Plasmonic quantum dots for nonlinear optical applications [Invited]

M. Klopfer; R. K. Jain

doi:10.1364/OME.1.001353

1. Motivation and issues

High-efficiency light absorbing and emitting nanostructures are critically needed for a large range of opto-electronic devices and systems applications, ranging from solar cells and simple detectors to advanced light emitter-based applications, including those based on multiphoton light absorption. As a case in point, two-photon absorption-induced fluorescence (TPAF) has been demonstrated as a powerful nonlinear optical phenomenon for several bio-imaging applications – particularly for deep-tissue imaging [1] – and for photodynamic therapy [2]. In photodynamic therapy, the photon generated by two-photon upconversion is used to generate cytotoxic reactive oxygen species (ROS) in cancer tissue. In the latter case, focusing intense near-infrared radiation (NIR) in cancer tissue that is relatively transparent to the NIR (whose wavelength is in the tissue optical transparency window of 600–1300 nm) can result in deep tissue penetration followed by selective destruction of malignant cells via efficient TPAF-induced ROS generation [2]. Additional targeting of specific tissue can also be achieved by functionalizing the TPAF nanoparticles with biomolecules to cause increased accumulation in the target tissue, both for photodynamic therapy and for imaging applications.

With regard to nanostructures for TPAF-based bioimaging, there has been a long-standing need for nonphotobleaching and nontoxic TPAF fluorophores at the highest brightnesses achievable. Because of their numerous advantages over other fluorophores, including: (a) broad absorption spectra and readily tunable emission options (b) high quantum yields, (c) relatively high photochemical stability, and (d) relatively large two-photon absorption cross sections, semiconductor quantum dots (QDs) have attracted significant attention as TPAF nanoparticle labels; nevertheless, the cytotoxicity of several elements (such as cadmium) contained in QDs –along with the need for higher brightness nanoparticles of sub-100 nm dimensions – has created an unresolved need for new nanoparticle emitters, particularly for in vivo clinical applications.

2. Proposed solution

We have previously proposed relatively simple plasmonic quantum dot (PQD) structures for use as such high-brightness light emitters [3–6]; these comprise one or more QDs enclosed in an appropriate noble metal (typically gold or silver) nanoshell, as shown schematically in Figure 1 (for the case of a single concentric QD structure), with an appropriate dielectric insulating layer between the QDs and the metallic nanoshell to minimize nonradiative decay and optimize the plasmonic resonant enhancement. In appropriately-designed and optimised PQD structures, the proposed dielectric and metallic nanoshell layers will not only help enhance the electric fields in the center of the nanostructure, thus increasing the brightness of the nanoparticles, but will also chemically isolate the QDs from the tissue and significantly reduce the toxicity of such TPAF nanoparticles.

Fig. 1 Schematic of a basic double-shelled PQD nanostructure with dielectric spacer

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The use of similar noble metal nanoshells for field enhancement and study of their plasmonic properties has also been discussed earlier by several researchers [7–21]. However, most of this previous research has focussed on properties such as location and shift of the plasma resonances, elucidation of far-field optical properties such as absorption and extinction spectra, and the study of field enhancements external to the metal nanoshell structures. In particular, it was shown that the plasmon-plasmon interaction of the inner and outer concentric surfaces of metallic nanoshells results in a hybridization of the symmetric and antisymmetric plasmon resonances in these nanostructures [13], and that single and multilayered core-shell nanostructures can significantly enhance the electric fields and the surface-enhanced Raman scattering (SERS) properties external to these nanostructures [12,14,15]. This paper focuses on optimization of the enhancement of the fields within the quantum dot/dielectric shell/metallic nanoshell structures to enable the highest field enhancements at the location of the quantum dots near the center of the nanostructures, thereby enabling the design of ultrahigh brightness plasmonic quantum dot emitters, particularly for TPAF applications.

