## Nanoparticle array based optical frequency selective surfaces: theory and design |

Optics Express, Vol. 21, Issue 13, pp. 16170-16180 (2013)

http://dx.doi.org/10.1364/OE.21.016170

Acrobat PDF (1230 KB)

### Abstract

We demonstrate a synthesis procedure for designing a bandstop optical frequency selective surface (FSS) composed of nanoparticle (NP) elements. The proposed FSS uses two-dimensional (2-D) periodic arrays of NPs with subwavelength unit-cell dimensions. We derive equivalent circuit for a nanoparticle array (NPA) using the closed-form solution for a 2-D NPA excited by a plane wave in the limit of the dipole approximation, which includes contribution from both individual and collective plasmon modes. Using the extracted equivalent circuit, we demonstrate synthesis of an optical FSS using cascaded NPA layers as coupled resonators, which we validate with both circuit model and full-wave simulation for a third-order Butterworth bandstop prototype.

© 2013 OSA

## 1. Introduction

3. M. Al-Joumayly and N. Behdad, “A new technique for design of low-profile, second-order, bandpass frequency selective surfaces,” IEEE Trans. Antennas and Propagat. **57**, 452–459 (2009) [CrossRef] .

4. S. Gupta, G. Tuttle, M. Sigalas, and K. M. Ho, “Infrared filters using metallic photonic band gap structures on flexible substrates,” Appl. Phys. Lett. **71**, 2412–2414 (1997) [CrossRef] .

5. H. A. Smith, M. Rebbert, and O. Sternberg, “Designer infrared filters using stacked metal lattices,” Appl. Phys. Lett. **82**, 3605–3607 (2003) [CrossRef] .

6. J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. P. Drupp, and L. Li, “The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications,” IEEE Trans. Antennas and Propagat. **54**, 1265–1276 (2006) [CrossRef] .

7. Y. Tang, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer metallodielectric nanostructures as dual-band midinfrared filters,” Appl. Phys. Lett. **92**, 263106 (2008) [CrossRef] .

8. S. Govindaswamy, J. East, F. Terry, E. Topsakal, J. L. Volakis, and G. I. Haddad, “Frequency-selective surface based bandpass filters in the near-infrared region,” Microw. Opt. Technol. Lett. **41**, 266–269 (2004) [CrossRef] .

9. D. Van Labeke, D. Grard, B. Guizal, F. I. Baida, and L. Li, “An angle-independent Frequency Selective Surface in the optical range,” Opt. Express **14**, 11945–11951 (2006) [CrossRef] [PubMed] .

10. G. Si, Y. Zhao, H. Liu, S. Teo, M. Zhang, T. J. Huang, A. J. Danner, and J. Teng, “Annular aperture array based color filter,” Appl. Phys. Lett. **99**, 033105 (2011) [CrossRef] .

11. J. Zhang, J. Y. Ou, N. Papasimakis, Y. Chen, K. F. MacDonald, and N. I. Zheludev, “Continuous metal plasmonic frequency selective surfaces,” Opt. Express **19**, 23279–23285 (2011) [CrossRef] [PubMed] .

13. A. Monti, F. Bilotti, A. Toscano, and L. Vegni, “Possible implementation of epsilon-near-zero metamaterials working at optical frequencies,” Opt. Commun. **285**, 3412–3418 (2012) [CrossRef] .

14. A. Di Falco, Y. Zhao, and A. Alu, “Optical metasurfaces with robust angular response on flexible substrates,” Appl. Phys. Lett. **99**, 163110 (2011) [CrossRef] .

15. P. C. Li and E. T. Yu, “Wide-angle wavelength-selective multilayer optical
metasurfaces robust to interlayer misalignment,” J. Opt. Soc. Am.
B **30**, 27–32 (2013) [CrossRef] .

17. B. Memarzadeh and H. Mosallaei, “Layered plasmonic tripods: an infrared frequency selective
surface nanofilter,” J. Opt. Soc. Am. B **29**, 2347–2351 (2012) [CrossRef] .

*ab-initio*design procedure. Instead, they involve identifying the configuration under study, and the extracted characteristics are shown to be a consequence of certain features associated with plasmonic resonances and interaction of light with the structure. Formalizing the wave/configuration interaction, defining the input and output, and specifying its functional behavior by means of equations, one can follow a synthesis procedure to obtain configuration parameters for a required functional behavior. With the goal of formulating the problem to achieve a synthesis method, we choose NPAs whose theory has been extensively studied [18

18. A. Alu and N. Engheta, “Optical wave interaction with two-dimensional arrays of plasmonic nanoparticles,” in *Structured Surfaces as Optical Metamaterials*, A. A. Maradudin, ed. (Cambridge University, 2011), pp. 58–93 [CrossRef] .

