Tunable Refractive Index Materials with Metallic Nano-Spheres

Tunable Refractive Index Materials with Metallic Nano-Spheres Dispersed in Organic Liquids Andres Diaza, Shoichi Kubob,c, Yan Tanga, Justin Lioua, Theresa S. Mayera, Iam Choon Khooa*, Thomas E. Malloukb* a Department of Electrical Engineering, and bDepartment of Chemisty, The Pennsylvania State University, University Park, PA 16802, USA; cChemical Resources Laboratory, Tokyo Institute of Technology, R1-11, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan ABSTRACT Metamaterials are of substantial current interest because they may exhibit unusual and/or configurable optical responses. We studied the optical properties of gold and silver nanoparticles dispersed in different organic liquids in the visible to near-IR. Calculation of the refractive indices of metallic nanospheres or metallic-coated silica spheres in liquid crystals show the possibility of tuning and varying the refractive index by reorientation of the liquid crystal molecules. Measurements of the refractive indices of gold nanoparticles in dodecane were experimentally studied by using spectroscopic ellipsometry and a reasonable agreement with the theoretical results based on Mie scattering was obtained. Finally, the effect of gold and silver nanospheres on the nonlinear absorption properties of an organic liquid (L34, a 4,4’dialkyl phenyleneethynylene) was studied. The results suggest that metallic nanoparticles dispersed in a host organic fluids can be good materials for fabrication of low and tunable index materials in the visible to near-IR wavelength range, and for the enhancement of the nonlinear absorption of liquids used in switching applications. Keywords: gold, silver, nanoparticles, liquid crystals, low-index materials, metamaterials, nonlinear optics

1. INTRODUCTION Metamaterials, which are composite materials with engineered optical properties, are of great current interest, both for fundamental reasons and because of their potential applications in optics and communication devices.1-16 In order to obtain such optical properties, which are quite different from those of natural materials, a number of artificially designed structures have been proposed and studied both theoretically and experimentally. They mainly consist of finely patterned metallic or dielectric materials, and the composite structures are referred to as metamaterials. In order to fabricate these complex metallodielectric patterns, it is typically necessary to use lithographic techniques.2, 3, 8, 9 Conventional lithographic fabrication is usually limited to a feature sizes not much smaller than microns. Therefore these structures respond to infrared or longer wavelengths (corresponding to THz and GHz frequencies) and there are few reports of optical metamaterials in the visible.2 The “top down” fabrication of optical metamaterials becomes increasingly difficult and expensive as the feature size approaches near IR and visible wavelengths. An alternate approach is to use nanospheres or nanoshells dispersed in a host medium.11, 12, 15, 16 It is theoretically expected that these structurally disordered systems can also exhibit low or negative refractive indices, and the existence of well established methods to synthesize monodisperse spheres or nanorods that contain plasmonic metals make it a cost-effective and simple alternative to lithography. Recently, we have proposed an optical metamaterial consisting of core-shell structure spheres dispersed in a nematic liquid crystal. In that theoretical study, it was shown that polaritonic dielectric core – metallic nanoshell composites could exhibit negative optical constants of permittivity, permeability, and refractive index in the µm wavelength range. Furthermore, by using the optical anisotropy of a liquid crystal, it should be possible to change the effective optical constants from negative through zero to positive values. Such tunability of optical properties would be very desirable for potential applications in, for example, switching devices. Although there have been many reports of the optical

* [email protected]; phone 1-814-863-2299; fax 1-814-865-4501; [email protected]; phone 1-814-863-9637; fax 1-814-863-8403. Liquid Crystals XI, edited by Iam Choon Khoo, Proc. of SPIE Vol. 6654, 66540V, (2007) · 0277-786X/07/$18 · doi: 10.1117/12.736552

Proc. of SPIE Vol. 6654 66540V-1

properties of plasmonic nanoparticles and core-shell particles, to our knowledge there are so far no experimental studies investigating the optical properties of polaritonic spherical and core-shell nanostructures in a tunable medium.

2. THEORY The complex refractive index of metallic nanoparticles in a medium of tunable permittivity was calculated using Mie theory to model light absorption and scattering.17 In this method, which is described in detail elsewhere, 18 the scattered magnetic field is decomposed into multipole terms, from which the 2m –pole coefficients of the electric and magnetic fields are calculated. The effective permittivity and permeability of the material are then calculated from these scattering coefficients through the ClausiusMosotti relations19,20, as summarized in the following expressions.

