1. Introduction

Optical spectroscopic imaging techniques are rapidly emerging for chemical [1] and biomolecular [2] sensing due to recent developments [3] that provide highly specific information while utilizing simple and affordable instrumentation. For applications that require detection of specifc analytes or those at low abundances [4], contrast agents are often employed to amplify optical signatures. In general, however, spectral properties of conventionally-used organic dyes make them poorly suitable [5] for multiplexing. They may also suffer from photo-instability [6] and photobleaching [7], which leads to complications in measurements, especially for time-resolved molecular tracking and analyses. In comparison, nanoparticle labels [8] offer stable optical spectra and often possess relatively narrow spectral characteristics that allow multiplexing. Semiconductor nanocrystals (Quantum dots, QDs) [9] and plasmon resonant (metal) nanoparticles [10] are two important classes of labels. QDs possess narrow emission characteristics that are size-tunable [11] and mixtures of QDs of different sizes can be excited using a single laser wavelength [12]. This has led to wide usage of QDs in ultrasensitive and multiplexed fluorescence imaging [13–15].

For broadband (UV/Vis and NIR) spectroscopic imaging using extinction or scattering properties, metallic nanoparticles also provide an alternative [16]. Metal nanoparticles possess size-dependent optical [17] and electronic [18] properties. While their scattering [19], absorption [20] and photoluminescence [21] spectra can directly be detected, it is also possible to achieve enhanced spectra for organic/dye molecules proximal to their surfaces [22] (for example in Raman [23], infrared [24], and fluorescence spectroscopy [25]). The photoluminescence of semiconductor crystal emitters can also be enhanced when in the vicinity of nanoparticles [26]. Metal nanoparticles however have relatively wide resonance peaks and their size tunability is limited. It is possible to achieve higher optical tunability using asymmetric nanoparticles [26], but at the expense of polarization effects and variability. Local structure in nanoparticle’s geometry has also been shown to alter its spectral response. For example, a layered nanosphere with metal shells interspersed by dielectric layers possesses resonances that are tunable by varying the sizes of different shells [27–34]. Two layered concentric spheres were proposed almost six decades ago [35] and resonances in layered spheres have been theoretically studied, validated [36,37] and applied [38,39]. The fabrication of particles with more than two layers has also recently been reported [40,41]. Similarly, spectroscopic tags based on dye-embedded gold-silica nanoparticles have also been reported [42] to possess immense Raman signals and have been employed [43] as labels in biological imaging. Despite these wide-ranging applications, the flexibility offered by layered nanospheres to design application-specific probes has not been fully appreciated.

Here, we present an approach to design and optimize layered nanospheres with alternating metal and dye-filled dielectric layers as optical probes. In reference to the structural design of various layers, we term these constructs Nano-Layered Alternating Metal-dielectric Probes (Nano-LAMPs) [33]. The concept of multilayer particles with a few layers [34, 36, 37] and sizes [31, 44] has previously been investigated for tunable far-field optical properties. With increasing fabrication capabilities, the constraints on complexity of LAMPs that can be fabricated have considerably relaxed. Further, although the possibility of achieving intense internal field resonances using mutilayered metal-dielectric systems has been previously identified [30], the ability of such systems in controlling and optimizing the resonances is unclear. Here, we report the potential for designing probes using gold-silica, silver-silica and copper-silica LAMPs. We first describe the theoretical framework for predicting LAMP response and a genetic algorithm adapted for selection to optimize structures. Second, we discuss the structure of the probe and its effect on the optical properties of LAMPs. Finally, we present a rational design of probes suitable for optical multiplexing. Both wavelengths of excitation and analyte abundances at a single wavelength of excitation are studied to establish the performance limits of LAMPs.

