## Plasmonic glasses: Optical properties of amorphous metal-dielectric composites |

Optics Express, Vol. 22, Issue 2, pp. 2031-2042 (2014)

http://dx.doi.org/10.1364/OE.22.002031

Acrobat PDF (1453 KB)

### Abstract

Plasmonic glasses composed of metallic inclusions in a host dielectric medium are investigated for their optical properties. Such structures characterized by short-range order can be easily fabricated using bottom-up, self-organization methods and may be utilized in a number of applications, thus, quantification of their properties is important. We show, using T-Matrix calculations of 1D, 2D, and 3D plasmonic glasses, that their plasmon resonance position oscillates as a function of the particle spacing yielding blue- and redshifts up to 0.3 eV in the visible range with respect to the single particle surface plasmon. Their properties are discussed in light of an analytical model of an average particle’s polarizability that originates from a coupled dipole methodology.

© 2014 Optical Society of America

## 1. Introduction

1. N. Liu, M. Hentschel, T. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science **332**, 1407–1410 (2011). [CrossRef] [PubMed]

2. R. Verre, K. Fleischer, J. F. McGilp, D. Fox, G. Behan, H. Zhang, and I. V. Shvets, “Controlled in situ growth of tunable plasmonic self-assembled nanoparticle arrays,” Nanotechnol. **23**, 035606 (2012). [CrossRef]

3. H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole-mask coloidal lithography,” Adv. Mater. **19**, 4297–4302 (2007). [CrossRef]

4. N. Homonnay, N. Geyer, B. Fuhrmann, and H. S. Leipner, “Advanced colloidal lithography for sub-100nm lift-off structures,” Vacuum **86**, 1232–1234 (2012). [CrossRef]

5. K. Güngör, E. Ünal, and H. V. Demir, “Nanoplasmonic surfaces enabling strong surface-normal electric field enhancement,” Opt. Express **21**, 23097–23106 (2013). [CrossRef] [PubMed]

6. A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science **282**, 897–901 (1998). [CrossRef] [PubMed]

7. A. Moroz, “Three-dimensional complete photonic-band-gap structures in the visible,” Phys. Rev. Lett. **83**, 5274–5277 (1999). [CrossRef]

8. W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. **84**, 2853–2856 (2000). [CrossRef] [PubMed]

9. B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: Influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. **84**, 4721–4724 (2000). [CrossRef] [PubMed]

10. C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Käll, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B **107**, 7337–7342 (2003). [CrossRef]

11. B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. **101**, 143902 (2008). [CrossRef] [PubMed]

12. V. V. Gozhenko, D. A. Smith, J. L. Vedral, V. V. Kravets, and A. O. Pinchuk, “Tunable resonance absorption of light in a chain of gold nanoparticles,” J. Phys. Chem. C **115**, 8911–8917 (2011). [CrossRef]

13. T. L. Temple and D. M. Bagnall, “Optical properties of gold and aluminium nanoparticles for silicon solar cell applications,” J. Appl. Phys. **109**, 084343 (2011). [CrossRef]

15. M. G. Nielsen, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Efficient absorption of visible radiation by gap plasmon gesonators,” Opt. Express **20**, 13311–13319 (2012). [CrossRef] [PubMed]

16. C. Hägglund and S. P. Apell, “Plasmonic near-field absorbers for ultrathin solar cells,” J. Phys Chem. Lett. **3**, 1275–1285 (2012). [CrossRef]

15. M. G. Nielsen, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Efficient absorption of visible radiation by gap plasmon gesonators,” Opt. Express **20**, 13311–13319 (2012). [CrossRef] [PubMed]

17. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. **108**, 047401 (2012). [CrossRef] [PubMed]

18. C. Rockstuhl and T. Scharf, eds., *Amorphous Nanophotonics* (Springer, 2013). [CrossRef]

19. M. Burresi, F. Pratesi, K. Vynck, M. Prasciolu, M. Tormen, and D. S. Wiersma, “Two-dimensional disorder for broadband, omnidirectional and polarization-insensitive absorption,” Opt. Express **21**, A268–A275 (2013). [CrossRef] [PubMed]

