OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26052–26068
« Show journal navigation

Tunable wavelength dependent nanoswitches enabled by simple plasmonic core-shell particles

Anastasios H. Panaretos and Douglas H. Werner  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26052-26068 (2013)
http://dx.doi.org/10.1364/OE.21.026052


View Full Text Article

Acrobat PDF (1565 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this paper we demonstrate the feasibility of using a plasmonic core-shell particle to function as a wavelength dependent switch for integration into nanoantenna structures. First, a quasistatic analysis is performed and the necessary conditions are derived which allow the particle to operate in either a short- or an open-circuit state. These conditions dictate that the core and the shell permittivity values need to have opposite sign. Consequently, at optical wavelengths where noble metals are modeled as Drude dielectrics, these conditions can be easily realized. As a matter of fact, it is demonstrated that a realistic core-shell particle can exhibit both the short- and open-circuit states, albeit at different wavelengths. Our analysis is extended by examining the same problem beyond the quasistatic limit. For this task we utilize an inhomogeneous spherical transmission line representation of the core-shell particle. The conditions are derived for the particle that yield either an input admittance or impedance equal to zero. It is further demonstrated that these conditions are the short wavelength generalization of their quasistatic counterparts.

© 2013 Optical Society of America

1. Introduction

One of the greatest challenges in modern nanophotonics technology is the development of nanodevices that allow light manipulation in a fully controlled manner. A characteristic example of such a structure would be an optical nanoantenna that exhibits tunable or reconfigurable radiation and scattering properties. Similar to their radio frequency and microwave counterparts, nanodevices could be loaded by nanocircuit elements in order to enable their tunable or reconfigurable operation. Towards this goal, the main obstacle that must be overcome in order to design realistic nanocircuits is the difficulty to manipulate materials, in terms of fabrication, at the nanoscale. As a consequence, nanocircuits should be ideally synthesized using readily available nanoparticles characterized by reduced complexity (i.e. they are simple to fabricate) and increased tunability with robust operation. Towards this end, herein we explore the optical properties of a plasmonic core-shell particle in the context of providing a practical solution for the development of a polarization independent and tunable nanocircuit element that behaves as an effective wavelength dependent switch.

The interaction of electromagnetic waves with inhomogeneous stratified spheres is a topic that has been extensively studied [1

1. J. R. Wait, Electromagnetic Waves in Stratified Media (Pergamon, 1962).

5

5. A. Sihvola and L. V. Lindell, “Polarizability and effective permittivity of layered and continuously inhomogeneous dielectric spheres,” J. Electromagnet. Wave. 3(1), 37–60 (1989). [CrossRef]

]. In the context of nanoelectromagnetics, one geometry in particular that has attracted a lot of attention is the two-layer plasmonic dielectric sphere, also referred to as a core-shell particle. The appealing attributes of these particles stem from the fact that their electromagnetic properties can be in principle tuned as desired by appropriately choosing the material constitution of the core and the shell, as well as the volume fraction (i.e. the ratio between the inner and outer radius). Specifically, in [6

6. J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76(24), 245403 (2007). [CrossRef]

] a Yagi-Uda nanoantenna was proposed where the necessary phasing of the director and the reflector elements was achieved by judiciously engineering the volume fraction, and thus the polarizability, of a 1-D arrangement of core-shell particles. A near field light concentrator was proposed in [7

7. A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A non-linear inverse scattering design approach,” Phys. Rev. B 82(3), 035117 (2010). [CrossRef]

], based on a 2-D array of core-shell particles, with appropriately tailored geometrical characteristics.

