Abstract

The concept of metamaterial-inspired nanocircuits, dubbed metatronics, was introduced in [Science 317, 1698 (2007); Phys. Rev. Lett. 95, 095504 (2005)]. It was suggested how optical lumped elements (nanoelements) can be made using subwavelength plasmonic or non-plasmonic particles. As a result, the optical metatronic equivalents of a number of electronic circuits, such as frequency mixers and filters, were suggested. In this work we further expand the concept of electronic lumped element networks into optical metatronic circuits and suggest a conceptual model applicable to various metatronic passive networks. In particular, we differentiate between the series and parallel networks using epsilon-near-zero (ENZ) and mu-near-zero (MNZ) materials. We employ layered structures with subwavelength thicknesses for the nanoelements as the building blocks of collections of metatronic networks. Furthermore, we explore how by choosing the non-zero constitutive parameters of the materials with specific dispersions, either Drude or Lorentzian dispersion with suitable parameters, capacitive and inductive responses can be achieved in both series and parallel networks. Next, we proceed with the one-to-one analogy between electronic circuits and optical metatronic filter layered networks and justify our analogies by comparing the frequency response of the two paradigms. Finally, we examine the material dispersion of near-zero relative permittivity as well as other physically important material considerations such as losses.

© 2014 Optical Society of America

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References

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  1. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
    [Crossref] [PubMed]
  2. A. Alu, A. Salandrino, and N. Engheta, “Parallel, series, and intermediate interconnections of optical nanocircuit elements: Nanocircuit and physical interpretation,” J. Opt. Soc. Am. B 24, 3014–3022 (2007).
    [Crossref]
  3. N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
    [Crossref] [PubMed]
  4. H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
    [Crossref] [PubMed]
  5. Y. Sun, B. Edwards, A. Alu, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11, 208–212 (2012).
    [Crossref] [PubMed]
  6. H. Liu and K. J. Webb, “Optical circuits from anisotropic films,” Phys. Rev. B 79, 094203 (2009).
    [Crossref]
  7. A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photon. 2, 307–310 (2008).
    [Crossref]
  8. A. Alu and N. Engheta, “All optical metamaterial circuit board at nanoscale,” Phys. Rev. Lett. 103, 143902 (2009).
    [Crossref]
  9. U. K. Chettiar and N. Engheta, “Optical frequency mixing through nanoantenna enhanced difference frequency generation: Metatronic mixer,” Phys. Rev. B 86, 075405 (2012).
    [Crossref]
  10. A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
    [Crossref]
  11. D. M. Pozar, Microwave Engineering (John Wiley, 2009).
  12. D. M. Pozar, Microwave and RF Design of Wireless Systems (John Wiley, 2000).
  13. W. R. Smythe, Electrostatics and Electrodynamics (McGraw-Hill, 1950).
  14. H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
    [Crossref] [PubMed]
  15. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998)
  16. A. H. Sihvola, Electromagnetic Mixing Formulas and Applications, IEEE Electromagnetic Waves Series (IEEE, 1999), Vol. 47.
    [Crossref]

2013 (2)

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

2012 (2)

Y. Sun, B. Edwards, A. Alu, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11, 208–212 (2012).
[Crossref] [PubMed]

U. K. Chettiar and N. Engheta, “Optical frequency mixing through nanoantenna enhanced difference frequency generation: Metatronic mixer,” Phys. Rev. B 86, 075405 (2012).
[Crossref]

2009 (2)

H. Liu and K. J. Webb, “Optical circuits from anisotropic films,” Phys. Rev. B 79, 094203 (2009).
[Crossref]

A. Alu and N. Engheta, “All optical metamaterial circuit board at nanoscale,” Phys. Rev. Lett. 103, 143902 (2009).
[Crossref]

2008 (2)

A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photon. 2, 307–310 (2008).
[Crossref]

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[Crossref]

2007 (2)

2005 (1)

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref] [PubMed]

Alu, A.