Even though at first glance, plasmonic field enhancements outside the metallic shell nanoparticles appear fairly obvious, the physics of the plasmonic enhancement of the fields inside the metallic nanoparticles is not as obvious. Noting however, that the thicknesses of the metallic shells are much less than the skin depths in these materials, and that attenuation of the optical frequencies of interest is not a significant issue, the behaviours of the strong surface plasmon resonances (SPRs) in these nanoparticles, and the spatial distribution of the fields – both inside and outside these nanoparticles – are best attributed to relatively complex but somewhat intangible SPR interactions that are most simply and most accurately describable by simple Mie scattering theory, with the primary focus of the past work having been on the electric field external to such multilayered nanoparticles [7,12,13]. Enderlein [10] has hypothesized that the external shell acts somewhat like a nanocavity for the field enhancement, while Liaw [20] has proposed that the net effect of the Mie scattering is similar to a focussing of the irradiated light into the center of the nanoshelled structures. However, neither of these authors substantiate the physics of the cavity-like behavior or the focussing behavior in any rigorous or tangible manner, such as by predicting the spectral location of the resonances or the degree of focussing as a function of nanocavity or nanoshell dimensions. Xu [14] further used the concept of an “optical condenser” and that of “collective coupling of surface plasmons between the multiple metal shells” to postulate that multilayered metal shells could act as more “effective optical condensers to focus the incident light toward the geometric center multiplicatively”, but focussed only on large field enhancements in multilayered structures with metallic cores, an area that was subsequently researched also by Kodali et al [16]. The latter researchers also demonstrated large field enhancements external to large-shell-number multilayered nanoshell structures in such “nanolayered alternating metal-dielectric probes” (“nano-LAMPs”) for SERS applications. We will also elaborate on the specific relevance of other related research [10, 14, 16, 18–21] to our work in the “Related work” section below.

3. Mathematical background and methodology used to compute fields and electric field enhancements

We use Mie scattering theory with a vector spherical harmonic (VSH) [22] model to analyse the EFE in multilayered nanostructures. The simplest geometric model used here for this Mie scattering analysis assumes nanoparticles (NP) that contain a single semiconductor quantum dot core, a single dielectric ”nanoshell” layer, and a single noble metal nanoshell layer, and that these nanoparticles are surrounded by water (since aqueous tissue is largely water), as is most relevant for bio-imaging applications. The analysis can be generalized to any semiconductor quantum dot material and size quite easily; however, we focus here primarily on TPA excitation of a 6 nm CdSe QD whose fluorescence peak occurs at a wavelength of approximately 600 nm, and whose optimum excitation wavelengths for TPA excitation lie in the 800 nm to 950 nm range.

Even though mathematical methods used here for our Mie scattering calculations have been described very well by several researchers [7, 14, 22], we describe a few relevant details of the specific mathematical methods used in this work for the convenience of the reader. Note that in the calculations presented here, we have ignored modifications to the bulk dielectric constants of the noble metals – caused by size-dependent and mean-free-path effects [14,19] in the ultra-thin shell thicknesses – as well as modifications to these dielectric constants [23,24] caused by experimental limitations (notably those in the fabrication of smooth and continuous ultrathin noble metal films), but will elaborate on these issues in Sections 4 (during the discussion of our results) and 7 (Summary) below.

The successive layer numbers are denoted by l, where the core corresponds to l = 1, and larger l numbers designating successive layers, with the largest layer number designating the surrounding medium (water). The electric and magnetic fields in each layer l can be expressed as sums of vector spherical harmonics $M_{nm}^{(i)} (k, r, Ω)$ , $N_{nm}^{(i)} (k, r, Ω)$ , as follows:

E^{l} = \sum_{n, m} α_{nm}^{l} M_{nm}^{(1)} (k_{l}, r, Ω) + δ_{nm}^{l} M_{nm}^{(3)} (k_{l}, r, Ω) + γ_{nm}^{l} N_{nm}^{(1)} (k_{l}, r, Ω) + β_{nm}^{l} N_{nm}^{(3)} (k_{l}, r, Ω)

H^{l} = \sum_{n, m} α_{nm}^{l} k_{l} N_{nm}^{(1)} (k_{l}, r) + δ_{nm}^{l} k_{l} N_{nm}^{(3)} (k_{l}, r) + γ_{nm}^{l} k_{l} M_{nm}^{(1)} (k_{l}, r) + β_{nm}^{l} k_{l} M_{nm}^{(3)} (k_{l}, r)