In this paper we explore a different property of plasmonic core-shell particles. More specifically we examine the feasibility of such particles to exhibit either zero input admittance, or zero input impedance. This requires the derivation of the necessary conditions so that the induced displacement current on the surface of the particle experiences either a short- or an open-circuit [8

8. N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005). [CrossRef] [PubMed]

]. The possibility of realizing these responses using Janus type particles has been investigated by Kettunen et al. in [9

9. H. Kettunen, H. Wallen, and A. Sihvola, “Electrostatic resonances of a negative-permittivity hemisphere,” J. Appl. Phys. 103(9), 094112 (2008). [CrossRef]

] as well as by Alu et al. in [10

10. A. Alù and N. Engheta, “Optical nanoswitch: An engineered plasmonic nanoparticle with extreme parameters and giant anisotropy,” New J. Phys. 11(1), 013026 (2009). [CrossRef]

,11

11. A. Alù and N. Engheta, “Optical metamaterials based on optical nanocircuits,” Proc. IEEE 99(10), 1669–1681 (2011). [CrossRef]

]. In the former paper is was demonstrated that in the static case, a hemisphere immersed in free space, with permittivity equal to -1, exhibits anisotropic polarizability. The polarizability component vertical to the hemisphere’s flat surface corresponds to that of a homogeneous sphere with permittivityεr, while the parallel component corresponds to a homogeneous sphere with permittivityεr=0. Along similar lines in the latter papers it has been demonstrated that a Janus type particle, whose two faces are comprised by material of opposite permittivity values, exhibits an internal resonance that resembles that of either a series or a parallel LC circuit. The nature of the resonance is determined by whether the polarization of the excitation electric field is either parallel or perpendicular to the plane that separates the two faces of the Janus particle. Additionally, it was shown through a quasistatic analysis, that when the particle resonates the potential on its surface satisfies a zero Dirichlet, and a zero Neumann condition, respectively.

Our analysis reveals that a plasmonic core-shell particle under certain conditions can behave as either a short- or an open circuit. These two states occur at different wavelengths, but unlike with the Janus particle, the response is independent of the excitation electric field polarization. These two frequencies can be tuned as desired by appropriately selecting the particle’s material constitution and geometrical characteristics. We begin our discussion with the quasistatic analysis of the problem, due to simplicity of the involved expressions, and the ease they offer in identifying the critical properties of the problem. Given the closed form expression for the potential distribution in a two-layer dielectric sphere, we apply the zero Dirichlet and the zero Neumann boundary conditions on the particle’s surface, and we obtain the two necessary conditions that establish the short- and the open-circuit behavior. The two conditions relate the particle’s volume fraction with the core and the shell constitution. It turns out that in order for these conditions to hold the product of the real part of the two permittivities must be negative.

In the second part of our analysis we examine the core-shell properties beyond the quasistatic limit. For this reason we examine the TMr input admittance of a core-shell particle, which essentially corresponds to the TMr input admittance of a radially inhomogeneous spherical transmission line. A set of conditions is derived that yield a zero input admittance, and a zero input impedance. The main characteristics of these conditions is that, as expected, they are functions of the structure’s wavenumbers as well as the input admittance of the core and the admittance of the fringing field in the shell region, due to scattering from the core. It is further demonstrated that in the limit of an electrically small core-shell particle, the short- and open-circuit conditions for the dynamic case yield the ones obtained from the quasistatic analysis. Throughout this paper the exp(jωt) time convention is adopted.

2. Quasi-static analysis

4.1 Loseless material

Let us consider the core-shell particle shown in Fig. 1
Fig. 1 Spherical core-shell particle geometry.
. The particle’s shell and core are characterized by a permittivity of ε2 and ε1respectively, while the surrounding medium is considered as free space.

The structure is assumed to be immersed in a uniform electric fieldE=z^E0. The electric potential in the region defined by the particle’s shell is given by [12

12. A. Sihvola, “Character of surface plasmons in layered spherical structures,” Prog. Electromagnetics Res. 62, 317–331 (2006). [CrossRef]

]:

φ2=E03(ε1+2ε2)3(ε1ε2)(a1/r)3(ε1+2)(ε1+2ε2)+2f(ε11)(ε1ε2)rcosθ
(1)

Note that a2 and a1 are the radii of the particle and the core respectively, and fcorresponds to the core’s volume fraction, with respect to the volume of the particle, defined asf(a1/a2)3.

