M. Jakob, and R. Marqués, “Nonlinear split-ring metamaterial slabs for magnetic resonance imaging,” Appl. Phys. Lett. 98(13), 133508 (2011).
[Crossref]

Belkin, M. A.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Bi, K.

Boehm, G.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Chen, P. Y.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Christopoulos, C.

Cui, T. J.

Cummer, S. A.

A. R. Katko, A. M. Hawkes, J. P. Barrett, and S. A. Cummer, “RF limiter metamaterial using PIN diodes,” IEEE 10, 1571–1574 (2011).
[Crossref]

Dayal, G.

G. Dayal and S. A. Ramakrishna, “Design of multi-band metamaterial perfect absorbers with stacked metal-dielectric disk,” J. Opt. 15(5), 055106 (2013).
[Crossref]

Decker, M.

Demmerle, F.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Enkrich, C.

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[Crossref] [PubMed]

Feresidis, A. P.

G. Goussetis, A. P. Feresidis, and N. K. Uzunoglu, “Artificial impedance surfaces for reduced dispersion in antenna feeding systems,” IEEE Trans. Antenn. Propag. 58(11), 3629–3636 (2010).
[Crossref]

Feth, N.

Freire, M. J.

M. A. Lopez, M. J. Freire, M. J. Algarin, V. C. Behr, P. M. Jakob, and R. Marqués, “Nonlinear split-ring metamaterial slabs for magnetic resonance imaging,” Appl. Phys. Lett. 98(13), 133508 (2011).
[Crossref]

Goussetis, G.

G. Goussetis, A. P. Feresidis, and N. K. Uzunoglu, “Artificial impedance surfaces for reduced dispersion in antenna feeding systems,” IEEE Trans. Antenn. Propag. 58(11), 3629–3636 (2010).
[Crossref]

Greedy, S.

Gustafsson, M.

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: Restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40(22), 7146–7151 (2007).
[Crossref]

Hawkes, A. M.

A. R. Katko, A. M. Hawkes, J. P. Barrett, and S. A. Cummer, “RF limiter metamaterial using PIN diodes,” IEEE 10, 1571–1574 (2011).
[Crossref]

Hirose, A.

Y. Luo, A. Hirose, and H. Toshiyoshi, “An Active Metamaterial Antenna With MEMS-Modulated Scanning Radiation Beams,” IEEE Electron Device Lett. 37(7), 920–923 (2016).
[Crossref]

Hoyer, W.

Jakob, P. M.

M. A. Lopez, M. J. Freire, M. J. Algarin, V. C. Behr, P. M. Jakob, and R. Marqués, “Nonlinear split-ring metamaterial slabs for magnetic resonance imaging,” Appl. Phys. Lett. 98(13), 133508 (2011).
[Crossref]

Jiang, W. X.

Katko, A. R.

A. R. Katko, A. M. Hawkes, J. P. Barrett, and S. A. Cummer, “RF limiter metamaterial using PIN diodes,” IEEE 10, 1571–1574 (2011).
[Crossref]

Kim, S.

S. Kim and D. Sievenpiper, “Theoretical Limitations for TM Surface Wave Attenuation by Lossy Coatings on Conducting Surfaces,” IEEE Trans. Antennas Prop. 62(1), 475–480 (2014).

S. Kim and D. Sievenpiper, “Theoretical Limitations for TM Surface Wave Attenuation by Lossy Coatings on Conducting Surfaces,” IEEE Trans. Antennas Prop. 62(1), 475 (2014).

H. Wakatsuchi, S. Kim, J. J. Rushton, and D. F. Sievenpiper, “Waveform-Dependent Absorbing Metasurfaces,” Phys. Rev. Lett. 111(24), 245501 (2013).
[Crossref] [PubMed]

A. Li, S. Kim, and D. Sievenpiper, “High-Power, Transistor-Based Tunable and Switchable Metasurface Absorber,” IEEE Trans. Microw. Theory Tech.in press.

Klein, M. W.

Koch, S. W.

Kristensson, G.

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: Restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40(22), 7146–7151 (2007).
[Crossref]

Lee, D.

Lee, J.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Li, A.

A. Li, S. Kim, and D. Sievenpiper, “High-Power, Transistor-Based Tunable and Switchable Metasurface Absorber,” IEEE Trans. Microw. Theory Tech.in press.

Li, B.

Li, H.

Lim, S.

Linden, S.

Liu, J.

Liu, X.

Lopez, M. A.