Where the unknown coefficients of the VSHs are denoted by $α_{nm}^{l}$ , $β_{nm}^{l}$ , $δ_{nm}^{l}$ , and $γ_{nm}^{l}$ . Note that the vector spherical harmonics are defined as:

M_{nm}^{(i)} (k, r, Ω) = \nabla \times r ξ^{(i)} (k, r, Ω) \hat{r},

N_{nm}^{(i)} (k, r, Ω) = \frac{1}{k} \nabla \times M_{nm}^{(i)} (k, r, Ω),

ξ^{(i)} (k, r, Ω) = \frac{1}{\sqrt{n (n + 1)}} z_{n}^{(i)} (k r) Y_{nm} (Ω),

z_{n}^{(1)} (k r) = j (k r),

z_{n}^{(3)} (k r) = h^{1} (k r),

where j is the spherical Bessel function and h¹ is the spherical Hankel function of the first kind. The spherical coordinates are denoted by r,θ,ϕ, with Ω = (θ,ϕ), the wavenumber is defined as

k = \sqrt{ɛ} ω / c

.

Integrating over the surface of a sphere leads to the following orthogonality relations:

\iint M_{nm}^{(i)} (k, r, Ω) \cdot N_{n^{'} m^{'}}^{(j)}^{*} (k, r, Ω) d Ω = 0

\iint N_{nm}^{(i)} (k, r, Ω) \cdot N_{n^{'} m^{'}}^{(j)}^{*} (k, r, Ω) d Ω = 0 \forall m \neq m^{'} \lor n \neq n^{'}

and

\iint M_{nm}^{(i)} (k, r, Ω) \cdot M_{n^{'} m^{'}}^{(j)}^{*} (k, r, Ω) d Ω = 0 \forall m \neq m^{'} \lor n \neq n^{'}

Defining $ℛ_{nm}^{l} (r) = α_{nm}^{l} M_{nm}^{(1)} (k_{l}, r, Ω) + δ_{nm}^{l} M_{nm}^{(3)} (k_{l}, r, Ω)$ , $𝒬_{nm}^{l} (r) = γ_{nm}^{l} N_{nm}^{(1)} (k_{l}, r, Ω) + β_{nm}^{l} N_{nm}^{(3)} (k_{l}, r, Ω)$ , $𝒮_{nm}^{l} (r) = α_{nm}^{l} k_{l} N_{nm}^{(1)} (k_{l}, r, Ω) + δ_{nm}^{l} k_{l} N_{nm}^{(3)} (k_{l}, r, Ω)$ and $𝒯_{nm}^{l} (r) = γ_{nm}^{l} k_{l} M_{nm}^{(1)} (k_{l}, r, Ω) + β_{nm}^{l} k_{l} M_{nm}^{(3)} (k_{l}, r, Ω)$ and applying the above orthogonality Eqs. (8)–(10) and using the requirement of the continuity of the tangential electric and magnetic fields at each interface between layers, we obtain:

ℛ_{nm}^{l} (r_{l}) \times \hat{r} = ℛ_{nm}^{l + 1} (r_{l}) \times \hat{r}

𝒬_{nm}^{l} (r_{l}) \times \hat{r} = 𝒬_{nm}^{l + 1} (r_{l}) \times \hat{r}

𝒮_{nm}^{l} (r_{l}) \times \hat{r} = 𝒮_{nm}^{l + 1} (r_{l}) \times \hat{r}

𝒯_{nm}^{l} (r_{l}) \times \hat{r} = 𝒯_{nm}^{l + 1} (r_{l}) \times \hat{r}

where r_l is the radius at the interface between layer l and layer l + 1.

For the core region (l=1) the electric and magnetic fields must be finite at the origin therefore $γ_{nm}^{1} = δ_{nm}^{1} = 0$ . The coefficients of the spherical harmonics for the incident plane wave Eⁱ in the surrounding media are given by

\begin{matrix} δ_{nm} = β_{nm} = 0 \forall n, m \\ α_{nm} = γ_{nm} = 0 \forall | m | \neq 1 \\ α_{n 1} = i^{n + 1} \sqrt{π (2 n + 1)} \end{matrix}

The scattered electromagnetic field E^s must satisfy the radiation condition thus is of the form