18. A. Alu and N. Engheta, “Optical wave interaction with two-dimensional arrays of plasmonic nanoparticles,” in *Structured Surfaces as Optical Metamaterials*, A. A. Maradudin, ed. (Cambridge University, 2011), pp. 58–93 [CrossRef] .

18. A. Alu and N. Engheta, “Optical wave interaction with two-dimensional arrays of plasmonic nanoparticles,” in *Structured Surfaces as Optical Metamaterials*, A. A. Maradudin, ed. (Cambridge University, 2011), pp. 58–93 [CrossRef] .

## 2. Modeling and parameter extraction for an NPA

20. A. S. Kumbhar, M. K Kinnan, and G. Chumanov, “Multipole plasmon resonances of submicron silver particles,” J. Am. Chem. Soc. **127**, 12444–12445 (2005) [CrossRef] [PubMed] .

*a*×

*a*and is excited by a normally-incident plane wave propagating along z direction and assuming the plane of incidence be

*x*= 0 electric field is polarized along one of the transverse directions (

*E*for TE and

_{x}*E*for TM polarization). One approach to evaluate the properties of the NPA is by assuming that an NP can be described by a polarizability

_{y}*α*that relates induced dipole moment

*P*to the local electric field

*E*by

_{loc}*P*=

*ε*

_{0}

*α*

*E*(

_{loc}*α*is in the direction of the applied field). Since the local field is superposition of applied field

*E*

_{0}and interaction field

*E*, and the interaction field is itself proportional to the dipole moment by means of an interaction constant

_{int}*β*(for normally-incident plane wave

*β*is the same for both TE and TM polarizations) as

*E*=

_{int}*βP/ε*

_{0}, self-consistent solution gives the equation for dipole moment as

*Structured Surfaces as Optical Metamaterials*, A. A. Maradudin, ed. (Cambridge University, 2011), pp. 58–93 [CrossRef] .

21. W. H. Eggimann and R. E. Collin, “Dynamic interaction fields in a two-dimensional lattice,” IEEE Trans. Microwave Theory Tech. **9**, 110–115 (1961) [CrossRef] .

23. Y. R. Zhen, K. H. Fung, and C. T. Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B **78**, 035419 (2008) [CrossRef] .

*a*

^{2}) from which the reflection and transmission coefficients can be conveniently found [18

*Structured Surfaces as Optical Metamaterials*, A. A. Maradudin, ed. (Cambridge University, 2011), pp. 58–93 [CrossRef] .

*k*is the free-space wave number. Note that the impedance is normalized to the characteristic impedance of the transmission line that equals the wave impedance of the medium in which the NPA is located. For normally-incident plane waves, this is simply the wave impedance

*η*.

*Z*can be written in real and imaginary parts indicating reactive and resistive components of the impedance respectively:

*α*

^{−1}−

*β*} can be found exactly from the energy conservation principle [19]: which by substituting it in

*R*in Eq. (2) yields zero, which is expected for the lossless case. For the reactive part of the impedance we use the closed-form of Maslovski and Tretyakov’s interaction constant for normal incidence of transverse plane waves in the limit where the distance between the particles is much smaller than the wavelength: where

*R*

_{0}/

*c*where

*c*is the speed of light. The first term in the reactive part of Eq. (2) can be thought of as the NP-in-array (NIA) impedance defined as

*α*. We can find a static field solution for the dipole moments of small ellipsoid- and sphere-shaped NPs readily. According to Stratton’s approach [24], the dipole polarizability of an ellipsoid of permittivity

*ε*with semiaxes

*l*

_{1},

*l*

_{2}, and

*l*

_{3}when a uniform field is applied along the

*l*axis, is where

_{i}*V*is the volume of the NP,

*ε*is the permittivity of the host medium, and

_{h}*L*is is the depolarization factor in the

_{i}*i*direction defined in [24] (

*i*subscript indicates the same direction as

*α*and we drop it for simplicity from here on). Here we use a modified Drude model to describe the complex dielectric function of dispersive materials given by: with the high-frequency limit of

*ε*,

_{a}*ε*the static dielectric constant, and

_{b}*ω*plasmon resonance frequency. Values

_{p}*ε*= 5.45,

_{a}*ε*= 6.18, and

_{b}*ω*= 1.7 × 10

_{p}^{16}

*rad/s*are extracted from fitting with experimental data for silver [25

25. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**, 4370 (1972) [CrossRef] .