M. A. Lopez, M. J. Freire, M. J. Algarin, V. C. Behr, P. M. Jakob, and R. Marqués, “Nonlinear split-ring metamaterial slabs for magnetic resonance imaging,” Appl. Phys. Lett. 98(13), 133508 (2011).
[Crossref]

Lu, F.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Luo, Y.

Y. Luo, A. Hirose, and H. Toshiyoshi, “An Active Metamaterial Antenna With MEMS-Modulated Scanning Radiation Beams,” IEEE Electron Device Lett. 37(7), 920–923 (2016).
[Crossref]

Ma, H. F.

Marqués, R.

M. A. Lopez, M. J. Freire, M. J. Algarin, V. C. Behr, P. M. Jakob, and R. Marqués, “Nonlinear split-ring metamaterial slabs for magnetic resonance imaging,” Appl. Phys. Lett. 98(13), 133508 (2011).
[Crossref]

Moloney, J. V.

Niesler, F. B.

Paul, J.

Pendry, J. B.

J. B. Pendry, “Time reversal and negative refraction,” Science 322(5898), 71–73 (2008).
[Crossref] [PubMed]

Ramakrishna, S. A.

G. Dayal and S. A. Ramakrishna, “Design of multi-band metamaterial perfect absorbers with stacked metal-dielectric disk,” J. Opt. 15(5), 055106 (2013).
[Crossref]

Rose, A.

Rozanov, K. N.

K. N. Rozanov, “Ultimate thickness to bandwidth ratio of radar absorbers,” IEEE Trans. Antenn. Propag. 48(8), 1230–1234 (2000).
[Crossref]

Rushton, J. J.

H. Wakatsuchi, S. Kim, J. J. Rushton, and D. F. Sievenpiper, “Waveform-Dependent Absorbing Metasurfaces,” Phys. Rev. Lett. 111(24), 245501 (2013).
[Crossref] [PubMed]

Shen, X.

Sievenpiper, D.

S. Kim and D. Sievenpiper, “Theoretical Limitations for TM Surface Wave Attenuation by Lossy Coatings on Conducting Surfaces,” IEEE Trans. Antennas Prop. 62(1), 475–480 (2014).

S. Kim and D. Sievenpiper, “Theoretical Limitations for TM Surface Wave Attenuation by Lossy Coatings on Conducting Surfaces,” IEEE Trans. Antennas Prop. 62(1), 475 (2014).

D. Sievenpiper, “Nonlinear Grounded Metasurfaces for Suppression of High-Power Pulsed RF Currents,” IEEE Antennas Wirel. Propag. Lett. 11, 1516–1519 (2012).

D. Sievenpiper, “Nonlinear grounded metasurfaces for suppression of high-power pulsed RF currents,” IEEE Antennas Wirel. Propag. Lett. 10, 1516–1519 (2011).
[Crossref]

A. Li, S. Kim, and D. Sievenpiper, “High-Power, Transistor-Based Tunable and Switchable Metasurface Absorber,” IEEE Trans. Microw. Theory Tech.in press.

Sievenpiper, D. F.

H. Wakatsuchi, S. Kim, J. J. Rushton, and D. F. Sievenpiper, “Waveform-Dependent Absorbing Metasurfaces,” Phys. Rev. Lett. 111(24), 245501 (2013).
[Crossref] [PubMed]

Smith, D. R.

Sohl, C.

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: Restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40(22), 7146–7151 (2007).
[Crossref]

Sung, H. K.

Toshiyoshi, H.

Y. Luo, A. Hirose, and H. Toshiyoshi, “An Active Metamaterial Antenna With MEMS-Modulated Scanning Radiation Beams,” IEEE Electron Device Lett. 37(7), 920–923 (2016).
[Crossref]

Trung, N. T.

Tymchenko, M.

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Uzunoglu, N. K.

G. Goussetis, A. P. Feresidis, and N. K. Uzunoglu, “Artificial impedance surfaces for reduced dispersion in antenna feeding systems,” IEEE Trans. Antenn. Propag. 58(11), 3629–3636 (2010).
[Crossref]

Wakatsuchi, H.

H. Wakatsuchi, S. Kim, J. J. Rushton, and D. F. Sievenpiper, “Waveform-Dependent Absorbing Metasurfaces,” Phys. Rev. Lett. 111(24), 245501 (2013).
[Crossref] [PubMed]

H. Wakatsuchi, S. Greedy, C. Christopoulos, and J. Paul, “Customised broadband metamaterial absorbers for arbitrary polarisation,” Opt. Express 18(21), 22187–22198 (2010).
[Crossref] [PubMed]

Wegener, M.

Zeng, Y.

Zhao, J.

Zhao, Q.