20. C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tüennermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B **79**, 233107 (2009). [CrossRef]

21. R. Sing, X. Lu, J. Gu, Z. Tian, and W. Zhang, “Random terahertz metamaterials,” J. Opt. **12**, 015101 (2012). [CrossRef]

22. S. Mülig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano **5**, 6586–6592 (2011). [CrossRef]

23. S. N. Sheikholeslami, H. Alaeian, A. L. Koh, and J. A. Dionne, “A metafluid exhibiting strong optical magnetism,” Nano Lett. **13**, 4137–4141 (2013). [CrossRef] [PubMed]

24. A. V. Panov, “Impact of interparticle dipoledipole interactions on optical nonlinearity of nanocomposites,” J. Mod. Opt. **60**, 915–919 (2013). [CrossRef]

25. J. Wang and A. Z. Genack, “Transport through modes in random media,” Nature **471**, 345–348 (2011). [CrossRef] [PubMed]

*i.e.*the minimum center-to-center (cc) distance between the metallic inclusions. In Section 4 we derive an average particle polarizability model that matches the T-Matrix calculated spectra and use it in Section 5 to discuss the origin and evolution of the observed spectral dependence on the minimum cc distance. After the conclusions we provide appendices that give additional information on the derivation of the average polarizability of plasmonic glasses.

## 2. Numerical simulations – the T-Matrix method

26. D. W. Mackowski, “Calculation of total cross section of multiple-sphere clusters,” J. Opt. Soc. Am. A **11**, 2851–2861 (1994). [CrossRef]

*N*spheres is decomposed into the sum of fields scattered by each sphere. The field acting onto the

*i*

^{th}sphere is the sum of the incident and scattered fields of all other particles. Using the addition theorem for spherical harmonics it is possible to express those scattered fields in terms of spherical harmonics centered about sphere

*i*. Transforming these into a cluster-centered T-matrix allows for calculation of various cross sections and other relevant quantities.

27. E. L. Hinrichsen, J. Feder, and T. Jøssang, “Geometry of random sequential adsorption,” J. Stat. Phys. **44**, 793–827 (1986). [CrossRef]

*r*

_{cc}=

*D𝒞*), where

*D*is the sphere diameter and

*𝒞*is the dimensionless center-to-center distance, the new sphere joins the ensemble. This is iteratively repeated until no new sphere can be added. Here, we use a Drude metal (

*h̄ω*= 6.2 eV,

_{p}*h̄γ*= 0.62 eV) spheres

*D*= 100 nm in diameter. We use a count of 6000 (6k) spheres and only to assess edge effects in the 2D case we also simulate 10k particles. As it will be shown later, T-Matrix calculated resonance positions for these two cases are almost identical. To fit 6k spheres we need 810

*μ*m, 9.2 × 9.2

*μ*m

^{2}, and 2 × 2 × 2

*μ*m

^{3}for 1D, 2D, and 3D, respectively for

*𝒞*= 1. In the T-Matrix calculations we include the first four spherical harmonics.

*g*(

*x*) that fits well to the calculated data and is easily integrable when multiplied by the dipole radiation function: where

*x*≡

*r/r*is a normalized radial parameter of the pair correlation function and Θ(

_{cc}*x*) is the Heaviside step function. Fitted PCFs for plasmonic glasses are shown in Fig. 1(d) with lines and the fitting parameters given in Table 1 in Appendix B.