26. P. G. Kik, A. Maier, and H. A. Atwater, “Image resolution of surface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources,” Phys. Rev. B **69**, 045418 (2004) [CrossRef] .

27. J. J. Xiao, J. P. Huang, and K. W. Yu, “Optical response of strongly coupled metal nanoparticles in dimer arrays,” Phys. Rev. B **71**, 045404 (2005) [CrossRef] .

*X*equation we describe the average NP reactance: where

^{NIA}*C*

_{2}as and from

*ω*

_{1}and

*ω*

_{2}, we get

*L*

_{1}and

*C*

_{1}as

*X*in Eq. (2), the final equivalent circuit representing the NPA can be configured as shown in the left side of transformation in Fig. 2(b), where

*C*

_{3}= −1/ (

*ω*

*X*) ≃ −

^{lattice}*a*/0.36

*c*. As it can be inferred, the equivalent circuit derived here stands valid for both TE and TM polarization, and the only parameter that changes switching between polarizations is the depolarization factor in Eq. (6).

*n*= 1.55). Figure 3 shows the frequency response for three different cases. In the optical range of frequency there is a good agreement except for less attenuation in the stop-band and broadening both due to dissipation loss. Besides the predicted peak for the reflection, it has a zero out of the optical range, which the circuit model fails to predict correctly. This is where the permittivity of the metal equals the permittivity of host medium (around 2.4). From Fig. 1 the Drude model reaches this point around 1350 THz; for the experimental curve, the closest it can get to 2.4 is around 950 THz, although beyond 800 THz is not of interest. In the transformed circuit in Fig. 2(b), the parallel capacitor

*C*in conjunction with the resonator is responsible for the null in the reflection response, which is not in of interest for our bandstop filter design procedure. Moreover, as seen in Fig. 3, ignoring this capacitor has negligible effect on the bandstop behavior of the circuit.

_{p}## 3. FSS design

### 3.1. Principles of operation

*ω*) of an NPA can be found considering the series

_{CPR}*LC*resonator in the equivalent circuit which in case of spherical NPs with

*L*= 1/3 (insensitive to polarization) it can be more simplified to where

*F*is the filling factor defined as

*r*=

*Fa*. knowing the host medium, the resonance frequency of the NPA is only a function of

*F*. Figure 4 shows the corresponding collective plasmon resonance frequencies achievable using different host media of air, S-FPL, silica, sapphire, P-SF68, ZrO2 with refractive indexes of 1, 1.42, 1.55, 1.77, 2.01, 2.21 respectively. Using different materials and optical glasses that are available provides a range of refractive index over which the whole optical frequency range can be swept. The lowest limit of

*F*is selected such that at least 9 dB attenuation in the stop-band can be achieved for a single layer of NPA. The highest limit for

*F*is set to avoid emerging higher order plasmon modes which cause red-shift in the dipole resonance location and add significant complexity. Although for an isolated NP emerging higher multipoles is only function of NP size [20

20. A. S. Kumbhar, M. K Kinnan, and G. Chumanov, “Multipole plasmon resonances of submicron silver particles,” J. Am. Chem. Soc. **127**, 12444–12445 (2005) [CrossRef] [PubMed] .

*F*> 0.45. This limit can be as low as 0.35 for higher angles of incidence.

### 3.2. Design procedure

*w*, its center frequency of operation

*ω*

_{0}, and the response type are generally known

*a priori*. To realize a spatial bandstop filter acting as FSS using NPAs, only shunt resonator branches are available. In order to convert them into series branches and to have ladder configurations of resonators, we need to use impedance inverters approximated by 90° line lengths, as shown in Fig. 5. The reactance slope parameters of this circuit in terms of the low-pass prototype parameters

*g*

_{0},

*g*

_{1}, ...,

*g*

_{n}_{+1}, and cut-off frequency

*ω′*are given in [28] as: where

_{c}*Z*=

_{l}*Z*

_{0}, we design for

*n*=

*odd*.