Zhou, J.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. A. Lopez, M. J. Freire, M. J. Algarin, V. C. Behr, P. M. Jakob, and R. Marqués, “Nonlinear split-ring metamaterial slabs for magnetic resonance imaging,” Appl. Phys. Lett. 98(13), 133508 (2011).
[Crossref]

IEEE (1)

A. R. Katko, A. M. Hawkes, J. P. Barrett, and S. A. Cummer, “RF limiter metamaterial using PIN diodes,” IEEE 10, 1571–1574 (2011).
[Crossref]

IEEE Antennas Wirel. Propag. Lett. (2)

D. Sievenpiper, “Nonlinear grounded metasurfaces for suppression of high-power pulsed RF currents,” IEEE Antennas Wirel. Propag. Lett. 10, 1516–1519 (2011).
[Crossref]

D. Sievenpiper, “Nonlinear Grounded Metasurfaces for Suppression of High-Power Pulsed RF Currents,” IEEE Antennas Wirel. Propag. Lett. 11, 1516–1519 (2012).

IEEE Electron Device Lett. (1)

Y. Luo, A. Hirose, and H. Toshiyoshi, “An Active Metamaterial Antenna With MEMS-Modulated Scanning Radiation Beams,” IEEE Electron Device Lett. 37(7), 920–923 (2016).
[Crossref]

IEEE Trans. Antenn. Propag. (2)

K. N. Rozanov, “Ultimate thickness to bandwidth ratio of radar absorbers,” IEEE Trans. Antenn. Propag. 48(8), 1230–1234 (2000).
[Crossref]

G. Goussetis, A. P. Feresidis, and N. K. Uzunoglu, “Artificial impedance surfaces for reduced dispersion in antenna feeding systems,” IEEE Trans. Antenn. Propag. 58(11), 3629–3636 (2010).
[Crossref]

IEEE Trans. Antennas Prop. (2)

S. Kim and D. Sievenpiper, “Theoretical Limitations for TM Surface Wave Attenuation by Lossy Coatings on Conducting Surfaces,” IEEE Trans. Antennas Prop. 62(1), 475 (2014).

S. Kim and D. Sievenpiper, “Theoretical Limitations for TM Surface Wave Attenuation by Lossy Coatings on Conducting Surfaces,” IEEE Trans. Antennas Prop. 62(1), 475–480 (2014).

J. Appl. Phys. (1)

S. Attwood, “Surface-wave propagation over a coated plane conductor,” J. Appl. Phys. 22(4), 504–509 (1951).
[Crossref]

J. Opt. (1)

G. Dayal and S. A. Ramakrishna, “Design of multi-band metamaterial perfect absorbers with stacked metal-dielectric disk,” J. Opt. 15(5), 055106 (2013).
[Crossref]

J. Phys. D (1)

C. Sohl, M. Gustafsson, and G. Kristensson, “Physical limitations on metamaterials: Restrictions on scattering and absorption over a frequency interval,” J. Phys. D 40(22), 7146–7151 (2007).
[Crossref]

Nature (1)

J. Lee, M. Tymchenko, C. Argyropoulos, P. Y. Chen, F. Lu, F. Demmerle, G. Boehm, M. C. Amann, A. Alù, and M. A. Belkin, “Giant nonlinear response from plasmonic metasurfaces coupled to intersubband transitions,” Nature 511(7507), 65–69 (2014).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. Lett. (1)

H. Wakatsuchi, S. Kim, J. J. Rushton, and D. F. Sievenpiper, “Waveform-Dependent Absorbing Metasurfaces,” Phys. Rev. Lett. 111(24), 245501 (2013).
[Crossref] [PubMed]

Science (2)

J. B. Pendry, “Time reversal and negative refraction,” Science 322(5898), 71–73 (2008).
[Crossref] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006).
[Crossref] [PubMed]

Other (3)

A. Li, S. Kim, and D. Sievenpiper, “High-Power, Transistor-Based Tunable and Switchable Metasurface Absorber,” IEEE Trans. Microw. Theory Tech.in press.

C. A. Balanis, Modern Antenna Handbook (John Wiley & Sons Inc, 2008).

R. E. Collin, Foundations for Microwave Engineering (John Wiley & Sons Inc, 2001).

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Figures (9)

Fig. 1
Fig. 1

(a) The concept of the nonlinear metesurface by assuming ideal diodes embedded in the top RC sheet to rectify induced currents to produce nonlinear harmonics including DC, 2f0 term, and 4f0 term. (b) Full-wave rectification case, in which a large proportion of power is converted to DC, and the DC term is confined and absorbed by the RC sheet. (c) The Fourier transform of full-wave rectification, which determines magnitude coefficient of nonlinear terms.