µ reff =

3 k host + j 4π Nb

1

(1)

3 k host − j 2π Nb

1

ε

eff r

3 ⎛ khost + j 4π Na = ε host ⎜ 3 ⎜ k − j 2π Na ⎝ host

1

1

⎞ ⎟⎟ ⎠

(2)

khost is the optical wavevector in the host fluid, εhost is the permittivity of the host (assumed to be non-magnetic), and N is the

volume density of the spheres, related to the filling fraction f by f = 4π Nrsphere / 3 . a1 and b1 are the Mie coefficients for either a 3

solid sphere (of radius r with optical parameters ε1 and µ1) or of a metal-coated silica-core structure as shown in Figure 1.12, 17

shell r2 core ε1 , µ1

r1

liquid crystal ε host , µhost µ1 ≈ µ2 ≈ µ host ≈ 1

ε 2 , µ2 Figure 1. Nanoshell structure and parameters.

Both gold and silver nanospheres and nanoshells were considered, with a complex permittivity that follows a Lorentz-Drude model to account for the free-electron and interband parts of the dielectric function.21 Tunability may be achieved by varying the permittivity of the host. If the host is a liquid crystal, this can readily be done by aligning the molecules in the liquid by using an external electric field or a polarized laser beam. In this case, the optical wave vector k3 may be calculated from the vacuum wave vector k0, the ordinary and extraordinary permittivities of the liquid crystal (εo and εe respectively), and the tilt angle θ of the liquid crystal molecules (itself a function of the alignment force): k host =

⎛

1/ 2

⎞ ⎟ k0 2 2 ⎝ ε e cos θ + ε o sin θ ⎠

ε 3 k0 = ⎜

ε eε o

(3)

For nanometer-sized metallic nanoparticles, confinement effects on the mean free path of the free electrons have to be considered, resulting in a drastic increase in the rate of scattering from the surface of the particle relative to bulk scattering. This is taken into account by adding to the damping constant γ 0 in the free-electron Drude model a surface scattering rate ω S = Av f / r , where vf is the Fermi velocity (e.g. v f = 1.4 × 108 cm/s for Au), r is the radius of the nanoparticle, and A is a proportionality factor of the order of unity. 22-24 We have taken this factor to be 1.4 for gold24, 25


and 0.25 for silver26. Therefore, the size-dependent permittivity as obtained from literature values21 of the bulk permittivity ( ε bulk ) may be expressed as:24

ε ( ω , r ) = ε bulk (ω ) +

ω p2 ω 2 + iωγ 0

−

ω p2 ω 2 + iω ( γ 0 + AvF / r )

where ω p is the plasma frequency (9.03 eV for gold and 9.01 eV for silver). As an example of the calculated properties of nanoparticle-doped liquids, consider the effect of gold or silver nanospheres in a dielectric host liquid. Figure 2a shows the calculated real and imaginary refractive indices of 2.5 nm diameter gold nanoparticles dispersed at a volume fraction of 0.25 in a host medium in which the dielectric constant (εhost) varies between 1.0 and 4.0. Figure 2b shows the same calculation for 4.5 nm diameter silver nanospheres in the same media. The sizes of the nanospheres match those synthesized, as described in the next section. (a)

3.5

1.4 1.2

εhost=4.0

3.0

εhost=4.0

1.0 2.5 k

n

0.8 0.6

2.0

0.4 1.5

1.0

(b)

εhost=1.0 400

0.2

600 800 1000 Wavelength (nm)

0.0

1200

6

400

600

800 1000 Wavelength (nm)

1200

5

εhost=4.0

5

4

εhost=4.0

4

3

3

k

n

εhost=1.0

2 2

εhost=1.0

1 0

400

εhost=1.0

1


1200

0

400

600


1200

Figure 2. Calculated real (n) and imaginary (k) refractive indices for (a) 2.5 nm diameter gold nanospheres and (b) 4.5 nm diameter silver nanospheres in a host medium of varying dielectric constant. For both figures the volume fraction is 0.25 and the relative permittivity of the host varies between 1.0 and 4.0 in steps of 0.5.