Y. Sun, B. Edwards, A. Alu, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11, 208–212 (2012).
[Crossref] [PubMed]

A. Alu and N. Engheta, “All optical metamaterial circuit board at nanoscale,” Phys. Rev. Lett. 103, 143902 (2009).
[Crossref]

A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photon. 2, 307–310 (2008).
[Crossref]

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[Crossref]

A. Alu, A. Salandrino, and N. Engheta, “Parallel, series, and intermediate interconnections of optical nanocircuit elements: Nanocircuit and physical interpretation,” J. Opt. Soc. Am. B 24, 3014–3022 (2007).
[Crossref]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref] [PubMed]

Caglayan, H.

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

Chettiar, U. K.

U. K. Chettiar and N. Engheta, “Optical frequency mixing through nanoantenna enhanced difference frequency generation: Metatronic mixer,” Phys. Rev. B 86, 075405 (2012).
[Crossref]

Edwards, B.

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

Y. Sun, B. Edwards, A. Alu, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11, 208–212 (2012).
[Crossref] [PubMed]

Engheta, N.

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

Y. Sun, B. Edwards, A. Alu, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11, 208–212 (2012).
[Crossref] [PubMed]

U. K. Chettiar and N. Engheta, “Optical frequency mixing through nanoantenna enhanced difference frequency generation: Metatronic mixer,” Phys. Rev. B 86, 075405 (2012).
[Crossref]

A. Alu and N. Engheta, “All optical metamaterial circuit board at nanoscale,” Phys. Rev. Lett. 103, 143902 (2009).
[Crossref]

A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photon. 2, 307–310 (2008).
[Crossref]

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[Crossref]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref] [PubMed]

A. Alu, A. Salandrino, and N. Engheta, “Parallel, series, and intermediate interconnections of optical nanocircuit elements: Nanocircuit and physical interpretation,” J. Opt. Soc. Am. B 24, 3014–3022 (2007).
[Crossref]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref] [PubMed]

Hong, S. H.

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

Kagan, C. R.

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

Liu, H.

H. Liu and K. J. Webb, “Optical circuits from anisotropic films,” Phys. Rev. B 79, 094203 (2009).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998)

Pozar, D. M.

D. M. Pozar, Microwave Engineering (John Wiley, 2009).

D. M. Pozar, Microwave and RF Design of Wireless Systems (John Wiley, 2000).

Salandrino, A.

A. Alu, A. Salandrino, and N. Engheta, “Parallel, series, and intermediate interconnections of optical nanocircuit elements: Nanocircuit and physical interpretation,” J. Opt. Soc. Am. B 24, 3014–3022 (2007).
[Crossref]

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref] [PubMed]

Sihvola, A. H.

A. H. Sihvola, Electromagnetic Mixing Formulas and Applications, IEEE Electromagnetic Waves Series (IEEE, 1999), Vol. 47.
[Crossref]

Smythe, W. R.

W. R. Smythe, Electrostatics and Electrodynamics (McGraw-Hill, 1950).

Sun, Y.

Y. Sun, B. Edwards, A. Alu, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11, 208–212 (2012).
[Crossref] [PubMed]

Webb, K. J.

H. Liu and K. J. Webb, “Optical circuits from anisotropic films,” Phys. Rev. B 79, 094203 (2009).
[Crossref]

Young, M. E.

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Mater. (1)

Y. Sun, B. Edwards, A. Alu, and N. Engheta, “Experimental realization of optical lumped nanocircuits at infrared wavelengths,” Nat. Mater. 11, 208–212 (2012).
[Crossref] [PubMed]

Nat. Photon. (1)

A. Alu and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photon. 2, 307–310 (2008).
[Crossref]

Phys. Rev. B (3)

H. Liu and K. J. Webb, “Optical circuits from anisotropic films,” Phys. Rev. B 79, 094203 (2009).
[Crossref]

U. K. Chettiar and N. Engheta, “Optical frequency mixing through nanoantenna enhanced difference frequency generation: Metatronic mixer,” Phys. Rev. B 86, 075405 (2012).
[Crossref]