E^{s} = \sum_{n, m} δ_{nm}^{l} M_{nm}^{(3)} (k_{l}, r, Ω) + β_{nm}^{l} N_{nm}^{(3)} (k_{l}, r, Ω)

There are two unknown coefficients in the core, two unknown coefficients in the outer media for the scattered field, and 4 unknown coefficients in each shell. Each interface between layers results in 4 equations similar to those in Eqs. (11)–(14). These coefficients can be used to calculate E^l(x) for any point, x in each layer l. The electric field enhancement (EFE) is thus calculated from |E^l(x)|/|Eⁱ|, which can be plotted as a function of the key parameters of this study, such as spatial co-ordinates, layer thicknesses, material parameters (such as dielectric constants and loss coefficients of the individual layer materials), and excitation wavelengths, as elaborated in Sections 4 and 5 below.

4. Double-shelled PQD nanostructures

4.1. Results

We calculated the electric field distribution and the electric field enhancements for numerous nanoparticle designs as a function of critical parameters, notably the metals used (gold/silver), the metal layer thicknesses, the relative permittivity of the dielectric layer, and its thickness. As seen below, the maximum EFE generally increases with a reduction in minimum shell thickness and as such we investigate the EFE for various dielectric permittivities and minimum bounds on layer thicknesses. These minimum layer thickness “bounds” were used to account for the practical issue of nanoparticle fabrication. The maximum EFE for each value of dielectric permittivity and thickness bound was obtained by using a gradient ascent search method, and thus there is no guarantee that a global maximum was found. Excitation wavelengths of 800 nm and 950 nm were used since both are in the tissue optical window and we want to observe the dependence of the EFE on the excitation wavelength. We obtained plots (Figures 2– 5) using both gold and silver for the structure shown in Fig. 1. In Figures 2 and 3, silver is modeled in the metal layers at the excitation wavelengths of 800 nm and 950 nm. Figures 4 and 5 show equivalent plots for gold. From these plots and the combined plot in Figure 6, it is apparent that silver results in higher EFE than gold and that excitation at 800 nm results in a higher EFE than at 950 nm, presumably because the 800 nm wavelength is closer to SPR resonances in both structures. Also EFE increases with a reduction in thicknesses but does not increase monotonically with the relative permittivity of the dielectric layer (see Fig. 6), which is further discussed below.

Fig. 2 EFE as a function of dielectric permittivity and noble metal layer thickness for silver-shelled NP at 800 nm

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Fig. 3 EFE as a function of dielectric permittivity and noble metal layer thickness for silver shelled NP at 950 nm

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Fig. 4 EFE as a function of dielectric permittivity and noble metal layer thickness for gold shelled NP at 800 nm

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Fig. 5 EFE as a function of dielectric permittivity and noble metal layer thickness for gold shelled NP at 950 nm

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Fig. 6 EFE at 800 nm and 950 nm as a function of dielectric rel. permittivity for 2.6 nm noble metal layer thickness

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To understand why the EFE does not increase monotonically with dielectric permittivity, we consider the intuitively simpler quasistatic approximation expression from Neeves et. al [25] for a dielectric core and metal shell structure surrounded by water, which yields the following expression for the electric field intensity in the core:

E_{1} = \frac{9 ɛ_{2} ɛ_{3}}{ɛ_{2} ɛ_{a} + 2 ɛ_{3} ɛ_{b}} E_{0} (cos θ \hat{r} - sin θ \hat{θ})

where ɛ_a = ɛ₁(3 – 2P) + 2ɛ₂P, ɛ_b = ɛ₁P + ɛ₂(3 – P), and P = 1 – (r₁/r₂)³, ɛ₁ and r₁ are the inner dielectric core permittivity and radius, ɛ₂ and r₂ are the metal shell permittivity and outer radius and ɛ₃ is the permittivity of water. The denominator, ɛ₂ɛ_a + 2ɛ₃ɛ_b, is complex since the gold permittivity is complex, but is a linear function of the dielectric permittivity ɛ₁ since ɛ_a and ɛ_b are linear functions of ɛ₁. Therefore since |ɛ₂ɛ_a + 2ɛ₃ɛ_b|² is positive and quadratic as a function of ɛ₁, it is either independent of ɛ₁ or has a unique minimum. This minimum is where |E₁| attains a maximum for each value of the ratio r₁/r₂, as seen in Figs. 7 and 8. Also note in Fig. 7 that for the structure analysed here, without a QD core, the maximum EFE increases for smaller dielectric permittivity while, as seen in Figures 2 – 5, for the QD core case the maximum EFE is attained for a relative dielectric permittivity of around 6. Note that this is close to the 6.9 relative permittivity of the CdSe QD core.