In both cases, the range of values of the real refractive index n is greater than that expected from variation of the host permittivity alone. For the gold nanoparticles, the effective index is always greater than the index of the host medium and always greater than 1.0, even if the volume fraction is increased to more than 60%. As suggested by our earlier calculations and experiments for gold nanoparticle dispersions, only when the radius is increased (while maintaining a very high nanosphere concentration) will the effective refractive index come close to 1.0.34 Silver nanospheres, on the other hand, show greater variation in the range of n and k (this would also be true in the Ag nanospheres were the same size as the Au spheres). Moreover, the clearly defined minima and maxima in the silver spectra may be tuned by varying the permittivity of the host medium, and the real refractive index can have values less than 1.0. For the case shown, a minimum of neff = 0.524 is obtained at a wavelength of 435 nm. The refractive index will exhibit values less than unity as long as the volume fraction is high enough (approximately 0.10 for εhost = 4.0).


Figure 3 shows the calculated refractive indices for gold (Fig. 3a) and silver (Fig. 3b) nanoshells. For both figures, a 25 nm diameter silica core is assumed, covered by a 5 nm thick metallic shell. The volume fraction is the same as in Fig. 2. In the case of nanoshells, both gold and silver exhibit a region of real effective refractive index less than unity. For gold nanoshells, a minimum neff = 0.635 is obtained at 779 nm for εhost = 2.0. The core-shell geometry is responsible for this effect, and a solid gold sphere of the same total diameter would exhibit a refractive index always greater than 1.0. In the case of silver nanoshells, the geometry also enhances the variation of the refractive index, and a lower refractive index (as compared with Fig 2b or with a solid 30 nm diameter silver sphere) is obtained. For the different host permittivities, the minimum value of neff varies between 0.4 and 0.55 in the range 640 to 850 nm. Nanoshell particles of this kind have been studied extensive, although mainly at larger dimensions, e.g., with >100 nm cores.27-34 These calculations suggest that nanoshells made with smaller cores may be very interesting as components of low-and tunable-refractive index fluids, particularly in the near infrared where the k value (and therefore loss) is relatively low, but n can be tuned over a broad range. (a)

5

4

εhost=4.0

εhost=4.0

4

3

k

n

3 2

2

εhost=1.0

1

0

(b)

400


1

0

1200

6

εhost=1.0

400

600


1200

5

εhost=4.0

εhost=4.0

5

4

4

k

n

3 3

εhost=1.0

2

εhost=1.0

2 1

1 0

400


1200

0

400

600


1200

Figure 3. Calculated real and imaginary refractive indices for (a) gold and (b) silver nanoshells. The core is a silica sphere with a diameter of 25nm and the shell is 5 nm thick. The volume fraction is 0.25 and the permittivity of the host medium is varied from 1.0 to 4.0 in steps of 0.5.

3. NANOPARTICLE SYNTHESIS AND CHARACTERIZATION Spherical gold and silver nanoparticles were synthesized by a two-phase method, as reported previously.18 The surfaces of nanoparticles made by this method are covered with self assembled monolayer of alkanethiols. The hydrophobic alkanethiol layer prevents aggregation of the nanoparticles and facilitates their dispersion in organic solvents. The diameters of the gold and silver nanoparticles were 2.5 and 4.5 nm, respectively, from transmission electron micrographs. The gold nanoparticles were re-dispersed in n-dodecane, which was used because of its low volatility and its chemical compatibility with the dodecanethiol monolayer. The nanoparticle suspensions were poured onto a frosted glass slide, and the refractive indices were measured by using spectroscopic ellipsometry.18 Gold and silver nanoparticles were also dispersed in nonlinear liquid L34 in order to study the enhancement of the nonlinear optical properties of L34 by the plasmonic particles.


4. RESULTS AND DISCUSSION Figure 4a shows the comparison of experimentally measured and theoretically calculated refractive indices of pure dodecane and of gold nanoparticles dispersed in dodecane at a volume fraction of 1.0 %. Both traces for real refractive index of gold-doped dodecane have dips at around 600 nm, and peak at around 600-700. In the case of the imaginary index k, there are shoulder peaks at about 550 nm. Those spectral features are quite different from those of bulk gold as expected, and can be attributed to the plasmon resonance of the nanospheres. Although there are differences between the calculated and experimental curves, the overall shapes of the curves are similar. (a)

1.47

0.03

1.46

Au-doped dodecane

0.02

1.45

Au-doped dodecane

1.44-

1.43

-— V

Pure dodecane

1.421

Pure dodecane

I 1.41 -4

400

500

600

700

800

900

400

600 700 Wavelength I nm

500

Wavelength I nm 1.455

1.455

Experiment Calculation


1.450 1.445

1.445

1.440

1.440

1.440

1.435

1.435

1.435

1.430

1.430

1.430

1.425

1.425

1.425

1.420

1.420

1.420

0.0

0.2 0.4 0.6 0.8 Volume fraction / %

1.0

0.0



1.450

1.445 n at 600 nm

n at 500 nm

1.450

900

1.455

n at 700 nm

(b)

800

1.0

0.0


1.0

Figure 4. (a) Real (n) and imaginary (k) parts of the refractive indices. Solid line: calculated results; markers: experimental results. (b) Variation of the real refractive index at 500, 600, and 700 nm for different volume fractions.