2. Simulations and optimization

2.1 Mie-based formulation

We use a formulation based on layered Mie theory to evaluate far-field characteristics and internal fields in LAMPs. The incident excitation wavelength is assumed to be much larger than the LAMPs, hence, only responses to plane wave excitations are evaluated. The electromagnetic (EM) fields within each layer are expanded in vector spherical harmonics (VSH) and, utilizing the field continuity between different layers a stable recursive formulation to evaluate coefficients of expansion is obtained [33, 45]. By using an appropriate cutoff [46] for the maximum order of VSH and stable recursive formulations of logarithmic derivative and ratio functions involved, expansion coefficients and internal fields within each layer are calculated. The appropriate cutoff for VSH varied from 4 to 15 depending on the sizes and properties considered. The far-field characteristics are dependent on the coefficients of the scattered field outside LAMP and are evaluated using asymptotic expansions. Both far-field and internal field characteristics are dependent on thicknesses as well as refractive indices of individual layers. For metal layers of thickness greater than 10 nm, it is typically acceptable to use the bulk values [47]. In case of metal shells thinner than 10 nm, a correction [44] is implemented to the imaginary part of refractive index to account for the reduced mean free path available for the electrons and the resulting effects. The effective mean free path is calculated using the outer radius of the shell and its thickness [44]. The correction applied is also dependent on the wavelength of plasma oscillations of the metal considered [44].

For applications in which the response of organic (dye) molecules in silica shells is detected, we ignore chemical enhancement (for example due to charge transfer in case of Raman scattering [23]). Although this approximation might underestimate enhancements, it provides a minimum value for the reliable enhancement in Raman/IR/Photoluminiscence signals. We further assume that the reporter molecules are dispersed uniformly in the dielectric layer, rather than being attached as a self assembled monolayer (SAM) to metal surfaces. The case of SAM forms a subset of our results since we seek to optimize fields as an average over the entire dielectric layer. The distribution of reporter in the entire dielectric volume instead of being at the surface of the metal also makes the CE lower as the number of surface active sites is small [48]. While enhancement in infrared absorption, fluorescence and photoluminescence scales with local field intensity (|E_loc(λ_inc)|²), Raman enhancement scales with square of local field enhancement (|E_loc(λ_inc)|²) multiplied with the square of shifted Raman field (|E_loc(λ_inc + δλ)|²) [49]. Here, E_loc is the field at incident wavelength λ shifted by a wavelength δλ. Typically, the scattered fields at incident and Raman shifted frequencies are of similar magnitudes; hence, the local enhancement near a reporter can be approximated as |E_loc(λ_inc)|⁴ [50].

2.2 Genetic Algorithm Selection

We have recently reported [51] the advantages of silver-silica LAMP configurations in designing Raman labels through genetic algorithms [52]. Here, we focus on gold-silica and copper-silica LAMPs to design the internal intensities over different excitation wavelengths and in general as applicable to different spectroscopy techniques. In this study, whenever required, we have employed an optimization of peak wavelength and height for far-field spectra and internal fields for Raman/fluorescence and photoluminescence spectra of reporter molecules. A set of 1000 probe structures is chosen at random and tournaments are conducted on sets of 4 probe structures to evaluate the best configuration (with maximal/minimal internal field in dielectric layers or minimal difference with requisite ratio of far-field spectral peak wavelength to peak width). These “fit” structures are entered into a mating pool and undergo a simulated binary cross over recombination with a probability of 0.9 and polynomial mutation recombination with a probability of 0.1. For each pair of structures undergoing recombination in cross over, on average half of the shell sizes are modified using either contracting or expanding crossover operations. The pairs of structures undergoing recombination in polynomial mutation the shell sizes expand or contract based on the closeness to upper or lower bounds. The population is then updated by replacing the “least fit” individuals with the recombined structures. The updates are performed iteratively until the convergence of fitness of the best individual structure in the population is apparent. Typically about 30 to 50 iterations were required for convergence.