Fig. 7 EFE of Silica/Gold NP using quasi static model

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Fig. 8 EFE as a function of dielectric rel. permittivity for r₁/r₂ ratio of .86

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In order to determine the effect of the quantum dot on the EFE, we compared a silica (relative permittivity of 2.31) core/gold shell (SG) structure (similar to Fig. 1 without the QD core) to a QD core/silica shell/gold shell (QDSG) structure. First we showed that the maximum field enhancement decreases with core radius for SG structures, and second that the field enhancement in a QDSG structure has decreased field enhancement in the QD compared to the field enhancement at the center of an SG nanoparticle. These structures are analyzed for an excitation wavelength of 800 nm. Figure 9 shows the EFE at the center of an SG structure for various radii and thicknesses. The decreased maximum enhancement for larger core radii when using VSH is not observed when using the quasistatic model, indicating the limitations of the quasistatic model. Figure 10 shows the enhancement at the center of the QDSG structure. For a gold shell thickness of 3 nm, the maximum EFE is 14 for the SG (Fig. 9) and 8 in the QDSG (Fig. 10) for a silica radius of around 23 nm, showing the reduction due to the presence of the QD core. The EFE of the QDSG nanoparticle (NP) will still result in a TPAF enhancement of > 2400. This reduction in the EFE is also apparent in Fig. 11 which plots the EFE as a function of the gold layer thickness for a fixed silica radius of 20 nm. Note that, as seen in Figure 12, which depicts the spatial distribution of the EFE for QDSG nanoparticle with a silica radius of 23 nm, and a gold shell thickness of 3 nm, the field enhancement just outside the quantum dot in the QDSG structure reaches a value of 18 (although the field enhancement is only 8 near the center of the quantum dot). Interestingly, this EFE of 18 just outside the QD is higher than the highest value of the EFE (approx. 15) observed in an SG nanoparticle of 23 nm silica radius, implying an exclusion of the electric field by the high permittivity quantum dot core, causing a net “squeezing” or “displacement and net enhancement” of the field.

Fig. 9 EFE as a function of silica radius and gold thickness for silica/gold (SG) NP

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Fig. 10 EFE as a function of silica radius and gold thickness for for QD/silica/gold (QDSG) NP

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Fig. 11 EFE plot with/without QD, silica radius= 20 nm

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Fig. 12 Spatial distribution of EFE within QDSG NP

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4.2. Related work

Wang et. al. [3] measured a 10x improvement in TPAF of QDs in proximity to gold nanoparticles. Wang et. al. [6] also demonstrated theoretical field enhancement of 50 for 800 nm excitation, in a core shell structure. Miao et. al. [19] have recently shown theoretical field enhancements for SiO2 core/gold shell nanoparticles using a quasistatic model with a size dependent loss in the ultrathin Au nanoshell. This modeling shows reduced field enhancement for thinner gold shells due to decreased electron mean free path (and thus increased loss in the gold) but the enhancement increases to the bulk quasistatic model value for larger shell thicknesses. For thicker shells, the gold has the bulk dielectric constant and the enhancement is only dependent on the ratio of core radius to outer radius according to the quasistatic approximation. The lack of attenuation for thicker shells in [19], does not appear to be physically plausible and is perhaps caused by the breakdown of the approximations in the quasistatic model. Enderlein [10] used vector spherical harmonic (VSH) analysis for a SiO2 core /silver shell structure and showed a maximum enhancement on the order of 17 (450 nm wavelength) for a single shell thickness of 5 nm in a plot of wavelengths vs core radii. Neither the effect of gold shell thickness on the EFE, dielectric layer permittivity effect on the EFE, multiple metal shells effect on the EFE nor the effect of a QD at the center of the structure are considered.