At this point we examine the behavior of Eq. (1) along the periphery of the core-shell particle. In particular, we determine the necessary core and shell material combinations such that the following Dirichlet and Neumann boundary conditions are satisfied:
φ2(r=a2)=0
(2)
and

rφ2(r=a2)=0
(3)

These are the necessary conditions so that the particle exhibits a response equivalent to that of a short- and open-circuit, respectively. Before proceeding with our analysis, it is instructive to derive the associated electric field conditions that Eq. (2) and Eq. (3) stem from. If we impose the condition that the tangential electric field on the surface of the particle is equal to zero, we obtain:

r^×E(r=a2)=0r^×θ^1a2θφ2(r=a2)=0
(4)

r^E(r=a2)=0r^φ2(r=a2)=0rφ2(r=a2)=0
(5)

Evidently, the zero Neumann boundary condition corresponding to the potential along the particle surface is equivalent to setting the radial electric field component on the same surface equal to zero. Returning to the boundary conditions given in Eq. (2) and Eq. (3), a straightforward algebraic manipulation leads to the following relations respectively:
ε1ε2ε1+2ε2=1f
(6)
and

ε1ε2ε1+2ε2=12f
(7)

Note how both conditions are dependent only on the core and shell material contrast as well as its volume fraction, and not on the object’s absolute dimensions. Given that the volume fraction is always positive, it is evident that in order for the conditions in Eq. (6) and Eq. (7) to hold, the core-shell particle must be comprised by a combination of two materials; one that exhibit a negative value of permittivity and the other a positive value.

Figs. 2(a)
Fig. 2 Electric field distribution in the space outside the particle under (a) short-circuit conditions and (b) open-circuit conditions. Potential distribution on and around the particle under (c) short-circuit conditions and (d) open-circuit conditions.
and 2(b) show the numerically predicted potential, along with the electric field distribution, when the two aforementioned boundary conditions are satisfied. It is evident that in the short-circuit case the electric field along the surface of the particle is radially oriented, since the tangential component vanishes, while the flux that enters the upper hemisphere, exits from the lower one. In the open-circuit case, the electric field on the surface of the particle is clearly tangential to it, since the radial component vanishes, as theoretically demonstrated previously. A more illustrative representation of the potential distribution for the two cases is shown in Figs. 2(c) and 2(d), respectively. In the short-circuit case it can be seen that the potential is zero on the surface of the particle. Moreover, in the open-circuit state the equipotential lines are radially distributed on the particle’s surface so that the potential is independent ofr.

α12ε1ε2ε1+2ε2
(9)

where the involved permittivities are relative with respect to that of free space. If we expand the terms of the numerator and the denominator in Eq. (8), and then divide them both by1fα12, we obtain

α=4πa23ε21+2fα121fα121ε21+2fα121fα12+2
(10)

The preceding expression reveals that under the quasistatic assumption the polarizability of the core-shell particle is equivalent to that of a homogeneous dielectric sphere of radiusa2, characterized by a relative permittivity valueεegiven by

εe=ε21+2fα121fα12
(11)

The expression in Eq. (11) corresponds to the Clausius-Mossotti (CM) mixing rule, for a mixture comprised by a filler with permittivityε1, diluted in a host material with permittivity ε2 at a volume fractionf. Having drawn this conclusion, a more illustrative demonstration of the core-shell particle response, under the short- and open-circuit conditions, is obtained if we substitute Eq. (6) and Eq. (7) into Eq. (11). This yields the following two outcomes:
limα12f±1εe=ε21+2f(f±1)1f(f±1)εe± 
(12)
and

εe=ε21+2f(2f)11f(2f)1εe=0 
(13)

These results are of paramount importance because they uniquely translate the short- and open-circuit boundary conditions to an effective dielectric material representation of the particle. Additionally, since permittivity is intuitively associated with the admittance of a lumped circuit element, the results in Eq. (12) and Eq. (13) indicate that the particle would exhibit an equivalent infinite and zero admittance, respectively, which is the typical characteristic of a short- and an open-circuit.