3. Results and discussion

3.1 Structure and properties

The potential use of LAMPs as sensing probes and their internal structure are shown in Fig. 1a and 1b, respectively. Well-established bioconjugation methods [53] can be used to link the outermost layer of the particle to molecular species. The outermost layer is a protective silica layer, which serves two important functions. First, it shields the biological material from the potentially toxic effects of the probe materials. Second, it ensures that spectra of the surroundings are not enhanced and/or altered and the analyte is detected via probe transduction alone. With alternating inner layers of metal and reporter-loaded dielectric, there are two different possible configurations: one with odd layers in which the core is a dielectric sphere and one with even layers in which the core is a metal sphere. The inter-plasmon coupling of the metal shells in LAMPs governs their optical properties. The mixing of dipolar contributions due to the metal shells typically results in stronger resonances at longer wavelengths while the higher order multipole contributions and their interactions result in weaker resonances at shorter wavelengths. The relative strength of interaction and their manifestation in far-field characteristics is strongly dependent on the overall size of the particle, the relative thicknesses and compositions of each layer. For example, extinction spectra are shown in Fig. 1c for a 5-layered gold-silica LAMP (r₁ = 5, r₂ = 15, r₃ = 30, r₄ = 44 and r₅ = 50 nm) and a 6-layered gold-silica LAMP (r₁ = 5, r₂ = 10, r₃ = 26, r₄ = 34, r₄ = 44 and r₆ = 50 nm). In the spectra shown, there exist two distinct peaks at wavelengths of 531 and 676 nm for 5-layered LAMP and at 543 and 837 nm for the six-layered structure. The peaks at shorter wavelengths can be observed to be a combination of resonances, which are due to higher order multipole modes. In addition, the contributions from different metal shells can be understood by examining the local reorganization of electric field within and in the vicinity of LAMPs when illuminated at resonant wavelengths. In Fig. 1d, this reorganization can be seen in the intensity distributions in the incident plane.

 

Fig. 1 Probe Structure, far-field and near-field characteristics of nano-LAMPs. (a) LAMPs with linkers can label analyte molecules and the response of the probe to an incident electro-magnetic field can be used for detection. (b) Mid-sectional view of odd- and even-layered LAMP configurations (c) Extinction efficiencies for gold-silica LAMPs consisting of 5 layers ({r₁, r₂, r₃, r₄, r₅} = {5, 15, 30, 44, 50 nm}) and 6 layers ({r₁, r₂, r₃, r₄, r₅, r₆} = {5, 10, 26, 34, 44, 50 nm}). (d) Internal intensity distribution in the incident plane for 5-layered (top) and 6-layered (bottom) LAMPs in (c) when illuminated by plane waves at resonant wavelengths. The boundaries of different layers are indicated using black circles.

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For the 5-layered structure, a relatively stronger resonance at 676 nm illumination results in the fields being enhanced up to 3 orders of magnitude in the outer dielectric layer. At 531 nm, the field is enhanced only up to 1-2 orders of magnitude indicating a weaker resonance. For the 6-layered structure, the contributions due to plasmonic interaction of different metal layers are more apparent. At 543 nm illumination, the coupling between the core and the first metal layer is dominant, resulting in enhanced fields of higher magnitudes in the innermost dielectric layer. At 837 nm illumination, the coupling of the first and second outer metal layers is stronger resulting in enhanced fields of higher magnitudes for the second dielectric layer. The ability to reorganize the enhanced and depleted regions into different dielectric layers can be employed to design probe structures with different enhancement characteristics for dye molecules filled in different layers [54].

The resonances in far-field spectra can be directly related to the strength of the local field, E_loc, within specific dielectric layers and modeling this relationship is key to optimizing the construction and use of LAMPs. One approach may be to utilize a plasmon hybridization model [36, 37] and evaluate the coupling of various plasmon modes with the optical fields. Using the models, insights can be readily gained into engineering the thicknesses of various layers for simple structures. Considering plasmon modes of higher number of metal layers can prove to be cumbersome however, and alternate methods of designing probes can be explored. Here, we explore the use of Mie theory calculations to predict the fields and far field spectra while employing optimization strategies to precisely tune the structure to the desired response.