Liaw et. al. [20] averaged the fluorescence enhancement over all positions and orientations of a dipole in the silica core having a gold or silver nanoshell. They noted increased enhancement factors for thinner shells. They determined the radiation efficiency factor (REF), which includes the effect of the nanoshell on the far field radiation of the dipole as well as the EFE, and is the ratio of far field fluorescent radiation intensity of the dipole fluorophore in a nanoshell to the fluorophore without a nanoshell. They analysed a silica core with a silver or gold nanoshell, for two shell thicknesses, 5 or 10 nm, and obtain a maximum REF of 120 for a wavelength of 775 nm, a 40 nm radius silica core and 5 nm thick silver nanoshell. Since REF is a ratio of intensities instead of electric fields, this corresponds to an EFE of approximately 11. The maximum REF computed for gold at a wavelength of 820 nm was 40 for a 40 nm radius silica core and 5 nm thick nanoshell. The REF value of 40 corresponds to an EFE of approximately 6.3. Norton et. al. [21] analysed the fluorescence enhancement for a radially oriented dipole at various radii inside and outside a silver nanoshell with free space core and surrounding media. The maximum EFE obtained in [21] is 5.5 for an inner radius of 45 nm and an outer radius of 50 nm at a 600 nm excitation wavelength. This low value compared to our paper may be due to the free space permittivity of the core, the size dependent silver permittivity which has increased loss and the limited range of core radii and shell thicknesses considered. In contrast, we have maximized the EFE for a nanoshelled structure over a wide range of metal nanoshell thicknesses, variations in the dielectric layer permittivity and with a QD at the center.

5. Multi-shelled plasmonic nanostructures

Xu [14] used Mie theory to analyse alternating silica-silver shelled structures with a silver core in a vacuum environment. No attempts are made in [14] to look at dielectric cores. Xu calculated an intensity enhancement of 1.2×10⁵ in a 1 nm thick innermost silica shell for a structure with a silver core and 8 alternating silica-silver shells (4 metal shells) in a vacuum. The 1 nm silica layer is too thin for our proposed fluorescent quantum dot nanoparticle, and may result in significant quenching of the fluorophore due to its proximity to the metal layers. It also may be difficult to fabricate reliably, motivating us to seek improved EFE in an alternate multilayered structure (see below). Kodali et. al. [16] also optimized field enhancement in multiple dielectric-metal layers, however the constraint in the minimum layer thickness was not clear in their optimization. As previously noted, such a constraint is necessary since otherwise the field enhancement increases for smaller layer thicknesses. The NP structures in Fig. 3 of [16] have small EFE in the dielectric core, and were not optimized for the maximum EFE in their core.

The improved EFE for high relative permittivity dielectrics seen above, motivated us to examine the EFE in the core of the multi-shelled nanostructure (MSN) shown in Fig. 13. This structure is analyzed for an excitation wavelength of 800 nm. The EFE for this structure with an 80 nm outer diameter titania (relative permittivity of 6.2), and an 8 nm thick Ag outer shell is shown in Figure 14. As in the case of the silica nanostructure in Figure 10, the maximum EFE increases with small layer thicknesses however even for an inner gold layer as large as 6 nm the maximum EFE observed was 23. Figure 15 shows the EFE for a 6 nm thick inner gold layer and 12 nm radius inner titania layer as a function of the outer layer thicknesses. The maximum EFE structure found has a 12 nm radius inner titania layer, 6 nm thick inner Ag shell, 80 nm thick outer titania layer, and an outer Ag shell of 8 nm thickness. The EFE of this structure is 23 in the core which corresponds to a TPAF enhancement of 160,000 for the QD in the core. A spatial field enhancement plot of this optimal structure is shown in Figure 16 and a “zoomed-in” plot for the inner layers shown in Figure 17.

Fig. 13 Schematic of a 4-shell (two metal shells) PQD NP

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Fig. 14 EFE for 4-shell NP as function of innermost layer thicknesses

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Fig. 15 EFE for 4-shell NP as function of outermost layer thicknesses

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Fig. 16 Spatial distribution of EFE for 4-shell NP

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Fig. 17 Magnified spatial EFE plot for 4-shell NP

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6. Preliminary experiments on nanoparticle synthesis

Gao et. al. [18] recently synthesized a QD core in a 3–5 nm thick polymer shell in a 2–3 nm gold shell. They measured a quantum yield of 39% which could be improved by changing the polymer and gold shell thicknesses. This suggests a promising approach for synthesizing thin shells corresponding to the greatest EFE predicted by our models (see Figures 2 – 5).