*F*and

*a*) of different layers of NPA representing different branches of the filter. If frequencies of the edges are

*ω′*

_{1}and

*ω′*

_{2}(the prime is to avoid confusion with

*ω*

_{1}and

*ω*

_{2}in Eq. (8)) stop bandwidth and the center frequency can be defined respectively as

*ω*

_{0}to be the collective plasmon resonance frequency

*ω*of the NPA. Doing so for NPA of nanospheres we get the first design equation for the first geometrical parameter

_{CPR}*F*as

*a*. For this goal we use equation

*L′*we obtain Equating

*L*and

_{i}*L′*we derive the second design equation as where

*E*is as defined in Eq. (16). Now, extracted design equations for designing NPA-based branches of the spatial filter can be directly adapted to design an optical FSS.

### 3.3. Design example

*ω*

_{0}= 555 THz and

*w*= 18%. We choose a third-order Butterworth response and P-SF68 as the host medium. The element values for the low-pass prototype circuit can be found in [28]. These parameters along with geometrical parameters calculated from (15) and (17) are listed in Table 1. Figure 6 shows a three-dimensional topology of different layers of the FSS. The structure is composed of three different NPA layers with quarter-wavelength separation. We briefly discuss the effect of dissipation on the response of the FSS, which happens in realistic full wave simulation. In Fig. 7 the solid line shows the response of a typical bandstop filter where the resonators have no dissipation loss. The dashed line illustrates the effect of dissipation loss on the response. For the dashed line,the attenuation no longer goes to infinity and it has greater 3 dB bandwidth. Since plasmonic NPs are involved, a noticeable level of absorbtion is experienced on the NPA, particularly near the array resonance. for normal angle of incidence 1 − |

*R*|

^{2}− |

*T*|

^{2}corresponds to the absorbed power. Thus the same behavior as in Fig. 7 is expected.

*θ*= 0° to 50° in 10 degree steps. The frequency response of the FSS is not affected as the angle of incidence increases from 0° to 20° for both polarizations. Beyond 20°, however, the response starts to deviate from normal incidence. The bandwidth variations can be attributed to the change in wave impedance

*η*, which changes the loaded quality factor

*Q*of the resonators of the coupled resonator FSS [3

_{L}3. M. Al-Joumayly and N. Behdad, “A new technique for design of low-profile, second-order, bandpass frequency selective surfaces,” IEEE Trans. Antennas and Propagat. **57**, 452–459 (2009) [CrossRef] .

*η*/cos(

*θ*). Therefore, the loaded quality factor of the series resonators of Fig. 5 decreases for larger incidence angles, and subsequently the bandwidth of each resonator increases. On the other hand, for the TM polarization, the wave impedance changes as

*η*cos(

*θ*). Therefore, for larger incidence angles,

*Q*increases which leads to decrease of the bandwidth of each resonator in the FSS. It is also observed that for an increasing angle of incidence, the attenuation decreases. The reason is due to the fact that in TM polarization, the tangential component of the field on the surface of the array decreases for larger angles of incidence. Thus, the polarization of the NPs and consequently the effective averaged currents decrease which means lower level of reflection and rejection [18

_{L}*Structured Surfaces as Optical Metamaterials*, A. A. Maradudin, ed. (Cambridge University, 2011), pp. 58–93 [CrossRef] .

## 4. Conclusion

## Acknowledgments

## References and links

1. | B. A. Munk, |

2. | K. Sarabandi and N. Behdad, “A frequency selective surface with miniaturized elements,” IEEE Trans. Antennas and Propagat. |

3. | M. Al-Joumayly and N. Behdad, “A new technique for design of low-profile, second-order, bandpass frequency selective surfaces,” IEEE Trans. Antennas and Propagat. |

4. | S. Gupta, G. Tuttle, M. Sigalas, and K. M. Ho, “Infrared filters using metallic photonic band gap structures on flexible substrates,” Appl. Phys. Lett. |

5. | H. A. Smith, M. Rebbert, and O. Sternberg, “Designer infrared filters using stacked metal lattices,” Appl. Phys. Lett. |

6. | J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. P. Drupp, and L. Li, “The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications,” IEEE Trans. Antennas and Propagat. |

7. | Y. Tang, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer metallodielectric nanostructures as dual-band midinfrared filters,” Appl. Phys. Lett. |