A. Alu, M. E. Young, and N. Engheta, “Design of nanofilters for optical nanocircuits,” Phys. Rev. B 77, 144107 (2008).
[Crossref]

Phys. Rev. Lett. (4)

N. Engheta, A. Salandrino, and A. Alu, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95, 095504 (2005).
[Crossref] [PubMed]

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

A. Alu and N. Engheta, “All optical metamaterial circuit board at nanoscale,” Phys. Rev. Lett. 103, 143902 (2009).
[Crossref]

H. Caglayan, S. H. Hong, B. Edwards, C. R. Kagan, and N. Engheta, “Near-infrared metatronic nanocircuits by design,” Phys. Rev. Lett. 111, 073904 (2013).
[Crossref] [PubMed]

Science (1)

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref] [PubMed]

Other (5)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998)

A. H. Sihvola, Electromagnetic Mixing Formulas and Applications, IEEE Electromagnetic Waves Series (IEEE, 1999), Vol. 47.
[Crossref]

D. M. Pozar, Microwave Engineering (John Wiley, 2009).

D. M. Pozar, Microwave and RF Design of Wireless Systems (John Wiley, 2000).

W. R. Smythe, Electrostatics and Electrodynamics (McGraw-Hill, 1950).

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Figures (7)

Fig. 1
Fig. 1 Two-port networks: a) and b) A parallel electronic element and its metatronic equivalent, utilizing a mu-near-zero (MNZ) slab. c) and d) A series electronic element and its metatronic equivalent with an epsilon-near-zero (ENZ) slab. The slabs are infinitely extent in the x and y directions, while they have finite subwavelength thickness in the z direction.
Fig. 2
Fig. 2 Schematic of metatronic slab elements for lossless linear passive two-port networks consisting of a single element utilizing the layered topology. The slabs are infinitely extent in the x and y directions, while they have finite subwavelength thickness in the z direction.
Fig. 3
Fig. 3 a) Bandstop filter using parallel inductor-capacitor (LC) circuit connected in series configuration and its equivalent metatronic arrangement. b) Transmittance of electronic (green curve, analytical) and metatronic (blue curve, simulation) filter. The structure is periodically extent in the x and y directions.
Fig. 4
Fig. 4 Basic bandstop and bandpass filters for optical metatronic filter networks. Colors of blocks consistent with Fig. 2. The structure is periodically extent in the x and y directions.
Fig. 5
Fig. 5 Fifth-order maximally flat metatronic filter. a) Electronic circuit and its equivalent optical metatronic layered network. b) Transmittance of the electronic (green cruve, analytical method) and metatronic (blue curve, simulation) circuits. The structure is periodically extent in the x and y directions.
Fig. 6
Fig. 6 Repeating the simulation of the circuit in Fig. 3, except here the near-zero permittivity of the two layers follows the Drude dispersion. The dispersion of the near-zero permittivity is shown in the inset.
Fig. 7
Fig. 7 a) A bandstop filter consisting of two LC stages and its equivalent optical metatronic circuit using Drude-type metal and Silicon. b) The transmittance of the electronic (green curve, analytical method) and metatronic (blue curve, simulation) circuits. The structure is periodically extent in the x and y directions.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

A B C D = [ cos ( β l ) i Z 0 sin ( β l ) i Z 0 sin ( β l ) cos ( β l ) ]
A B C D [ 1 i ω μ l i ω ε l 1 ]
A B C D [ 1 0 i ω ε l 1 ] .
A B C D = [ 1 0 Y 1 ]
A B C D [ 1 i ω μ l 0 1 ]
A B C D = [ 1 Z 0 1 ] .
d H d z = i ω ε 0 ε r E
Δ H = i ω ε r ε 0 l E .
C = ε r ε 0 l .
E = i ω 1 ε 0 ω p 2 l Δ H .
L = 1 ε 0 ω p 2 l .
Δ E = i ω μ r μ 0 l H
H = i ω 1 ω p 2 μ 0 l Δ E
L = μ r μ 0 l
C = 1 ω p 2 μ 0 l .

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