We are working on a fabrication method that combines coating of QDs [26] with silica or titania and a method [27] to gold coat such dielectric nanospheres in order to fabricate our proposed QD core/silica shell/gold shell structures. The method described by Koole et. al. [26] uses reverse microemulsion where the QD, tetraethylorthosilicate and ammonia localize to reverse micelles resulting in the growth of a silica layer on the QD. A TEM image of the silica-coated QDs is shown in Figure 18 where spheres with a < 40 nm diameter and a dark core are evident. The method described by Kim et. al [27] grows a gold nanoshell on silica nanoparticles by first attaching gold nanoparticles to the surface of the silica using aminopropyltrimethoxysilane. The gold nanoparticles were subsequently used to nucleate the growth of a complete gold shell. In our preliminary experiment we had problems with agglomeration of the nanoparticles when gold coating our silica coated QDs using the method of [27]. Rasch et. al. [17] also reported problems with agglomeration when synthesizing nanoshells on < 100 nm diameter silica nanospheres.

Fig. 18 TEM image of synthesized silica coated QDs

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7. Summary

We used the bulk dielectric constant of gold and silver in our modeling, however there are some recent results [23,24] in the measurement of the permittivity of ultra thin layers (2–10 nm thick ) of noble metals. Wang et. al. [24] used picometrology but only provided data at 532 and 488nm wavelengths which is not extremely relevant for our study. Hovel et. al. [23] used ellipsometry to determine the complex relative dielectric constant for wavelengths from 280 nm to 1.7 μm. For 800 nm, one of the wavelengths of interest, [23] provided data on the real relative dielectric constant in the range (−20, 17) and imaginary relative dielectric constant in the range (2,30) for gold thicknesses from 3–10 nm. The size-dependent dielectric of gold film thicknesses as measured in [23] has an increased imaginary component which would result in increased loss and reduced EFE. The films they study are discontinuous at a thickness of 3 nm so additional experiments are needed to determine how different fabrication methods affect permittivity.

Moroz [28] thoroughly reviewed previously proposed surface scattering based estimates of the changes in metal permittivity due to size dependent modification to the electron mean free path and demonstrates that the billiard or Lambertian scattering models are most consistent with the experimental results of [29] and also fit the mean free path obtained from the quantum mechanical analysis in [30].

For photodynamic therapy. the energy from two photon absorption in the QD must be non-radiatively transferred to a photosensitizing molecule on the surface of the NP. The efficiency of this nonradiative energy transfer along with the radiation efficiency from the QD to the far field for estimating the fluorescence efficiency will be the subject of a subsequent publication.

If the shells can be fabricated with a dielectric constant close to that of bulk gold, then the 100 nm radius, multi-shelled nanostructure (MSN) discussed in this paper is expected to enable a TPAF signal enhancement of > 160,000. The shells around the QD core should also result in reduced toxicity, allowing these nanoparticles to be used for biomedical applications such deep tissue imaging. The minimum shell thickness in the MSN is 6 nm, making it easier to fabricate, although smaller core and thinner shell nanoparticles are expected to lead to larger TPAF signal enhancements.

Acknowledgments

We are very grateful to the Air Force Office of Scientific Research (Program Managers Schlossberg and Pomrenke, Contract #s FA9550-10-1-0252 and FA9550-09-1-0202) and NSF’s GAANN (Graduate Assistance in Areas of National Need) Program for support of this research.

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Plasmonic quantum dots for nonlinear optical applications [Invited]

Abstract

1. Motivation and issues

2. Proposed solution

3. Mathematical background and methodology used to compute fields and electric field enhancements

4. Double-shelled PQD nanostructures

4.1. Results

4.2. Related work

5. Multi-shelled plasmonic nanostructures

6. Preliminary experiments on nanoparticle synthesis

7. Summary

Acknowledgments

References and links

Cited By

Figures (18)

Equations (17)

Optical Materials Express