## 3. Optical properties of plasmonic glasses

### 3.1. Two dimensional plasmonic glass

28. T. J. Antosiewicz, S. P. Apell, M. Zäch, I. Zorić, and C. Langhammer, “Oscillatory optical response of an amorphous two-dimensional array of gold nanoparticles,” Phys. Rev. Lett. **109**, 247401 (2012). [CrossRef]

*vice versa*. Note the small spread in numerically obtained points for both large and small arrays, which is indicative of a relatively weak edge effect observed for as few as 6k particles and well defined average properties of these glasses. The only exception is observed for

*𝒞*= 4.5. The reason for this is the close matching of the resonance position (

*ca.*450 nm) to the minimum distance between the particles (also 450 nm), resulting in in-phase coupling of neighboring spheres. For this cc value small changes in positioning may lead to comparatively large changes in the spectral response at resonance. Finally, we point out that the line marking the analytically calculated resonance position (see derivation of the model in Sec. 4), follows closely the T-Matrix results.

### 3.2. One dimensional plasmonic glass

*π*/2, vary from (

*θ*

_{0}= 0,

*ϕ*

_{0}= 0) – incidence along the chain – to normal incidence for the electric field parallel to the chain (1,0) and perpendicular to it (1,1). When light propagates along the chain the optical response is shifted by 0.5 eV to the red from the single particle resonance. Additionally, small oscillations are superimposed onto the redshift. As the chain is tilted in

*θ*to (0.5,0) the redshift decreases quickly, followed by an almost complete disappearance of the oscillations at (1,0) with the exception for small cc values (less than 0.1 eV difference relative to the single particle value). As the chain is rotated towards perpendicular orientation relative to the electric field the oscillations increase to their maximum value of 0.15 eV. The subsequent tilting in

*θ*to grazing incidence restores the slightly modulated redshift.

### 3.3. Three dimensional plasmonic glass

*𝒞*= 2 from a single particle value of 2.9 eV. The absorption peak shift is much smaller and it can be seen that the relation of the absorption and scattering peaks is exchanged. For sparse arrays (and indeed for the single particle) scattering is to the blue of the absorption peak, but for

*𝒞*≈ 6 this reverses. The analytical description of the average properties is less accurate than in the low dimensional materials with the extinction cross section being accurate only down to a cc distance of

*𝒞*= 5. For denser glasses the peak shift is only qualitatively accurate showing a larger red shift for

*𝒞*= 2 than obtained from the T-Matrix formalism.

## 4. Continuous-dipolar-medium approach

*α*and is further modified by interparticle coupling. The polarizability of a spherical nanoparticle in the modified long wavelength approximation (MLWA) [29

29. A. Moroz, “Depolarization field of spheroidal particles,” J. Opt. Soc. Am. B **26**, 517–527 (2009). [CrossRef]

*α*

^{q}= 4

*πε*

_{0}

*R*

^{3}(

*ε*− 1)/(

*ε*+ 2) is the quasistatic polarizability, for simplicity, in vacuum,

*k*= 2

*π/λ*,

*ε*is the permittivity of the particle, and

*s*is a length associated with the particle size.

30. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A **11**, 1491–1499 (1994). [CrossRef]

*i*, including the contribution from all other particles (

*j*), is

**E**

_{loc,}

*=*

_{i}**E**

_{inc,}

*− ∑*

_{i}

_{j}_{≠}

_{i}**A**

_{ij}**P**

*, where we assume that the incident field propagates along the*

_{j}*z*-axis

**E**

_{inc}=

**E**

_{0}

*e*and

^{ikz}**A**

_{ij}**P**

*determines the dipole radiation. It is important to notice, that in a medium composed of identical average particles the polarizability of each is the same, albeit shifted in phase with respect to each other. Here we define the average particle as having the same optical spectrum as the ensemble except for the amplitude which is*

_{j}*N*times smaller. Setting as a point of reference a particle placed in the center of the coordinate system (having

**P**

_{0}), the polarization of all other average particle

*j*located in a plane with coordinate

*z*is

_{j}**P**

*=*

_{j}**P**

_{0}

*e*

^{ikzj}.