4.2 Lossy material

From the analysis so far it is apparent that the key element for the realization of the short- and open-circuit conditions solely depends on the ability to devise a core-shell with the material contrast dictated by either Eq. (6) or Eq. (7). Given that at optical wavelengths noble metals are typically characterized by negative permittivity, plasmonic core-shell particles are expected to exhibit the two aforementioned circuit responses.

Before proceeding with our analysis let us rewrite Eq. (6) and Eq. (7) as
ε1(ω)=ε21+2f11f
(14)
and

ε1(ω)=ε211f1+12f
(15)

3. Dynamic analysis

3.1 Spherical transmission line representation of a core-shell particle

For the analysis presented here we introduce the following quantities: the wavenumber in the core, the shell, and the surrounding medium are defined respectively ask1=ωε0μ0ε1, k2=ωε0μ0ε2, and k3=ωε0μ0. Additionally, the refractive index of the core and the shell are given by m1=k1/k3andm2=k2/k3. Finally, the electrical length of the particle and the core with respect to the wavenumber of the surrounding medium isνk3a2andαk3a1, respectively.

Although we are considering non-magnetic particles which are small enough that their behavior is primarily dominated by their TMr response, for completeness we include the TEr expressions as well. The quantities corresponding to the TMr excitation are denoted by the “(e)” superscript, while those associated with the TEr excitation are denoted by the “(m)” superscript. Additionally, in what follows the various quantities are presented in pairs, and in particular we use admittances for TMr and impedances for TEr excitation. The input TMr admittance and TEr impedance of the core-shell particle, normalized to Y0=ε0/μ0 andZ0=Y01, are given respectively by [14

14. J. R. Wait, “Electromagnetic scattering from a radially inhomogeneous sphere,” Appl. Sci. Res., Sect. B, Electrophys. Acoust. Opt. Math. Methods 10(5-6), 441–450 (1962). [CrossRef]

]
Y2n(e)=jm2ψn(m2ν)Anχn(m2v)ψn(m2ν)Anχn(m2v)
(17)
Z2n(m)=jm2ψn(m2ν)Bnχn(m2v)ψn(m2ν)Bnχn(m2v)
(18)
where
An=m2ψn(m1α)ψn(m2α)m1ψn(m2α)ψn(m1α)m2ψn(m1α)χn(m2α)m1χn(m2α)ψn(m1α)
(19)
and

Bn=m1ψn(m1α)ψn(m2α)m2ψn(m2α)ψn(m1α)m1ψn(m1α)χn(m2α)m2χn(m2α)ψn(m1α)
(20)

The Riccati-Bessel functions in the preceding expressions are defined as
ψn(ρ)=πρ2Jn+1/2(ρ)
(21)
and
χn(ρ)=πρ2Hn+1/2(2)(ρ)
(22)
where Jn+1/2() and Hn+1/2(2)()are the half-order Bessel and Hankel functions of the first and second kind, respectively.

Yext,n(e)(ν)=1jχn(ν)χn(ν)
(23)

Zext,n(m)(ν)=1jχn(ν)χn(ν)
(25)

As expected there is no crossing between the two functions indicating that this TEr mode contributes insignificantly to the particle’s optical response.

3.2 Short- and open-circuit conditions

In order to facilitate our analysis we introduce a set of auxiliary quantities. First, the input TMr admittance and TEr impedance of the core, normalized to Y0 andZ0, are defined respectively as
Y1n(e)=jm1ψn(m1α)ψn(m1α)
(26)
and

Z1n(m)=jm1ψn(m1α)ψn(m1α)
(27)

Furthermore, similar to Eq. (23) and Eq. (25), the fringing fields in the core exterior, or the field in the shell due to scattering by the core, are characterized by the TMr admittance
Yext,n(e)(m2α)=m2jχn(m2α)χn(m2α)
(28)
and the following TEr impedance

Zext,n(m)(m2α)=1jm2χn(m2α)χn(m2α)
(29)

Next, we define the characteristic TMr admittance and TEr impedance of a spherical transmission line (looking towards its origin) with a refractive indexmand a radiusr=r0. The expressions for the admittance/impedance are given by
Y0,n(e)(mk3r0)=jmψn(mk3r0)ψn(mk3r0)
(30)
and

Z0,n(m)(mk3r0)=jmψn(mk3r0)ψn(mk3r0)
(31)

At this point we rewrite the coefficientAnin two different ways as shown in Eq. (32) and Eq. (33).