3.2 Design of optical probes for multiplexing

We first explore the use of LAMPs directly for sensing through their extinction spectra. By varying layer thicknesses in a LAMP, different higher order multipole modes can be excited resulting in resonances at different wavelengths. The optical tunability can be employed to design LAMPs as probes in a multiplexing application. While the tunability can be further extended by considering probes of different compositions and total sizes, here we restrict ourselves to designing probes of a specific size and composition to illustrate our approach as well as to provide a basis for comparison. The constant total size is relevant in designing probes of similar diffusion characteristics and similar availability to the labeled sites while a single composition simplifies fabrication. For biological imaging, probes of a size below 100 nm are relevant [55]. Hence, as a specific example, we demonstrate the design of silver-silica LAMPs of 100 nm size that have designed spectral peaks in the 200-1200 nm range of excitation. For smaller layer sizes, it is often difficult to fabricate a continuous and uniform layer in practice. Hence, we impose a constraint that the metal layers and dielectric layers are at least 10 nm and 5 nm respectively. We first examine the problem of tailoring resonance peak position to design a palette of probes for multiplexing. Here, we employ a simple contrast ratio (=Cumulative extinction in the desired illumination wavelength region/Cumulative extinction in rest of the range) as the cost function to be maximized. Figure 2a shows the radii and extinction efficiency spectra of 3-layered silver-silica LAMPs obtained using a genetic algorithm to select optimal layer thicknesses by maximizing the cost function. Simply changing layer thickness results in a change of the probes’ spectral features due to a change in plasmonic coupling. Several characteristics may be noticed here. In structures with thinner metal layers, with the radii denoted in short as a set of numbers - ({35,45,50}, {33,44,50}, {28,38,50}, {22,32,50}, and {9,19,50}}, stronger interaction of plasmons results in stronger and narrower resonances. The thicker outer silica layer, however, lowers the strength of this resonance. In contrast, the structures with thicker metal layers ({6,45,50}, {20,44,50}) possess broader peaks. While the thicker layer can effectively isolate the plasmons of two surfaces, the size available for separation is not large enough to result in two well separated peaks. Figure 2b depicts the radii and distinct extinction spectra of 5-layered silver-silica LAMPs. The presence of two metal layers and the interaction of multipole contributions due to these layers can be utilized to achieve multiple resonances. It can also be observed that the resonances at longer wavelengths can be shifted further into near-infrared for the 5-layered LAMPs. Moreover, the resonances for the 5-layered LAMPs are better separated in comparison to those for 3-layered LAMPs due to increased spectral range.

 

Fig. 2 Odd-layered Silver-Silica LAMPs of 100 nm size with distinct extinction spectra in 200-1200 nm excitation range. (a) 3-layered LAMPs (b) 5-layered LAMPs.

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A notable characteristic of the optimization was that it predicted structures with the thinnest possible metal layers. The presence of a thin outer metal layer ensures the existence of a resonance at longer wavelengths. Using the thinnest outer metal layer further maximizes this resonance. This is likely due to the cost function chosen for optimization is biased towards maximizing the strength of resonances. A different cost function could be chosen to optimize for the width of the peak and/or achieving higher number of peaks. More complicated cost functions and constraints can also be visualized; for example, a cost function to control peak width can be optimized subject to the constraint of a specific contrast ratio.

While Fig. 2 examined an odd number of layers for 100 nm LAMPs, the 4-layered and 6-layered Siver-Silica LAMPs and their distinct extinction spectra (Fig. 3 ) indicate that similar results could be achieved with even-layered structures. For the optimized 4-layered Silver-Silica LAMPs with near-infrared resonances, the thickness obtained for the silica layer between the metal layers is minimal, which is consistent with the scaling law for plasmon resonance shift proposed in case of gold-silica-gold spheres. The presence of the extra (protective) silica layer here, further red-shifts the resonances. As in the case of 3-layered and 5-layered LAMPs, the outermost metal layer is the thinnest possible for achieving resonances in the near-infrared wavelengths, but the core is larger. As the core size becomes smaller and the outer metal layer becomes thicker the resonances at shorter wavelengths become stronger and broader. The presence of additional metal and silica layers in the designed six-layered LAMPs result in distinguishable peaks at the shorter wavelengths as shown in Fig. 3b. As in the case of odd layered LAMPs, the additional layers add to the optical tunability and structures with resonances further into near-infrared can be achieved. For both odd-layed and even-layered LAMPs, the multiple peaks achieved are easily distinguishable. With a multivariate curve resolution algorithm, for example, the probes could be easily employed for multiplexed analyses. Several other interesting aspects of the design are apparent: The plasmonic interaction between metal layers in smaller particles (sizes below 100 nm) can be relatively weaker and all the plasmon modes might not be resonant. For a given total size, LAMPs with a larger number of layers can result in resonances at longer wavelengths. The extinction characteristics of LAMPs are due to contributions from both scattering and absorption. Scattering is dominant for the LAMPs considered here. Just as we optimized the LAMPs to tune spectral properties, the ratio of scattering to absorption can be optimized and multiplexing probes could be realized for various spectroscopic modalities.