*α*^{*}is thus where

**is the polarizability tensor of a single nanoparticle and we introduce a coupling term**

*α**𝒮*≡ ∑

_{j}_{≠0}

**A**

_{0}

_{j}e^{ikzj}which runs over all other particles [31

31. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B **107**, 7343–7350 (2003). [CrossRef]

*𝒮*as an integral of a structure factor over the volume occupied by the object (see Appendix A for details). For the structures considered here the structure factor is the PCF

*g*(

*r*) which describes the stochastic arrangement of particles. Dropping the tensor formalism and assuming linearly polarized light in the

*x*direction, the interaction term becomes where

*σ*=

*σ*

_{0}/

*r*is the particle density in the considered dimensionality (

^{d}*d*= 1, 2, 3 for 1D, 2D, and 3D, respectively),

*σ*

_{0}is a packing parameter, and

*A*is given by Eq. (12) in Appendix A. Thus, the polarizability of the medium becomes Using Eq. (4), extinction is calculated as

_{xx}*C*

_{ext}∝

*k*Im(

*α*

^{*}). From these calculations we extract the resonance positions for all considered plasmonic glasses and plot them in preceding figures together with the T-Matrix results. The key to calculating the average particle properties lies in evaluating Eq. (3) to yield

*𝒮*for all dimensionalities, which are given in Appendix B.

## 5. Discussion

32. W. Rechberger, A. Hohenau, A. Leitner, J. Krenn, B. Lamprecht, and F. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. **220**, 137–141 (2003). [CrossRef]

*𝒞*< 2, as reported by Rechberger

*et al.*[32

32. W. Rechberger, A. Hohenau, A. Leitner, J. Krenn, B. Lamprecht, and F. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. **220**, 137–141 (2003). [CrossRef]

*z*-position. This means, that two hypothetical particles placed symmetrically to either side of the central one have a phase shift of

*e*

^{±}

*relative to the central one. Adding the retardation phase shift as well as a small Δ phase delay due to reradiation, the scattered fields of the preceding one will illuminate the central one with a phase shift of*

^{ikz}*e*

^{i}^{Δ}, while the following one with

*e*

^{2}

^{ikz}^{+}

^{i}^{Δ}. This means, that the coupling will be attractive for certain values of the minimum cc distance resulting in a redshift, as seen for the (0,0)-orientation. However, if we considered unphysical values of the cc distance smaller than one (mathematically overlapping particles with no common volume), then the phase shifts due to particle positioning would be very small and repulsive interaction would be restored giving an expected blue shift [32

32. W. Rechberger, A. Hohenau, A. Leitner, J. Krenn, B. Lamprecht, and F. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. **220**, 137–141 (2003). [CrossRef]

*𝒞*< 2 and will influence the optical response, however, we do not consider them in the analytical model.

*𝒞*= 4 are 0.09 eV and 0.17 eV for scattering and absorption, respectively. Noting that extinction is a sum of the other two cross sections, we have the extinction cross section expressed as and the scattering cross section is For individual particles

*α*is constant, but the coupling term

*𝒮*varies as the minimum cc distance changes. In the case of scattering, only the denominator is a function of the coupling term, but for extinction also the numerator is a function of

*𝒮*, thus the oscillations of extinction are indeed larger than for scattering. Furthermore, with extinction being the sum of scattering and absorption, it is reasonable that absorption experiences larger oscillations than scattering.

*𝒞*∼ 2) is expected, as it can be viewed as a combination of the 1D (1,0)- and (1,1)-orientations (in-phase excitation), which both exhibit a blueshift and the latter one strong oscillations.

*front*and

*back*halves induces a redshift for all dipole orientations, similar as in the 1D (0,0) chain orientation, and this coupling is always strong, as it occurs via both near- and far-field coupling. On the other hand, the interaction between the central particle and the

*left/right*sides depends on their relative phases and the resulting blueshift (at small cc values) is weaker than the redshift. Thus, 3D glass exhibits a redshift of the resonance position for decreasing

*𝒞*.

## 6. Conclusions and summary

*i.e.*minimum cc values, we have demonstrated significant changes to the optical cross sections.