A constant value of A = 1.4 was assumed for the proportionality factor in the electron mean free path correction. In reality, this proportionality factor may be a function of the particle size and the frequency, and better agreement between the theoretical values and the experimental measurements is expected if further corrections of A are taken into account (to be explored in a future study). To measure the effects of Au and Ag nanoparticles on the optical properties of a nonlinear host medium, 2 mm-thick samples of gold and silver nanospheres in the N,N’-dialkyl-phenyleneethynylene liquid L34 were prepared. L34 is a single constituent liquid synthesized at Penn State with molecular structure shown in Figure 5. Characterization of the molecular and optical parameters of L34 has been done through picosecond and nanosecond z-scans and time delayed picosecond pump-probe studies conducted at UCF –CREOL.35, 36 The general model of the nonlinear optical response of L34, which leads to optical switching effects, is two-photon absorption from the ground level and further transition into


triplet states.37 The switching effects can also be derived from defocusing effects which are caused by the dependence of refractive indices on the intensity of incident light. C3H7

C

C

C4H9

Figure 5. Molecular structure of L34. Transmission measurements were taken as a function of the input energy using 250 ns FWHM (full width at halfmaximum) pulses from an Alexandrite laser at 748.5nm. The beam was focused into the sample using a lens with focal length f=50mm, and the output was collected using a similar lens. The results are shown in Figure 6. 1.0E-05 1

1.0E-04

1.0E-03

1.0E-02

Transmittance

0.1

0.01

Pure L34 Au-doped L34 Ag-doped L34

0.001 Input Energy (J)

Figure 6. Transmission measurements for 2-mm thick samples of pure L34, and gold- and silver-doped L34.

The L34 samples doped with gold and silver nanospheres show an enhanced nonlinearity represented by a greater variation in the range of transmittance values (by comparison, a completely linear response would have zero slope). To quantify this behavior, consider for example the drop in the transmittance in the decade of 80 to 800 µJ. This drop is 37% for pure L34 but approximately twice for Au-doped and Ag-doped L34 (78% and 67% respectively). We attribute this effect to the enhancement of the incident electric field around the metallic nanoparticles which in turn increases the two-photon absorption effect of L34. The field enhancement occurs when the incident light is resonant with the plasmons at the surface of the nanospheres.38, 39 In order to distinguish the effects of non-linear absorption and defocusing, another series of measurements was carried out in which an aperture was placed in front of the detector in order to remove defocused light. The transmittances collected with and without the aperture were almost same. This shows that non-linear absorption, rather than defocusing, is the principal cause of optical switching. A more detailed study of this effect will be reported in a future publication.

5. CONCLUSIONS It has been shown that metallic dispersed spheres in organic liquids (dodecane, L34, and liquid crystals) are very interesting materials for achieving tunability of the refractive index, resonances in the visible, and enhancement of nonlinear optical properties. The optical properties of Au- and Ag-doped n-dodecane were modeled theoretically and studied experimentally by using spectroscopic ellipsometry. These calculations show that gold and in particular silver


nanoshells, when dispersed in fluid dielectric media, should have spectral regions of low refractive index, and that the real part of the refractive index should be highly tunable in the near infrared. In proof-of-concept experiments with dispersed gold nanospheres, the measured spectra agree with the calculated results based on Mie scattering theory. As expected, resonances in the refractive indices became more pronounced as the volume fraction of the dopants is increased. Metallic nanosphere dopants were also shown experimentally to increase the nonlinear absorption of the organic liquid L34, suggesting a simple way to improve the switching response of such nonlinear absorbers. In the future we will explore the effects of increasing the concentration metallic nanodopants, in order to test the theoretical prediction of low refractive index in the region of plasmon resonance bands. These experimental conditions should be achievable with the use of other solvents and/or surfactants to improve nanoparticle dispersion.

6. ACKNOWLEDGMENTS This work was supported by the National Science Foundation Materials Research Science and Engineering Center (MRSEC) at Penn State under grant DMR-0213623. S. K. was also supported by Research Fellowships of the Japan Society for the Promotion of Science on Young Scientists.

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