 

Fig. 3 Even-layered Silver-Silica LAMPs of 100 nm size with extinction spectra in 200-1200 nm excitation range. (a) 4-layered LAMPs (b) 6-layered LAMPs.

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3.3 Designing probes with tunable responses

LAMPs can be designed such that their signal arises not directly from the overall scattering and absorption of the probe but from the emission or inelastic scattering characteristics of molecules (reporters) doped into the dielectric layers. Reporter signals can be tuned at a particular wavelength through the electric fields induced in the dielectric layers. In addition, the interaction with the metal for the molecules could be reduced through the separation offered by the dielectric material. This ensures the reliability of enhancement in the signal by basing it purely on the composition and structure of the probe and not on the specifics of metal-reporter interactions [51]. There are two aspects to using LAMPs with embedded reporters: first, stronger enhancements can be achieved with multilayer particles that are difficult to achieve with simpler geometries. Second, LAMPs can be designed to possess a specified amplification of response or may be optimized for specific wavelengths. We have previously examined silver-silica LAMPs in designing Raman probes [51]. Here, we focus on employing Copper-Silica and Gold-Silica LAMPs to design Raman probes for comparison. The tunability of amplification is demonstrated in the internal field distributions provided for 6-layered Gold-Silica LAMPs at 785 nm excitation in Fig. 4 . The structures can be designed such that the maximal field achieved within the particle can be tuned to be 1-5 orders of magnitude larger than the incident field. We observed that choosing a very thick outermost metal shell dampens fields inside compared to outside the LAMP. When the inner metal and silica layers and the outer most silica layers are chosen to be thicker, the enhancement is higher. For structures with greater enhancements, we observed that the metal layers are typically separated by thin dielectric layers and one of the inner metal layers (core or the first outer metal layer) is large. It can be observed that the stronger enhancement regions achieved within LAMPs extend over a large part of the dielectric layer; hence, a uniform reporter distribution is likely beneficial. The strongest enhancements are much higher than what could be achieved with the single nanoparticles and the extent of enhanced regions is much larger compared to simple nanoparticle aggregates [56].

 

Fig. 4 The tunability of enhancement in the internal fields in dielectric layers using 100 nm sized six-layered gold-silica LAMPs of various layer thicknesses when illuminated by a plane wave of wavelength 785 nm. The distributions are shown in the indicent plane with incident field polarized horizontally. The structures shown have radii (a) 5,14,16,17,48,50 nm, (b) 7,17,20,21,44,50 nm, (c) 8,23,25,26,35,50 nm (d) 6,18,23,26,31,50 nm (e) 15,25,32,36,40,50 nm (f)13,20,25,35,40,50 nm (g) 10,14,22,32,41,50 nm (h) 18,22,33,38,41,50 nm (i) 14,16,28,34,46,50 nm (j) 7,8,26,38,48,50 nm. The boundaries of different layers are depicted using black lines.