22. S. Mülig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano **5**, 6586–6592 (2011). [CrossRef]

23. S. N. Sheikholeslami, H. Alaeian, A. L. Koh, and J. A. Dionne, “A metafluid exhibiting strong optical magnetism,” Nano Lett. **13**, 4137–4141 (2013). [CrossRef] [PubMed]

## Appendix A: Continuous-dipolar-medium approach

*i*including the contribution from all other particles (

*j*) in the CDA is

**E**

_{loc,}

*=*

_{i}**E**

_{inc,}

*− ∑*

_{i}

_{j}_{≠}

_{i}**A**

_{ij}**P**

*, where we assume that the incident field propagates along the*

_{j}*z*-axis

**E**

_{inc}=

**E**

_{0}

*e*and

^{ikz}**A**

_{ij}**P**

*determines the dipole radiation. The important assumption here is that the polarizability of average particles in a medium composed of such particles is the same. However, a defined axis of light propagation (*

_{j}*z*-axis) causes a phase shift of

*e*. This means, that the polarization of an average particle

^{ikz}*j*located in a plane with coordinate

*z*is where

_{j}**P**

_{0}is the polarization of the particle in the center of the coordinate system. Thus, the field polarizing the average sphere at the center of the coordinate system (

*i*= 0) and the resulting average polarizability

*α*^{*}can now be written as The polarization of the average particle is

**P**

_{0}=

*α*E_{loc,0}and after substituting into it Eq. (8) we get where

**is the polarizability tensor of a single nanoparticle. In the above equation the single particle polarizability**

*α***is modified by a term arising from the coupling**

*α**𝒮*≡ ∑

_{j}_{≠0}

**A**

_{0}

_{j}e^{ikzj}. This term can be rewritten in the following form where

*δ*(

**x**−

**x**

*) describes the particle arrangement in space. We change the order of the integral and the sum and let*

_{j}*G*(

**x**) ≡ ∑

_{j}_{≠0}

*δ*(

**x**−

**x**

*) be a structure factor. Thus, the interaction term now depends on the function*

_{j}*G*(

**x**) which can describe any particle arrangement. In the considered case of a plasmonic glass, the distribution of metal particles is quasi-random with distinct short-range order and lack of long-range order. The stochastic nature of this arrangement is best described by a PCF, see Fig. 1(d). In order to assure the correct dimensionality of the integral the PCF is multiplied by the average particle density

*σ*. We let

*G*(

**x**) ≡

*σg*(

*r*), where

*g*(

*r*) is the PCF. Thus dropping the tensor formalism and assuming linearly polarized light in the

*x*direction, the interaction term becomes where

*A*in usual spherical coordinates (

_{xx}*r*,

*θ*,

*ϕ*) is Consideration of only the

*A*term in the analytical treatment is justified by the fact that in calculating the off-diagonal terms one needs to perform an azimuthal integral which yields zero. They are

_{xx}*y*- and

*z*-components of polarization will be present due to the randomness in particle arrangement.

## Appendix B: Analytical description of plasmonic glasses

## Three dimensional plasmonic glass

*e*

^{−}

*, which can physically be understood as an illuminating beam of a finite cross section, where*

^{ar}*a*determines how quickly the beam amplitude decays.

## Two dimensional plasmonic glass

*yz*-plane and is given by

*z*=

*By*[see Fig. 1(b)], where the slope is

*B*= cot

*θ*

_{m}and

*θ*

_{m}is the angle between the

*z*-axis and the 2D plane. For TE light we have in spherical coordinates

*θ*= arccot(cot

*θ*

_{m}sin

*ϕ*) which indicates, that for every angle

*ϕ*there is a certain angle

*θ*which defines a part of the 2D plane. Thus the integral is multiplied by

*θ*=

*π*/2 and Eq. (14) simplifies to the case described previously [28

28. T. J. Antosiewicz, S. P. Apell, M. Zäch, I. Zorić, and C. Langhammer, “Oscillatory optical response of an amorphous two-dimensional array of gold nanoparticles,” Phys. Rev. Lett. **109**, 247401 (2012). [CrossRef]