An(d)=ψn(m2α)χn(m2α)jm2ψn(m2α)ψn(m2α)+jm1ψn(m1α)ψn(m1α)m2jχn(m2α)χn(m2α)+jm1ψn(m1α)ψn(m1α)
(32)
An(u)=ψn(m2α)χn(m2α)1jm1ψn(m1α)ψn(m1α)1jm2ψn(m2α)ψn(m2α)1jm1ψn(m1α)ψn(m1α)+jm2χn(m2α)χn(m2α)
(33)

Similarly, we rewrite the coefficientBn as
Bn(d)=ψn(m2α)χn(m2α)jm2ψn(m2α)ψn(m2α)jm1ψn(m1α)ψn(m1α)jm2χn(m2α)χn(m2α)jm1ψn(m1α)ψn(m1α)
(34)
and

Bn(u)=ψn(m2α)χn(m2α)m1jψn(m1α)ψn(m1α)m2jψn(m2α)ψn(m2α)m1jψn(m1α)ψn(m1α)m2jχn(m2α)χn(m2α)
(35)

Given the expressions in Eqs. (32)-(35), the particle’s TMr admittance and TEr impedance may be rewritten as
Y2n(e)=jm2ψn(m2ν)ψn(m2ν)1An(u)χn(m2v)ψn(m2ν)1An(d)χn(m2v)ψn(m2ν)
(36)
and

Z2n(m)=jm2ψn(m2ν)ψn(m2ν)1Bn(u)χn(m2v)ψn(m2ν)1Bn(d)χn(m2v)ψn(m2ν)
(37)

If we further define Ψ()andΩ()as
Ψ(x,y)χn(x)ψn(x)ψn(y)χn(y)
(38)
and
Ω(x,y)χn(x)ψn(x)ψn(y)χn(y)
(39)
then Eq. (36) and Eq. (37) may be written in the following compact form:
Y2n(e)=Y0,n(e)(m2ν)1Ψ(m2ν,m2α)1Y1n(e)1Y0,n(e)(m2α)1Y1n(e)+1Yext,n(e)(m2α)1Ω(m2ν,m2α)Y0,n(e)(m2α)+Y1n(e)Yext,n(e)(m2α)+Y1n(e)
(40)
and

Z2n(m)=Z0,n(m)(m2ν)1Ψ(m2ν,m2α)1Z1n(m)1Z0,n(m)(m2α)1Z1n(m)+1Zext,n(m)(m2α)1Ω(m2ν,m2α)Z1n(m)Z0,n(m)(m2α)Z1n(m)+Zext,n(m)(m2α)
(41)

The form of the preceding formulas is similar to the ones introduced by Wait in [13

13. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

]. From Eq. (40) it is evident that the particle’s admittance becomes infinite when the denominator goes to zero which results in the following condition:

Y1n(e)Y0,n(e)(m2α)Y1n(e)+Yext,n(e)(m2α)=1Ω(m2ν,m2α)
(42)

Furthermore, the same admittance becomes zero when the numerator in Eq. (40) goes to zero, or when

Y1n(e)Y0,n(e)(m2α)Y1n(e)+Yext,n(e)(m2α)=Y0,n(e)(m2α)Yext,n(e)(m2α)1Ψ(m2ν,m2α)
(43)