Fig. 2
Fig. 2

Side view of the three channels which contain nonlinear terms. When rectifying, the Fourier Transform determines magnitude coefficient of each nonlinear term, and each mode is self-consistent by matching the boundary conditions above/below the parallel RC sheet [22,23].

Fig. 3
Fig. 3

For all figures, linear and nonlinear absorbers have these parameters: ϵ2 = 3, tanδ = 0.0013, µ2 = 1, thickness = 1.524 mm, R = 377 Ω/Square, C = 2.5/4 Pf/Square (for nonlinear case), C = 2.5 Pf/Square (for linear case) and air box is infinite. Variable parameters are indicated in each figure. (a) Different capacitance values of RC sheet lead to different resonant frequencies, and nonlinear advantages show good frequency flexibility. (b) Different resistance values of the RC sheet lead to different attenuation magnitudes, and nonlinear advantages show good resistance flexibility.

Fig. 4
Fig. 4

For all figures, the nonlinear absorber has these parameters: ϵ2 = 3, tanδ = 0.0013, µ2 = 1, thickness a = 1.524 mm, C = 2.5 Pf/Square for linear metasurfaces, C = 2.5/4 Pf/Square for nonlinear metasurfaces, and air box is infinite. Resistance value is the variable parameter that is indicated in each figure. (a) & (b) the nonlinear advantages in magnitude and bandwidth with resistance R as the variable parameter. The attenuation bandwidth is calculated as the 3 dB normalized power loss (1-e-2αz where α is the attenuation, and z is the distance).

Fig. 5
Fig. 5

For all figures, the nonlinear absorber has these parameters: ϵ2 = 3, tanδ = 0.0013, µ2 = 1, R = 377 Ω/Square, C = 2.5 Pf/Square for linear metasurfaces, C = 2.5/4 Pf/Square for nonlinear metasurfaces, and air box is infinite. Thickness a is the variable parameter that is indicated in each figure. (a) & (b) with different substrate thickness, nonlinear absorbing metasurfaces demonstrate significant advantages in attenuation and the relative bandwidth.

Fig. 6
Fig. 6

(a) Multiple peaks exist in the nonlinear metasurface, while linear case has single peak. It is because rectification produces nonlinear terms and the nonlinearity leads to multi-resonance. (b) shows an example by comparing the power concentration (including in air and substrate) of linear and nonlinear case, and two bottoms are marked that leads to the two peaks, while in linear case, there is only one. (c) First frequency bands of thin nonlinear metasurfaces.

Fig. 7
Fig. 7

The layout of diode-rectifier-based nonlinear network. (a) & (b) are the unit cells of periodical metasurfaces. We use the layout of (b) as the full-wave simulation model with the dimension are as: a = 7.6 mm, b = 4.7 mm, c = 30.85 mm, d = 4.5 mm, f = 3.1 mm, and other parameters are set as: ϵ2 = 3, tanδ = 0.0013, µ2 = 1, R = 377 Ω/Square, C = 2.5 Pf/Square (for E, G), and C = 2.5/4 Pf/Square (for F). The air box is 25 mm height. With full-wave simulations, (c) demonstrates the nonlinear advantages in all of the resonances.

Fig. 8
Fig. 8

Nonlinear advantages are demonstrated in both attenuation (a) & (c) and bandwidth (b) & (d). Comparisons include theoretical analysis in both linear and nonlinear case, full-wave simulation with uniform pattern and periodical pattern (as Fig. 6(b)), and the nonlinear full-wave simulation using periodical pattern as Fig. 6(b). The parameters are the same as in Fig. 7, and the air box height is kept as 25 mm when the substrate thickness is increased.

Fig. 9
Fig. 9

To implement full-wave nonlinear simulations, periodic pattern is used due to it is compatible to insert diodes in the split gaps. With full-wave simulation, as shown in (a), the difference of periodic-pattern-based and uniform-pattern-based metasurface is that periodic case has higher attenuation magnitude but decreased bandwidth. (b)Compared with using ideal diode model, using real diode model in the simulation shifts down the resonant frequency, decreases the attenuation magnitude and expands the bandwidth.