## Random chain – 1D plasmonic glass

*π*relative to the incident wave. Figure 1(a) shows the geometry where the chain orientation is defined by a polar angle

*θ*

_{0}and an azimuthal

*ϕ*

_{0}. To confine the integration volume to the chain we write the integral in two parts

*δ*(

*θ*−

*θ*

_{0})

*δ*(

*ϕ*−

*ϕ*

_{0}) and

*δ*(

*θ*− (

*π*−

*θ*

_{0}))

*δ*(

*ϕ*− (

*ϕ*

_{0}+

*π*)) with both expressions divided by

*r*

^{2}sin

*θ*. This simplifies the integrations to only the radial one

## Acknowledgments

## References and links

1. | N. Liu, M. Hentschel, T. Weiss, A. P. Alivisatos, and H. Giessen, “Three-dimensional plasmon rulers,” Science |

2. | R. Verre, K. Fleischer, J. F. McGilp, D. Fox, G. Behan, H. Zhang, and I. V. Shvets, “Controlled in situ growth of tunable plasmonic self-assembled nanoparticle arrays,” Nanotechnol. |

3. | H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole-mask coloidal lithography,” Adv. Mater. |

4. | N. Homonnay, N. Geyer, B. Fuhrmann, and H. S. Leipner, “Advanced colloidal lithography for sub-100nm lift-off structures,” Vacuum |

5. | K. Güngör, E. Ünal, and H. V. Demir, “Nanoplasmonic surfaces enabling strong surface-normal electric field enhancement,” Opt. Express |

6. | A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, and V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science |

7. | A. Moroz, “Three-dimensional complete photonic-band-gap structures in the visible,” Phys. Rev. Lett. |

8. | W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, and P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. |

9. | B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Metal nanoparticle gratings: Influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. |

10. | C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, and M. Käll, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B |

11. | B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. |

12. | V. V. Gozhenko, D. A. Smith, J. L. Vedral, V. V. Kravets, and A. O. Pinchuk, “Tunable resonance absorption of light in a chain of gold nanoparticles,” J. Phys. Chem. C |

13. | T. L. Temple and D. M. Bagnall, “Optical properties of gold and aluminium nanoparticles for silicon solar cell applications,” J. Appl. Phys. |

14. | K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nature Mater. |

15. | M. G. Nielsen, A. Pors, O. Albrektsen, and S. I. Bozhevolnyi, “Efficient absorption of visible radiation by gap plasmon gesonators,” Opt. Express |

16. | C. Hägglund and S. P. Apell, “Plasmonic near-field absorbers for ultrathin solar cells,” J. Phys Chem. Lett. |

17. | S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. |

18. | C. Rockstuhl and T. Scharf, eds., |

19. | M. Burresi, F. Pratesi, K. Vynck, M. Prasciolu, M. Tormen, and D. S. Wiersma, “Two-dimensional disorder for broadband, omnidirectional and polarization-insensitive absorption,” Opt. Express |

20. | C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tüennermann, F. Lederer, and T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B |

21. | R. Sing, X. Lu, J. Gu, Z. Tian, and W. Zhang, “Random terahertz metamaterials,” J. Opt. |

22. | S. Mülig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, and F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano |

23. | S. N. Sheikholeslami, H. Alaeian, A. L. Koh, and J. A. Dionne, “A metafluid exhibiting strong optical magnetism,” Nano Lett. |

24. | A. V. Panov, “Impact of interparticle dipoledipole interactions on optical nonlinearity of nanocomposites,” J. Mod. Opt. |

25. | J. Wang and A. Z. Genack, “Transport through modes in random media,” Nature |

26. | D. W. Mackowski, “Calculation of total cross section of multiple-sphere clusters,” J. Opt. Soc. Am. A |