The expressions in Eq. (42) and Eq. (43) constitute the necessary conditions such that a non-magnetic two layer spherical particle can exhibit either zero input admittance or zero input impedance. One can immediately recognize the similarities between this pair of conditions and the corresponding expressions derived earlier for the quasistatic case. As a matter of fact, the similarities between the two pairs are better revealed if we take the Taylor expansion of the expressions given in Eq. (42) and Eq. (43). Following this procedure, it is straightforward to show that
1Ω(m2ν,m2α)=1f+O[(m2α)2]
(44)
and

Y0,n(e)(m2α)Yext,n(e)(m2α)1Ψ(m2ν,m2α)=12f+O[(m2α)2]
(45)

Moreover, it can be shown that by invoking the small argument approximation the left-hand side of Eq. (42) and Eq. (43) can be written as
Y1n(e)Y0,n(e)(m2α)Y1n(e)+Yext,n(e)(m2α)=m1(m1α)m2(m2α)+O[(m1α)3+(m2α)3]m1(m1α)+2m2(m2α)+O[(m1α)3+(m2α)3]
(46)
or

Y1n(e)Y0,n(e)(m2α)Y1n(e)+Yext,n(e)(m2α)ε1ε2ε1+2ε2
(47)

In other words there is a direct relationship between the two sets of conditions and as expected the expressions derived for the dynamic case are a generalization of those obtained based on the quasistatic analysis.

3.3 Discussion

One of the interesting outcomes from the quasistatic analysis performed previously was the fact that the short- and the open-circuit states of a core-shell particle can be mimicked by an effective homogeneous dielectric sphere whose permittivity value becomes zero and infinite, respectively. This was further supported by demonstrating that in the realistic case of a core-shell particle where its effective dielectric properties follow a Lorentzian-type behavior. This result is the outcome of mixing a Drude filler (core) in a non-dispersive host (shell), where in this particular case the medium is governed by the CM mixing rule.

Now, if we compute the small argument approximation of Eq. (36) we arrive at

Y2n(e)Y0jωa2ε02ε21+2fα121fα12
(48)

In other words, there is clear evidence that even in the dynamic case the TMr input admittance of a core-shell particle can be associated to that of a homogeneous sphere whose permittivity properties are described by Eq. (11). In order to validate this statement the following task was performed: a homogeneous sphere was assumed with a radius of 20 nm and a permittivity that can be represented as the equivalent of a parallel connection of RLC circuits [16

16. R. E. Diaz and N. G. Alexopoulos, “An analytic continuation method for the analysis and design of dispersive materials,” IEEE Trans. Antenn. Propag. 45(11), 1602–1610 (1997). [CrossRef]

], such that

εe=ε+i=1N1Li1LiCi+jωRiLiω2
(49)

Next, through a data-fitting approach, the number of these RLC circuits and the values of the corresponding circuit elements were determined such that the TMr admittance and the TEr impedance of the homogeneous sphere given by Eq. (30) and Eq. (31) are equivalent to Eq. (40) and Eq. (41), respectively. In this analysis only mode n=1 was considered.

Fig. 5
Fig. 5 Core-shell effective permittivity computed according to Eq. (49) and Eq. (11). (a) Real part. (b) Imaginary part.
shows the core-shell effective permittivity as computed after performing the data fitting, along with the effective permittivity value obtained from Eq. (11), i.e. from direct application of the CM mixing rule. It can be seen that the effective permittivity obtained by the dynamic analysis exhibits its Lorentz resonance at a frequency shifted with respect to the one predicted by the quasistatic formulation.