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LAMPs of the same size can also be designed for different wavelengths of excitation using both Copper-Silica and Gold-Silica composites. Figure 5 shows the internal field distributions in LAMPs designed that possess maximal and minimal enhancements in the innermost dielectric layer for wavelengths of excitation 532 nm and 785 nm – which are commonly employed excitation wavelengths for Raman spectroscopy. The structures with minimal enhancements can provide quenching of the response and together with structures of maximal enhancements can be used to probe analytes of widely varying abundances in a multiplexed fashion. At 785 nm excitation, the structures designed for maximal enhancement utilizing Copper-Silica and Gold-Silica are the same. The structures for minimal enhancements derived are also similar. Moreover, the achieved maximal and minimal enhancements are of similar magnitude and at longer wavelengths of excitation. The summary conclusion is that Copper or Gold could be employed to design probes with equal effectiveness. At 532 nm excitation however, the maximal and minimal enhancements are higher for Gold-Silica LAMPs. This is due to the plasmon modes for Gold layer sizes considered being resonant at wavelengths closer to 532 nm compared to the Copper layers. In all cases shown, the structures for minimal enhancements possess a thicker outermost metal or silica layer and the structures for maximal enhancements possess thinner dielectric layers, which is consistent with observations made in Fig. 4.

 

Fig. 5 Internal field distributions in 60 nm sized six-layered Gold-Silica LAMPs ((a) and (b)) and Copper-Silica LAMPs((c) and (d)) designed for minimal and maximal enhancements at excitation wavelengths 532 nm ((a) and (c)) and 785 nm ((b) and (d)). The distributions are shown in the incident plane with incident field polarized horizontally. The structures shown have radii (a) minimal-left:{5,7,9,10,12,30 nm}, maximal-right: {5,9,13,17,28,30 nm} (b) minimal-left: {5,11,13,14,26,30 nm}, maximal-right: {7,8,18,24,29,30 nm} (c) minimal-left: {5,6,8,10,12,30 nm}, maximal-right: {6,7,13,19,29,30 nm} (d) minimal-left: {6,12,14,15,27,30 nm}, maximal-right: {7,8,18,24,29,30 nm}. The boundaries of different layers are depicted using black circles.

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In evaluating the ability of LAMPs for multiplexed probing of analytes with different concentrations, the range to which the magnitudes of their responses can be scaled is relevant. As an example we evaluate such ability of LAMPs as Raman probes. To quantify a LAMP’s Raman response we introduce net enhancement factor (NEF). The NEF achieved within a LAMP of reporter loading factor can be integrated over the reporter-filled dielectric volume and is defined as:

 

Fig. 6 Dynamic range of achievable Raman Net Enhancement Factors using Gold-Silica and Copper-Silica LAMPs of different sizes over different number of layers for excitation wavelengths (a) 532 nm and (b) 785 nm. The data points plotted are connected by smooth piece-wise cubic interpolation.

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The NEFs in LAMPs are a cumulative contribution of the dielectric volume (and reporter loading) and coupled electromagnetic enhancement (measure of the reorganized fields). As the total size increases, the numerical contribution to the NEF increases while the electromagnetic enhancement decreases. The sizes at which the combined effect of both contributions is maximized are typically around 100 nm. At smaller sizes, the maximal NEF’s are achievable with LAMPs with smaller number of layers, while a larger number of layers is beneficial for LAMPs with larger sizes. The 3-layered LAMPs further offer a unique capability to reorganize the fields into the protective silica layer or outside the LAMP. Hence, they are very effective in quenching the fields inside the silica core. At larger particle sizes this could lead to LAMPs with greatly quenched Raman responses as shown in the data points with minimal NEFs in Fig. 6. As size increases the dynamic ranges achieved through maximal and minimal NEFs increases in extent. Along with the observations reported here, the fields could be further reorganized into different dielectric layers and the multiplexing capabilities of probes are further enhanced by choosing reporters of different (resonant and non-resonant) scattering properties.

4. Conclusions

Here we demonstrate that nano-LAMPs offer a flexible design for creating probes for multiplexed detection. Both the overall optical response of the LAMPs and the internal reorganization of the optical fields, when excited by different wavelengths, can be utilized to devise sets of probes in different optical spectroscopic imaging techniques. LAMPs provide a ready template for designing a palette of probes due to the degrees of freedom available in tuning their structure. Subject to experimental feasibility, application-specific size constraints and incident laser characteristics, the layer thicknesses of LAMPs can be optimized for desired responses. The genetic algorithm based optimization provides a simple method to theoretically fashion different structures. We anticipate that this method in combination with the recently reported fabrication techniques will greatly improve the capabilities of nanoparticle label-based detection and assays.