27. | E. L. Hinrichsen, J. Feder, and T. Jøssang, “Geometry of random sequential adsorption,” J. Stat. Phys. |

28. | T. J. Antosiewicz, S. P. Apell, M. Zäch, I. Zorić, and C. Langhammer, “Oscillatory optical response of an amorphous two-dimensional array of gold nanoparticles,” Phys. Rev. Lett. |

29. | A. Moroz, “Depolarization field of spheroidal particles,” J. Opt. Soc. Am. B |

30. | B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A |

31. | L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B |

32. | W. Rechberger, A. Hohenau, A. Leitner, J. Krenn, B. Lamprecht, and F. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. |

**OCIS Codes**

(160.2750) Materials : Glass and other amorphous materials

(160.4760) Materials : Optical properties

(240.6680) Optics at surfaces : Surface plasmons

(290.2200) Scattering : Extinction

(160.4236) Materials : Nanomaterials

**ToC Category:**

Plasmonics

**History**

Original Manuscript: October 4, 2013

Revised Manuscript: November 5, 2013

Manuscript Accepted: November 12, 2013

Published: January 23, 2014

**Citation**

Tomasz J. Antosiewicz and S. Peter Apell, "Plasmonic glasses: Optical properties of amorphous metal-dielectric composites," Opt. Express **22**, 2031-2042 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-2031