Tables (1)

Tables Icon

Table 1 The power proportion and spatial distribution of nonlinear and linear absorbing metasurfaces

Equations (23)

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| sin( ωt ) |= 2 π 4 π n=2,4,6 cos( nωt ) n 2 1 ,
P sub NL ( f 0 )= n=1 P sub ' ( 2n f 0 ) P sub ' ( 2 f 0 )+ P sub ' ( 4 f 0 ),
P SubL = K Z 2 1 4 k 2 β ω ε 2 [ k 2 a+ 1 2 sin( 2 k 2 a ) ],
K Z = H X2 | y=0 =A ω ε 2 k 2 ,
K SZ = ( H X3 H X2 )| y=a =A ω ε 3 k 3 sin( k 2 a )+A ω ε 2 k 2 cos( k 2 a )
K Z = K SZ [ cos( k 2 a ) ε 3 ε 2 k 2 k 3 sin( k 2 a ) ] .
P SubL = K SZ 2 [ cos( k 2 a ) ε 3 ε 2 k 2 k 3 sin( k 2 a ) ] 2 1 4 k 2 β ω ε 2 [ k 2 a+ 1 2 sin( 2 k 2 a ) ].
P sub ' ( n f 0 )= A n f 0 K SZ 2 [ cos( k 2_n f 0 a ) ε 3 ε 2 k 2_n f 0 k 3_n f 0 sin( k 2_n f 0 a ) ] 2 1 4 k 2_n f 0 β n f 0 ( nω ) ε 2 [ k 2_n f 0 a+ 1 2 sin( 2 k 2_n f 0 a ) ],
P air NL ( f 0 ) P air ' ( 2 f 0 )+ P air ' ( 4 f 0 ),
P air ' ( n f 0 )= A n f 0 K SZ 2 [ cos( k 2_n f 0 a ) ε 3 ε 2 k 2_n f 0 k 3_n f 0 sin( k 2_n f 0 a ) ] 2 1 4 ε 3 ε 2 k 2_n f 0 2 k 3_n f 0 3 β n f 0 ( nω ) ε 2 sin 2 ( k 2_n f 0 a ),
P airL = K Z 2 1 4 ε 3 ε 2 k 2 2 k 3 3 β ω ε 2 sin 2 ( k 2 a ).
P sub_loss NL ( f 0 ) P sub_loss ' ( 2 f 0 )+ P sub_loss ' ( 4 f 0 ),
P sub_loss ' ( n f 0 )= A n f 0 K SZ 2 [ cos( k 2_n f 0 a ) ε 3 ε 2 k 2_n f 0 sin( k 2_n f 0 a ) k 3_n f 0 ] 2 ( nω )ε" 4 ( nωε ) 2 [ ( β n f 0 2 + k 2_n f 0 2 )a+ ( β n f 0 2 k 2_n f 0 2 )sin( 2 k 2_n f 0 a ) 2 k 2_n f 0 ],
P Sub_lossL = K Z 2 ωε" 4 ( ωε ) 2 [ ( β 2 + k 2 2 )a+ ( β 2 k 2 2 )sin( 2 k 2 a ) 2 k 2 ].
P Sheet_Loss L = 1 2R E Z2 2 | y=a = 1 2R K SZ 2 [ cos( k 2 a ) ε 3 ε 2 k 2 k 3 sin( k 2 a ) ] 2 ( k 2 ω ε 2 sin( k 2 a ) ) 2 ,
P Sheet_Loss NL = P Sheet_Loss ' ( DC )+ P Sheet_Loss ' ( 2 f 0 )+ P Sheet_Loss ' ( 4 f 0 ),
P Sheet_Loss ' ( DC )= 1 R A DC K SZ 2 [ cos( k 2 a ) ε 3 ε 2 k 2 k 3 sin( k 2 a ) ] 2 ( k 2 ω ε 2 sin( k 2 a ) ) 2 ,
P Sheet_Loss ' ( n f 0 )= 1 2R A n f 0 K SZ 2 [ cos( k 2_n f 0 a ) ε 3 ε 2 k 2_n f 0 k 3_n f 0 sin( k 2_n f 0 a ) ] 2 ( k 2_n f 0 ( nω ) ε 2 sin( k 2_n f 0 a ) ) 2 ,
α NL = P Sub_Loss NL + P Sheet_Loss NL 2( P air NL + P sub NL ) ,
α L = P Sub_Loss L + P Sheet_Loss L 2( P air L + P sub L ) ,
β 2 f 0 2 = ( 2ω ) 2 ε 2 μ 2 k 2_2 f 0 2 ,
k 3_2 f 0 2 = ( 2ω ) 2 ε 3 μ 3 β 2 f 0 2 .
k 2_2 f 0 2 + ( ( 2ω ) ε 3 ( 2ω ) ε 2 k 2_2 f 0 cot( a k 2_2 f 0 )( ( 2ω )C+ 1 R 2 ( 2ω )C ) ) 2 = ( 2ω ) 2 ( ε 2 μ 2 ε 3 μ 3 ).