8. | S. Govindaswamy, J. East, F. Terry, E. Topsakal, J. L. Volakis, and G. I. Haddad, “Frequency-selective surface based bandpass filters in the near-infrared region,” Microw. Opt. Technol. Lett. |

9. | D. Van Labeke, D. Grard, B. Guizal, F. I. Baida, and L. Li, “An angle-independent Frequency Selective Surface in the optical range,” Opt. Express |

10. | G. Si, Y. Zhao, H. Liu, S. Teo, M. Zhang, T. J. Huang, A. J. Danner, and J. Teng, “Annular aperture array based color filter,” Appl. Phys. Lett. |

11. | J. Zhang, J. Y. Ou, N. Papasimakis, Y. Chen, K. F. MacDonald, and N. I. Zheludev, “Continuous metal plasmonic frequency selective surfaces,” Opt. Express |

12. | D. H. Werner, T. S. Mayer, and C. R. Baleine, “Multi-spectral filters, mirrors and anti-reflective coatings with subwavelength periodic features for optical devices,” U.S. Patent Application 12/900,967, (April2011). |

13. | A. Monti, F. Bilotti, A. Toscano, and L. Vegni, “Possible implementation of epsilon-near-zero metamaterials working at optical frequencies,” Opt. Commun. |

14. | A. Di Falco, Y. Zhao, and A. Alu, “Optical metasurfaces with robust angular response on flexible substrates,” Appl. Phys. Lett. |

15. | P. C. Li and E. T. Yu, “Wide-angle wavelength-selective multilayer optical
metasurfaces robust to interlayer misalignment,” J. Opt. Soc. Am.
B |

16. | C. Saeidi and D. van der Weide, “Spatial filter for optical frequencies using plasmonic metasurfaces,” accepted to IEEE Int. Symp. Antennas and Propagation (APS/URSI) (2013). |

17. | B. Memarzadeh and H. Mosallaei, “Layered plasmonic tripods: an infrared frequency selective
surface nanofilter,” J. Opt. Soc. Am. B |

18. | A. Alu and N. Engheta, “Optical wave interaction with two-dimensional arrays of plasmonic nanoparticles,” in |

19. | S. Tretyakov, |

20. | A. S. Kumbhar, M. K Kinnan, and G. Chumanov, “Multipole plasmon resonances of submicron silver particles,” J. Am. Chem. Soc. |

21. | W. H. Eggimann and R. E. Collin, “Dynamic interaction fields in a two-dimensional lattice,” IEEE Trans. Microwave Theory Tech. |

22. | S. I. Maslovski and S. A. Tretyakov, “Full-wave interaction field in two-dimensional arrays of dipole scatterers,” Int. J. Electron. Commun. |

23. | Y. R. Zhen, K. H. Fung, and C. T. Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B |

24. | R. E. Collin, |

25. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

26. | P. G. Kik, A. Maier, and H. A. Atwater, “Image resolution of surface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources,” Phys. Rev. B |

27. | J. J. Xiao, J. P. Huang, and K. W. Yu, “Optical response of strongly coupled metal nanoparticles in dimer arrays,” Phys. Rev. B |

28. | G. L. Matthaei, L. Young, and E. M. T. Jones, |

**OCIS Codes**

(290.5850) Scattering : Scattering, particles

(350.4600) Other areas of optics : Optical engineering

**ToC Category:**

Optical Devices

**History**

Original Manuscript: May 3, 2013

Revised Manuscript: June 17, 2013

Manuscript Accepted: June 19, 2013

Published: June 28, 2013

**Citation**

Chiya Saeidi and Daniel van der Weide, "Nanoparticle array based optical frequency selective surfaces: theory and design," Opt. Express **21**, 16170-16180 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-16170