Additionally, in order to gain a better insight into the properties of the effective homogeneous sphere, we plot the resistance and reactance for both the TMr and TEr polarizations in Fig. 6
Fig. 6 Comparison between the input impedance of the core-shell particle and an equivalent effective homogeneous dielectric sphere. (a) ZTM resistance. (b) ZTM reactance. (c) ZTE resistance. (d) ZTE reactance.
, along with the corresponding quantities for the core-shell particle. Evidently, the effective homogeneous sphere can mimic very well the TMr impedance of the core-shell particle, however it is noticed that a minor discrepancy occurs in the TEr response. The spurious resonance displayed by ZTE occurs at the same frequency where the real part of the effective permittivity exhibits its Lorentz resonance. In order to get a better understanding of the nature of this artifact we perform a Taylor expansion on Eq. (31), which yields

Z0,n(m)(mk3r0)=jmk3r02m{1+O[(mk3r)2]}
(50)

Evidently, the TEr impedance is proportional to the properties of the homogeneous sphere. Consequently, when the latter resonates, the impedance will also exhibit a Lorentz-type resonance, as indicated in Fig. 6(c) and 6(d). This artifact is also translated into a spurious peak in the effective particle’s extinction efficiency as can be seen in Fig. 7
Fig. 7 Extinction efficiency comparison: core-shell vs. effective homogenous sphere with permittivity given by Eq. (49).
. However, the magnitude of this peak is extremely minute, which is in accordance with the fact that the values of ZTM are three orders of magnitude larger than those of ZTE.

As a final comment it should be mentioned that the most complete effective description of the core-shell particle under consideration is through a combination of anisotropic surface impedances where ZTMZθ corresponds to the ZTM input impedance of a homogeneous sphere whose permittivity is given by Eq. (49). On the other hand, ZTEZφ is given by the ZTE input impedance of a homogeneous sphere whose dielectric properties are equal to those of the shell. This last conclusion can be drawn from the observation that for the particular core-shell particle under consideration we have

Z2n(m)Z0,n(m)(m2ν)
(51)

4. Conclusions

We have introduced a transformative approach for the design of tunable, wavelength dependent nanoswitches that are robust and can be easily synthesized using standard nanofabrication techniques. The attractive characteristics of the proposed methodology stem from the fact that the desired high impedance and high admittance conditions are realized by utilizing readily available core-shell particles, instead of some engineered artificial material that may require a considerable fabrication effort. Second, our approach exploits the fact that electrically small core-shell particles can be treated as nanomixtures whose material properties are governed by the CM mixing rule. As a result by judiciously choosing the material constitution or the volume fraction of the particle, it is possible to tune the nanoswitch response in a fully controlled manner. The results obtained here clearly demonstrate the inherent tunability that plasmonic core-shell particles offer, and how they can provide a compact solution for the practical realization of optical switching functionality at the nanoscale. Their switching properties are polarization independent, therefore no additional effort is required to appropriately align them when incorporated into more complex nanostructures, such as arbitrary optical nanoantenna configurations.

In our analysis we focused on demonstrating the feasibility of utilizing a core-shell particle to exhibit high impedance and high admittance characteristics. Towards this end we employed the inhomogeneous spherical transmission line theory to characterize core-shell particles in terms of their input impedance. This representation was utilized to investigate and ultimately establish the necessary conditions that would allow a core-shell particle to function as a frequency dependent nanoswitch, operating as either a short- or an open-circuit termination, for an impinging plane wave. It was demonstrated that in order for these conditions to hold the core and the shell regions need to have permittivity values that are opposite in sign. This requirement can be trivially realized in the optical frequency range where noble metals exhibit negative permittivity values.

References and links

1.

J. R. Wait, Electromagnetic Waves in Stratified Media (Pergamon, 1962).

2.

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995).

3.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

4.

A. Sihvola and L. V. Lindell, “Transmission line analogy for calculating the effective permittivity of mixtures with spherical multilayer scatterers,” J. Electromagnet. Wave. 2(2), 741–756 (1988).

5.

A. Sihvola and L. V. Lindell, “Polarizability and effective permittivity of layered and continuously inhomogeneous dielectric spheres,” J. Electromagnet. Wave. 3(1), 37–60 (1989). [CrossRef]

6.

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76(24), 245403 (2007). [CrossRef]

7.

A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A non-linear inverse scattering design approach,” Phys. Rev. B 82(3), 035117 (2010). [CrossRef]

8.

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005). [CrossRef] [PubMed]

9.