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### References

- N. Liu, M. Hentschel, T. Weiss, A. P. Alivisatos, H. Giessen, “Three-dimensional plasmon rulers,” Science 332, 1407–1410 (2011). [CrossRef] [PubMed]
- R. Verre, K. Fleischer, J. F. McGilp, D. Fox, G. Behan, H. Zhang, I. V. Shvets, “Controlled in situ growth of tunable plasmonic self-assembled nanoparticle arrays,” Nanotechnol. 23, 035606 (2012). [CrossRef]
- H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, B. Kasemo, “Hole-mask coloidal lithography,” Adv. Mater. 19, 4297–4302 (2007). [CrossRef]
- N. Homonnay, N. Geyer, B. Fuhrmann, H. S. Leipner, “Advanced colloidal lithography for sub-100nm lift-off structures,” Vacuum 86, 1232–1234 (2012). [CrossRef]
- K. Güngör, E. Ünal, H. V. Demir, “Nanoplasmonic surfaces enabling strong surface-normal electric field enhancement,” Opt. Express 21, 23097–23106 (2013). [CrossRef] [PubMed]
- A. A. Zakhidov, R. H. Baughman, Z. Iqbal, C. Cui, I. Khayrullin, S. O. Dantas, J. Marti, V. G. Ralchenko, “Carbon structures with three-dimensional periodicity at optical wavelengths,” Science 282, 897–901 (1998). [CrossRef] [PubMed]
- A. Moroz, “Three-dimensional complete photonic-band-gap structures in the visible,” Phys. Rev. Lett. 83, 5274–5277 (1999). [CrossRef]
- W. Y. Zhang, X. Y. Lei, Z. L. Wang, D. G. Zheng, W. Y. Tam, C. T. Chan, P. Sheng, “Robust photonic band gap from tunable scatterers,” Phys. Rev. Lett. 84, 2853–2856 (2000). [CrossRef] [PubMed]
- B. Lamprecht, G. Schider, R. T. Lechner, H. Ditlbacher, J. R. Krenn, A. Leitner, F. R. Aussenegg, “Metal nanoparticle gratings: Influence of dipolar particle interaction on the plasmon resonance,” Phys. Rev. Lett. 84, 4721–4724 (2000). [CrossRef] [PubMed]
- C. L. Haynes, A. D. McFarland, L. Zhao, R. P. Van Duyne, G. C. Schatz, L. Gunnarsson, J. Prikulis, B. Kasemo, M. Käll, “Nanoparticle optics: The importance of radiative dipole coupling in two-dimensional nanoparticle arrays,” J. Phys. Chem. B 107, 7337–7342 (2003). [CrossRef]
- B. Auguié, W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101, 143902 (2008). [CrossRef] [PubMed]
- V. V. Gozhenko, D. A. Smith, J. L. Vedral, V. V. Kravets, A. O. Pinchuk, “Tunable resonance absorption of light in a chain of gold nanoparticles,” J. Phys. Chem. C 115, 8911–8917 (2011). [CrossRef]
- T. L. Temple, D. M. Bagnall, “Optical properties of gold and aluminium nanoparticles for silicon solar cell applications,” J. Appl. Phys. 109, 084343 (2011). [CrossRef]
- K. Vynck, M. Burresi, F. Riboli, D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nature Mater. 11, 1017–1022 (2012).
- M. G. Nielsen, A. Pors, O. Albrektsen, S. I. Bozhevolnyi, “Efficient absorption of visible radiation by gap plasmon gesonators,” Opt. Express 20, 13311–13319 (2012). [CrossRef] [PubMed]
- C. Hägglund, S. P. Apell, “Plasmonic near-field absorbers for ultrathin solar cells,” J. Phys Chem. Lett. 3, 1275–1285 (2012). [CrossRef]
- S. Thongrattanasiri, F. H. L. Koppens, F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012). [CrossRef] [PubMed]
- C. Rockstuhl, T. Scharf, eds., Amorphous Nanophotonics (Springer, 2013). [CrossRef]
- M. Burresi, F. Pratesi, K. Vynck, M. Prasciolu, M. Tormen, D. S. Wiersma, “Two-dimensional disorder for broadband, omnidirectional and polarization-insensitive absorption,” Opt. Express 21, A268–A275 (2013). [CrossRef] [PubMed]
- C. Helgert, C. Rockstuhl, C. Etrich, C. Menzel, E.-B. Kley, A. Tüennermann, F. Lederer, T. Pertsch, “Effective properties of amorphous metamaterials,” Phys. Rev. B 79, 233107 (2009). [CrossRef]
- R. Sing, X. Lu, J. Gu, Z. Tian, W. Zhang, “Random terahertz metamaterials,” J. Opt. 12, 015101 (2012). [CrossRef]
- S. Mülig, A. Cunningham, S. Scheeler, C. Pacholski, T. Bürgi, C. Rockstuhl, F. Lederer, “Self-assembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range,” ACS Nano 5, 6586–6592 (2011). [CrossRef]
- S. N. Sheikholeslami, H. Alaeian, A. L. Koh, J. A. Dionne, “A metafluid exhibiting strong optical magnetism,” Nano Lett. 13, 4137–4141 (2013). [CrossRef] [PubMed]
- A. V. Panov, “Impact of interparticle dipoledipole interactions on optical nonlinearity of nanocomposites,” J. Mod. Opt. 60, 915–919 (2013). [CrossRef]
- J. Wang, A. Z. Genack, “Transport through modes in random media,” Nature 471, 345–348 (2011). [CrossRef] [PubMed]
- D. W. Mackowski, “Calculation of total cross section of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994). [CrossRef]
- E. L. Hinrichsen, J. Feder, T. Jøssang, “Geometry of random sequential adsorption,” J. Stat. Phys. 44, 793–827 (1986). [CrossRef]
- T. J. Antosiewicz, S. P. Apell, M. Zäch, I. Zorić, C. Langhammer, “Oscillatory optical response of an amorphous two-dimensional array of gold nanoparticles,” Phys. Rev. Lett. 109, 247401 (2012). [CrossRef]
- A. Moroz, “Depolarization field of spheroidal particles,” J. Opt. Soc. Am. B 26, 517–527 (2009). [CrossRef]
- B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
- L. Zhao, K. L. Kelly, G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: Influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107, 7343–7350 (2003). [CrossRef]
- W. Rechberger, A. Hohenau, A. Leitner, J. Krenn, B. Lamprecht, F. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220, 137–141 (2003). [CrossRef]

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