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### References

- B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley-Interscience, 2005).
- K. Sarabandi and N. Behdad, “A frequency selective surface with miniaturized elements,” IEEE Trans. Antennas and Propagat.55, 1239–1245 (2007). [CrossRef]
- M. Al-Joumayly and N. Behdad, “A new technique for design of low-profile, second-order, bandpass frequency selective surfaces,” IEEE Trans. Antennas and Propagat.57, 452–459 (2009). [CrossRef]
- S. Gupta, G. Tuttle, M. Sigalas, and K. M. Ho, “Infrared filters using metallic photonic band gap structures on flexible substrates,” Appl. Phys. Lett.71, 2412–2414 (1997). [CrossRef]
- H. A. Smith, M. Rebbert, and O. Sternberg, “Designer infrared filters using stacked metal lattices,” Appl. Phys. Lett.82, 3605–3607 (2003). [CrossRef]
- J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. U. Tang, R. P. Drupp, and L. Li, “The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications,” IEEE Trans. Antennas and Propagat.54, 1265–1276 (2006). [CrossRef]
- Y. Tang, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer metallodielectric nanostructures as dual-band midinfrared filters,” Appl. Phys. Lett.92, 263106 (2008). [CrossRef]
- S. Govindaswamy, J. East, F. Terry, E. Topsakal, J. L. Volakis, and G. I. Haddad, “Frequency-selective surface based bandpass filters in the near-infrared region,” Microw. Opt. Technol. Lett.41, 266–269 (2004). [CrossRef]
- D. Van Labeke, D. Grard, B. Guizal, F. I. Baida, and L. Li, “An angle-independent Frequency Selective Surface in the optical range,” Opt. Express14, 11945–11951 (2006). [CrossRef] [PubMed]
- G. Si, Y. Zhao, H. Liu, S. Teo, M. Zhang, T. J. Huang, A. J. Danner, and J. Teng, “Annular aperture array based color filter,” Appl. Phys. Lett.99, 033105 (2011). [CrossRef]
- J. Zhang, J. Y. Ou, N. Papasimakis, Y. Chen, K. F. MacDonald, and N. I. Zheludev, “Continuous metal plasmonic frequency selective surfaces,” Opt. Express19, 23279–23285 (2011). [CrossRef] [PubMed]
- D. H. Werner, T. S. Mayer, and C. R. Baleine, “Multi-spectral filters, mirrors and anti-reflective coatings with subwavelength periodic features for optical devices,” U.S. Patent Application 12/900,967, (April2011).
- A. Monti, F. Bilotti, A. Toscano, and L. Vegni, “Possible implementation of epsilon-near-zero metamaterials working at optical frequencies,” Opt. Commun.285, 3412–3418 (2012). [CrossRef]
- A. Di Falco, Y. Zhao, and A. Alu, “Optical metasurfaces with robust angular response on flexible substrates,” Appl. Phys. Lett.99, 163110 (2011). [CrossRef]
- P. C. Li and E. T. Yu, “Wide-angle wavelength-selective multilayer optical metasurfaces robust to interlayer misalignment,” J. Opt. Soc. Am. B30, 27–32 (2013). [CrossRef]
- C. Saeidi and D. van der Weide, “Spatial filter for optical frequencies using plasmonic metasurfaces,” accepted to IEEE Int. Symp. Antennas and Propagation (APS/URSI) (2013).
- B. Memarzadeh and H. Mosallaei, “Layered plasmonic tripods: an infrared frequency selective surface nanofilter,” J. Opt. Soc. Am. B29, 2347–2351 (2012). [CrossRef]
- A. Alu and N. Engheta, “Optical wave interaction with two-dimensional arrays of plasmonic nanoparticles,” in Structured Surfaces as Optical Metamaterials, A. A. Maradudin, ed. (Cambridge University, 2011), pp. 58–93. [CrossRef]
- S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House Publishers, 2003).
- A. S. Kumbhar, M. K Kinnan, and G. Chumanov, “Multipole plasmon resonances of submicron silver particles,” J. Am. Chem. Soc.127, 12444–12445 (2005). [CrossRef] [PubMed]
- W. H. Eggimann and R. E. Collin, “Dynamic interaction fields in a two-dimensional lattice,” IEEE Trans. Microwave Theory Tech.9, 110–115 (1961). [CrossRef]
- S. I. Maslovski and S. A. Tretyakov, “Full-wave interaction field in two-dimensional arrays of dipole scatterers,” Int. J. Electron. Commun.53, 135–139 (1999).
- Y. R. Zhen, K. H. Fung, and C. T. Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B78, 035419 (2008). [CrossRef]
- R. E. Collin, Field Theory of Guided Waves (IEEE, 1991).
- P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370 (1972). [CrossRef]
- P. G. Kik, A. Maier, and H. A. Atwater, “Image resolution of surface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources,” Phys. Rev. B69, 045418 (2004). [CrossRef]
- J. J. Xiao, J. P. Huang, and K. W. Yu, “Optical response of strongly coupled metal nanoparticles in dimer arrays,” Phys. Rev. B71, 045404 (2005). [CrossRef]
- G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (McGraw-Hill, 1964).

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