H. Kettunen, H. Wallen, and A. Sihvola, “Electrostatic resonances of a negative-permittivity hemisphere,” J. Appl. Phys. 103(9), 094112 (2008). [CrossRef]

10.

A. Alù and N. Engheta, “Optical nanoswitch: An engineered plasmonic nanoparticle with extreme parameters and giant anisotropy,” New J. Phys. 11(1), 013026 (2009). [CrossRef]

11.

A. Alù and N. Engheta, “Optical metamaterials based on optical nanocircuits,” Proc. IEEE 99(10), 1669–1681 (2011). [CrossRef]

12.

A. Sihvola, “Character of surface plasmons in layered spherical structures,” Prog. Electromagnetics Res. 62, 317–331 (2006). [CrossRef]

13.

P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

14.

J. R. Wait, “Electromagnetic scattering from a radially inhomogeneous sphere,” Appl. Sci. Res., Sect. B, Electrophys. Acoust. Opt. Math. Methods 10(5-6), 441–450 (1962). [CrossRef]

15.

A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22(10), 1242–1246 (1951). [CrossRef]

16.

R. E. Diaz and N. G. Alexopoulos, “An analytic continuation method for the analysis and design of dispersive materials,” IEEE Trans. Antenn. Propag. 45(11), 1602–1610 (1997). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(290.5850) Scattering : Scattering, particles
(260.2065) Physical optics : Effective medium theory

ToC Category:
Plasmonics

History
Original Manuscript: August 14, 2013
Revised Manuscript: October 2, 2013
Manuscript Accepted: October 3, 2013
Published: October 24, 2013

Citation
Anastasios H. Panaretos and Douglas H. Werner, "Tunable wavelength dependent nanoswitches enabled by simple plasmonic core-shell particles," Opt. Express 21, 26052-26068 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26052


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. R. Wait, Electromagnetic Waves in Stratified Media (Pergamon, 1962).
  2. W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE, 1995).
  3. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).
  4. A. Sihvola and L. V. Lindell, “Transmission line analogy for calculating the effective permittivity of mixtures with spherical multilayer scatterers,” J. Electromagnet. Wave.2(2), 741–756 (1988).
  5. A. Sihvola and L. V. Lindell, “Polarizability and effective permittivity of layered and continuously inhomogeneous dielectric spheres,” J. Electromagnet. Wave.3(1), 37–60 (1989). [CrossRef]
  6. J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B76(24), 245403 (2007). [CrossRef]
  7. A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A non-linear inverse scattering design approach,” Phys. Rev. B82(3), 035117 (2010). [CrossRef]
  8. N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett.95(9), 095504 (2005). [CrossRef] [PubMed]
  9. H. Kettunen, H. Wallen, and A. Sihvola, “Electrostatic resonances of a negative-permittivity hemisphere,” J. Appl. Phys.103(9), 094112 (2008). [CrossRef]
  10. A. Alù and N. Engheta, “Optical nanoswitch: An engineered plasmonic nanoparticle with extreme parameters and giant anisotropy,” New J. Phys.11(1), 013026 (2009). [CrossRef]
  11. A. Alù and N. Engheta, “Optical metamaterials based on optical nanocircuits,” Proc. IEEE99(10), 1669–1681 (2011). [CrossRef]
  12. A. Sihvola, “Character of surface plasmons in layered spherical structures,” Prog. Electromagnetics Res.62, 317–331 (2006). [CrossRef]
  13. P. B. Johnson and R. W. Christy, “Optical constants of noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  14. J. R. Wait, “Electromagnetic scattering from a radially inhomogeneous sphere,” Appl. Sci. Res., Sect. B, Electrophys. Acoust. Opt. Math. Methods10(5-6), 441–450 (1962). [CrossRef]
  15. A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys.22(10), 1242–1246 (1951). [CrossRef]
  16. R. E. Diaz and N. G. Alexopoulos, “An analytic continuation method for the analysis and design of dispersive materials,” IEEE Trans. Antenn. Propag.45(11), 1602–1610 (1997). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited