Plasmon Hybridization Mediated Structure-Specific Refractive Index

Mar 8, 2016 - The refractive index sensitivity of plasmonic nanoantennas depends on the plasmon field strength and its distribution (sensing volume)...
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Plasmon-Hybridization Mediated Structure-Specific Refractive Index Sensitivity of Hollow Gold Nanoprism in the Vis-NIR Region Bidhan Hazra, and Manabendra Chandra ACS Sens., Just Accepted Manuscript • DOI: 10.1021/acssensors.5b00314 • Publication Date (Web): 08 Mar 2016 Downloaded from http://pubs.acs.org on March 11, 2016

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Plasmon-Hybridization Mediated Structure-Specific Refractive Index Sensitivity of Hollow Gold Nanoprism in the Vis-NIR Region Bidhan Hazra and Manabendra Chandra* Department of Chemistry, Indian Institute of technology, Kanpur (UP)-208016, India. E-mail: [email protected] KEYWORDS Hollow nanoparticle, nanoprism, refractive index sensing, plasmon hybridization, FDTD.

ABSTRACT: The refractive index sensitivity of plasmonic nanoantennas depends on the plasmon field strength and its distribution (sensing volume). As a result, the sensitivity factors can be larger for hollow nanoparticles than for solid ones of comparable dimensions due to their larger sensing volume and the strong local-electric fields resulting from the plasmon-hybridization between the external and internal surfaces. The plasmonic field strength of a hollow nanostructure is further enhanced when it has anisotropic shape. In the present paper, the plasmon resonances along with the associated local-electric fields and the RI sensitivity factors of an anisotropic hollow nanostructure, namely, hollow gold nanoprism (HGN, an equilateral triangular gold nanoprism with a circular cavity) of different cavity-size and thickness have been determined by finite-difference time-domain simulation. The dependence of the RI-sensitivity factors on the prism thickness, the size and the position of the cavity, and shape defects such as corner-rounding or snipping has been determined and discussed. The RI-sensitivity increases linearly with the aspect ratio of the HGN. The RI-sensitivity is especially sensitive to the position of the cavity of the HGNs. We show that properly designed HGNs have RI-sensitivity values that are more than several hundred units higher than those of solid gold nanoprisms and even gold nanoframes of comparable size. Moreover, the loss in sensitivity factor due to shape defects such as corner rounding or snipping is much less in HGNs than their solid analogues. All these properties of HGNs make them superior material for chemical- and biosensing applications than any other plasmonic nanostructure of similar dimension.

In recent years plasmon-supporting metal nanostructures have emerged as attractive signal transducers in optical chemo- and bio-sensors.1-5 The transducer effects in these nanoscale plasmonic structures originate from the excitation of their localized surface plasmon resonances (LSPRs) which produces large local electric-fields at structure-specific frequencies allowing them to function as electromagnetic antennas. The structure-specific LSPR frequencies and the corresponding excitationinduced local electric-fields are highly dependent on the local dielectric environment.6-9 The local electromagnetic field associated with LSPR decays rapidly into the surroundings, providing a special type of transducer effect in which changes in the local refractive index are converted into a frequency shift of the plasmon mode.10 This effect has recently been exploited for trace-level detection, and LSPR peak shifts of plasmon-supporting nanoparticles have been used to detect optically transparent molecules.11,12 The efficiency of this type of transducer effect is quantified by so-called sensitivity factor, which is measured by the red-shift in the LSPR peak position (∆λ, in nanometers) per unit change in the refractive index (refractive index unit or RIU) of the surrounding medium. The value of the sensitivity factor for a nanostructure is dependent on various structural parameters such as, size, shape, type of nanoparticle, etc.13,14 Nanoparticles with higher sensitivity factors are the most desirable for the

practical application purpose in chemo- or bio-sensing devices. The RI sensitivity factors of a number of metal nanostructures have been investigated both theoretically as well as experimentally. It has been found by Chen et al that metal nanostructures such as solid gold nanospheres or nanocubes, whose size-dependent spectral tunabilities are somewhat limited, exhibit very small RI sensitivity, ~ 44 and 83 nmRIU-1 respectively.15 Whereas, higher values of sensitivity factor have been measured for anisotropic nanostructures such as gold nanorod (195-288 nmRIU-1), nanoprism (583 nmRIU-1), nanostars or bipyramids (150540 nmRIU-1 ) that exhibit large spectral tunabilities as well.15 Interestingly, hollow nanoparticles have been found to have much larger spectral tunability and enhanced RI sensitivity factors compared to solid nanoparticles. For example, spherical gold nanoshells show a RI sensitivity value of 125 nmRIU-1, which is larger than the RI sensitivity of solid gold nanospheres.16 Much larger RI sensitivity values of 408.8 nmRIU-1 and 620 nmRIU-1 have been measured for hollow gold nanocubes (nanocages) and hollow gold nanoframes, respectively.17,18 Theoretical calculations using discrete dipole approximation (DDA) technique yielded a sensitivity value of 712 nmRIU-1 for a gold nanoframe of 90 nm side length and 16 nm wall

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thickness.18 This is one of the highest RI-sensitivity values that have been reported for plasmonic nanoantennas.18,19 It is obvious from the on-going discussion that a thoughtfully designed plasmonic nanostructure that is hollow as well as anisotropic in shape can surpass the best known RI sensitivity values measured for structures like solid nanorods, nanostars, or hollow nanocages and even nanoframes. Synthesis of such an anisotropic hollow nanostructure, namely, hollow gold nanoprism has been recently reported.20 A hollow gold nanoprism (HGN) is essentially an equilateral triangular gold nanoprism with a circular cavity. Colloidal HGNs are synthesized using sacrificial galvanic replacement method.20 The LSPR peak position of this type of nanoprisms is extremely structure-specific and widely tunable, as we observe experimentally. Moreover, unprecedented large values of second-order nonlinear optical polarizabilities have been measured for the HGNs.20 This is suggestive of generation of extremely large local electric fields at the surfaces of the HGNs upon optical excitation. Being encouraged by these preliminary observations, in this work, we have numerically investigated the structure-specific optical properties including the RI sensing capabilities of HGNs of various different structures using finitedifference time-domain (FDTD) technique. The dependence of the plasmon field strength and the sensitivity factors on the prism thickness, the size and position of the cavity, and shape defects such as corner rounding or snipping has been systematically determined for HGNs of a fixed side length (100 nm) and compared to the solid gold nanoprisms. The LSPR spectra of the HGNs are found to be extremely sensitive to the thickness, cavity size and especially, the position of cavity. HGN’s LSPR can be controllably tuned from the visible to the most of the near-infrared region. We find that this tunability arises due to extremely efficient plasmon-hybridization involving multiple surfaces, including the cavity surface, of a hollow nanoprism. Increase in the cavity-size or decrease in the tip to cavity-surface distance increases the efficiency of plasmon-hybridization, which not only enhances the local E-field strength but also increases the its decay length which in turn, increases the sensing volume and hence the RI sensitivity values of the HGNs. For the HGNs studied in this work, the RI sensitivity factors can be controllably tuned from a moderate value of 288 nmRIU-1 to an enormous value of 1062 nmRIU-1. Interestingly, the RI sensing ability of HGN is less sensitive to corner rounding or snipping than its solid analogue.

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light waves (both propagating and evanescent) at the boundary with minimal reflections. This allows us to create a scenario where a single HGN is placed on a semiinfinite glass substrate. A maximum of 24 and minimum of 12 PMLs were used in our simulations. The solverdefined total-field scattered-field (TFSF) source that allows the definition of the plane-wave excitation within the volume enclosing only the simulation objects was used for the simulations. Frequency-dependent power monitors were used to obtain the absorption and scattering spectra as well as the charge-density distribution and electric-field enhancement for the nanoparticle. The scattering and absorption cross-sections were calculated from the power flowing outward through a volume enclosing the TFSF source (scattering cross-section) and the net power flowing inward through a rectangular cuboid inside the TFSF volume enclosing the HGN (absorption cross-section), respectively. The TFSF box had dimensions of 140 nm × 140 nm × 140 nm. The linearly (along the Y-axis) polarized plane-wave excitation (see SI for the justification of selecting Ypolarization) were incident normal to the nanoprism i.e., propagating along z (Fig. 1).

Figure 1. Schematic of the optical simulation configuration is shown. A single hollow gold nanoprism is placed on a glass substrate, in the xy plane, and the photon propagates along the z-direction. The polarization of light is kept fixed in y direction.

The incident plane-wave pulse had a spectral bandwidth of 2600 nm with spectral range from 400 nm to 3,000 nm and pulse duration of 2.66fs. We employed a conformal non-uniform mesh to accurately map the details of the HGN structure. The TFSF volume default grid was 7 nm × 7 nm × 2 nm and a mesh accuracy of 5 was applied. A volume with dimensions of 160 nm × 160 nm ×160 nm, encompassing the HGN structure, was discretized with a cubic mesh of 2 nm × 2 nm × 2 nm. Note that, a cubic mesh of 0.5 nm × 0.5 nm × 0.5 nm was used for NUMERICAL SIMULATION METHODS charge-density calculations, while 0.5 nm × 0.5 nm × 1.0 Three-dimensional FDTD simulations were performed nm meshing was applied for calculating the electric-field using the commercially available software package FDTD distribution. The maximum simulation time was set to TM solutions v8.12 (Lumerical ). A cubic volume of 2 µm x 2 300 fs. The time-stepping stability factor was set to 0.99, µm x 2 µm was created as the simulation region that conwhich corresponds to a time step of 0.00381315 fs. An autained all the simulation objects, sources and monitors. to-shut off level of 10-6 was set to make sure that the reAll simulation boundaries were set as perfectly matched sidual energy within the simulation box was negligible. A layers (PML) in order to have maximum absorption of standard convergence test was done to ensure negligible Page 2 of 9

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numerical errors resulting from the non-uniform meshing, PML distance, or monitor sampling. The average intensity of electric field within the gold nanoprism was obtained from a two-dimensional field monitor placed in the XY plane. All the simulations were done on single nanostructures, either solid gold nanoprism (SGN) or hollow gold nanoprism (HGN). All the SGN and HGN (an equilateral triangular prism with a circular cavity at the centre of mass) structures were created using the object library in conjunction with the material database built in the solver. Throughout all the simulations, the edge-lengths (L, also called side-length) of the HGNs were kept fixed at 100 nm while the thicknesses (T) of the HGNs or the diameters (2r) and positions of the cavities were varied. T was varied over a range from 4 nm to 60 nm for any given cavity diameter whereas, 2r was varied from 8 nm to 48 nm. All the HGNs were placed on glass substrates to replicate the actual experimental configuration that one uses to record spectra from single nanostructures. A background refractive index (RI) = 1 was used in all the simulations except for the cases where the effect of variation in RI itself were probed. The frequency-dependent dielectric constant value of Au was taken from the database tabulated by Johnson & Christy.21 The constant RI of 1.5 was used for the glass substrate to represent a borosilicate coverslip that we actually use for dark-field spectroscopy and imaging measurements in our lab. The dielectric dispersion of gold was fitted in the spectral range 400–3000 nm by a six-coefficient model. The multi-coefficient-model fitting was done with an imaginary weight of 1 and allowing a tolerance of 0.1, enforcing passivity.

RESULTS AND DISCUSION Fig. 2(a) shows the simulated absorption spectrum of an isolated HGN with L = 100 nm T = 40 nm and a cavity

and 90 nm red-shifted compared to the SGN. The observed LSPR band at λmax = 704 nm for the HGN is purely in-plane electric-dipolar in nature, very similar to the case of LSPR of SGN, as we can see from the electric-field distribution shown in Fig. 2(b). The LSPR peak shift, on going from SGN to HGN, is due to a strong plasmon coupling between the outer surfaces (sides other than the base) of the nanoprism and the cavity surface. The LSPR of an HGN can be expressed as a linear combination (plasmon hybridization) of the primitive plasmon modes associated with the two individual surfaces.22,23 A chargedensity distribution analysis (Fig. 2(C)) at λmax=704 nm reveals that a symmetric alignment of the primitive plasmon modes of the two surfaces give rise to the LSPR mode of the HGN. Such a symmetric alignment (see SI for detail description) of the primitive plasmon modes of the two surfaces lead to a favourable coupling between them and the formation of a new hybridized plasmon mode with a lower energy, i.e., a bonding plasmon mode.22,23 Strength of such bonding interaction between two surfaces or in other words, the extent of red shift in the LSPR

Figure 3. (a) Absorption spectra of HGNs (L = 100 nm, T = 40 nm) with various cavity diameters. (b) LSPR maxima of HGNs red shifts exponentially with the increase in cavity diameters (c) The strength of plasmonhybridization between the cavity surface and the sidewalls of HGNs. The fractional LSPR shift Δλλ falls off  exponentially with decreasing cavity diameter. A fit to the  data with an equation of the type Δλλ    ⁄τ , yields 

a decay constant, τ = 0.190 ± 0.005 suggesting that plasmon-hybridization in HGNs obeys the universal ‘plasmon-ruler’ relationship.

Figure 2. (a) Absorption spectra of isolated solid- and hollow gold nanoprisms of same outer dimension ( L = 100 nm, T = 40 nm ). The HGN has a 40 nm cavity. A red shift of 90 nm in case of HGN is clearly observed (b) Electric field distribution (in log scale) and (c) charge density distribution of the same hollow gold nanoprism at λmax=704 nm. The electric field distribution clearly reveals a dipolar nature of the LSPR of the HGN. A bonding mode of hybridization the cavity surface and the outside wall of the HGN is evident from the charge density map.

spectra of HGN, solely depend on the cavity size if the other dimensions of the nanoprism remain constant. Greater the cavity diameter, smaller is the distance between the two surfaces (R-r) and hence larger is the redshift. This behaviour is shown in Fig. 3a. The cavity diameter is varied from 0 nm (solid nanoprism) to a maximum of 48 nm. The LSPR spectra exponentially red-shifts with increase in cavity diameters: a large shift in LSPR maximum from 614 nm for the solid nanoprism to 814 nm for the HGN having 48 nm cavity is observed [Fig. 3(b)]. Interestingly, we find that this inter-surface distance dependent spectral tunability in the LSPR spectra for the HGN obeys the 'plasmon-ruler' relationship, which is typical for a system having two interacting metal nanoparticles.24 The 'plasmon-ruler' behaviour is shown in Fig. 3(c), where the shift in the HGN’s plasmon resonance wavelength, scaled by the SGN LSPR wavelength (∆λ/λ ), is plotted against the closest inter-surface distance, scaled

diameter (2r) of 40 nm. For comparison, the absorption spectrum of an SGN of identical dimension is also shown in the same plot. A single LSPR band is observed for the HGN at λ = 704 nm that is narrower, higher in intensity, Page 3 of 9

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by the cavity radius ((R-r)/r = x). A least-square fit to the  data with an equation of the type ∆λ/λ    ⁄τ , where τ is the exponential decay constant and A is a pre-factor, yields τ = 0.190 ± 0.005 and A= 0.803 ± 0.021. A decay constant value of 0.190 is very similar to what is obtained in case of two interacting solid gold nanospheres or in a gold nanoshell, where two surfaces interact.24 The extent of spectral tunability in HGN is not limited by the cavity size only. Plasmon resonances in HGNs show a strong dependence on the thickness too. Fig. 4(a) shows the absorption spectra of an HGN with 32 nm cavity and various thicknesses. The LSPR spectrum of an HGN red-shifts monotonically with decrease in its thickness. This is an observation common in all planar metal nanostructures e.g., solid nanodisk or nanoprism. The lowering of the plasmon resonance energy is caused by an allowed ‘bonding interaction’ between the plasmon modes associated with the top and the bottom surfaces of the nanostructure.22 Comparison between the chargedensity distributions (at the LSPR wavelengths) along the XZ plane in two HGNs with two different thicknesses (40 nm and 10 nm) proves this argument [Fig. 4(b)]. LSPR

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cies (of the LSPR peak positions) on L, T and r and define an aspect ratio (AR) for any HGN system as AR= L*R/T(Rr) such that λSPR ∝ AR. This proportionality holds good for an HGN with any combination of L, T and r, as long as the cavity is positioned at the centre of mass of the nanoprism. Fig. 5 shows the linear relation between λSPR and AR for several HGNs with different L, T, and r values.

Figure 5. Aspect ratio dependency of LSPR of HGNs. Aspect ratio is defined as L∗R/T(R-r), where L is side length, T is thickness, r is cavity radius and R is the shortest distance between the center of the cavity(coinciding with the center of mass) and side wall.

Table 1. Thickness dependence of the λmax of the dipolar LSPR of HGNs having 100 nm side length and varying cavity diameters.

Figure 4 . (a) Thickness dependence of the LSPR spectra of an HGN with 32 nm cavity and 100 nm side length. (b) Charge density distribution for two HGNs with two different thicknesses (10 nm and 40 nm ) along xz plane at the respective LSPR wavelengths. Stronger charge density and hence, stronger plasmon-hybridization is evident in the thinner HGN. (c) Comparison between the dependencies of λmax on L/T for HGNs (dashed line) and SGNs (solid line) having same outer dimension.

resonance peak position varies linearly with the length to thickness ratio (please note that in this work, the side length of the SGNs and HGNs are always kept fixed as 100 nm). Fig 4(c) shows the linear dependency of λmax on L/T for the HGNs, shown in Fig. 4 (a), and also for the SGNs with identical side lengths and thicknesses. Although the LSPR spectra of both SGN and HGN red shifts linearly with decreasing T or increasing L/T (please note that in Fig. 4(a) and (b) the L is constant) we find a striking difference between HGN and SGN in their spectral tunabilities. The slope of the λmax vs L/T plot is larger for HGN. In fact, an investigation into the thickness dependence of LSPR of HGNs with different cavity sizes (Table 1) reveals that an increase in the cavity size leads to large increase in the range of thickness dependent spectral tunability in HGN compared to SGN. It is obvious from Table 1 that the LSPR peak-position, specifically the bonding plasmon mode, is dictated by all three size parameters (L, T and r) together. We combine the observed individual dependen-

Thickness

λmax(nm)

(nm)

SGN

HGN

HGN

HGN

(no cavity)

(8 nm cavity)

(32 nm cavity)

(48 nm cavity)

10

732

736

831

1103

20

654

660

724

931

30

624

630

682

855

40

614

615

660

815

50

602

606

646

786

60

600

600

636

768

Next, we investigated the dependence of LSPR peak position on the location of the cavity. For this, we calculated the LSPR spectra of HGNs with the same length, thickness and cavity diameter but varying only the cavity positions in Y direction i.e., along the median of the triangular face. The cartoon in Fig. 6(a) schematically depicts six different locations of cavities (essentially the cavitycentres) that we have studied for the HGNs with L= 100 nm, T=40 nm and a cavity diameter of 32 nm. Please note that Fig. 6 (a) essentially depicts six different HGNs in a single cartoon. The resultant spectra are shown in Fig. 6(b), which reveals that λLSPR red-shifts exponentially as the cavity is moved further away from the base and closer to the tip. Interestingly, we also notice the appearance of a prominent in-plane quadrupolar mode as the cavity approaches the tip (see SI for the E-field distribution). The appearance of a quadrupolar mode in the spectra is not due to any increase in the volume of the particles but due to a drop in the inter-surface distance as the cavity

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approaches the tip. Such reduction in the inter-surface distance allows the excitation field to easily penetrate through the interior, leading to the generation of surface dipoles as well as interior dipoles of comparable magnitudes, which in turn leads to the appearance of higher order multipoles in the LSPR spectrum. This reveals how the extreme difference in structural parameters of the HGNs affects the LSPR. A detailed study on the structurespecific multipolar plasmon modes in HGNs is underway in our laboratory and will be published elsewhere. Let us now bring our attention back to the foregoing discussion on the spectral tunability caused by the shifting of the cavity. A huge red-shift of ~ 250 nm is observed by shifting the cavity only by 32 nm and the spectral shift is clearly an exponential function of the cavity displacement. This result clearly shows the extreme structure-specificity of the optical properties of HGN, a plasmonically hybrid nanostructure. Note that such an alteration in the cavity position does not change the particle volume, as it does when the cavity size, thickness or the side-length is changed. The only thing that is changed here is the distance between the cavity surface and the outside-wall surfaces. Closer the cavity to the side-walls, smaller are the inter-surface distances and hence higher is the coupling which in turn lowers the energy of the resulting bonding plasmon mode. Analysis of the electric field distributions in two HGNs with two different cavity

Figure 6. (a) Six different cavity positions for six HGNs are indicated in a single cartoon. (b) Cavity-position dependency of LSPR for six different HGNs having L=100 nm, T= 40 nm positions along the median provides clear evidence for this argument [Fig 6(c) and (d)].

and 2r=32 nm. The studied cavity positions are: 18 nm, 28 nm (this is CG), 38 nm, 44 nm, 48 nm, and 50 nm respectively, from the base of the nanoprism. Exponential shift in the LSPR and appearance of higher order multipoles in the spectra with decrease in tip to cavity surface distance are apparent. (c) Electric field distributions (in log scale) of HGN having the center of the cavity at the CG and (d) 50 nm from base. We now turn our attention to the refractive index (RI) sensing properties of the HGNs. Fig. 7(a) shows the absorption spectra of an HGN with L=100 nm, T=10 nm and 2r= 48 nm, calculated under various dielectric environments. For comparison, the absorption spectra of an SGN (having the same dimension as that of the HGN) were calculated under the identical dielectric environments and are shown in Fig. 7(b). Increase in the RI of the surrounding medium leads to red-shift of the LSPR in both

Figure 7. LSPR spectra of (a) an HGN with 48 nm cavity, and (b) an SGN as functions of refractive indices of the surrounding medium. The side-length and the thickness of both the nanoprisms are identical: L=100 nm, T=10 nm. (c) Linear dependence of the LSPR maxima[see (a) and (b)] of HGN and SGN on the bulk refractive index. The slope of the plot is the RI sensitivity (LSPR shift/change in RI) of the nanoparticle. Clearly, the sensitivity is much higher in HGN than SGN (d) Aspect ratio dependency of the RI sensitivities for the HGNs.

the cases. However, the extent of spectral shift is much higher in case of HGN. We calculate and compare the RI sensitivities (sensitivity = spectral shift/change in RI, i.e., ∆λ/∆n) for the HGN and the SGN (Fig. 7(c)). We also investigated the aspect ratio dependency of the RIsensitivities for the HGNs which are described in Fig. 7d). From the slopes of the plots in Fig 7(c) we find the RI sensitivities for the HGN and the SGN as 688 nmRIU-1 and 410 nmRIU-1, respectively. The observed RI sensitivity for the HGN under consideration is pretty similar to the value calculated for gold nanoframes.18 RI sensitivity of an LSPR mode originates from the reduction in the repulsion between the coherently oscillating electronic dipoles of that particular plasmon band upon the increase in the RI of the surrounding medium. As a result, the LSPR bands with the larger average induced electric-field strength around the nanoparticle can be stabilized more in a medium with a certain refractive index. The overall RI sensitivity of a nanostructure is determined by the strength and also the decay length of the nanoparticle’s plasmonic electric field (see SI for a detailed discussion on the dependence of RI sensitivity on the strength and spread of the local E-field).25 More the local E-field, greater the RI sesitivity. Also, larger the spread of the local electric field, larger is the sensing volume and therefore higher sensitivity. For example, a plasmonic nanoparticle-dimer shows higher RI-sensitivity than an isolated particle due to an enhancement of local electric-fields caused by plasmon-hybridization.26 Like a plasmonic nanoparticle-dimer, HGN too is a plasmonically hybrid system. Therefore HGN too can have very strong plasmonic fields on account of the coupling between their interior and exterior surface plasmons. The coupling between these two plasmon modes can give the hollow nanoprisms additional electric fields which are expected to greatly enhance the RI sensitivity. Moreover, by tuning the inter-surface gap, the electric-fields and thereby the RI-sensitivities of the HGNs can be controllably tuned. In order to examine the effect of the coupling between the plasmons on the cavity surface and outer surface (side walls) of the HGN, we calculated the field enhancement factors for two HGNs with two different cavity sizes (32

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nm and 48 nm, T=10 nm, L= 100 nm) at the respective LSPR maxima and compared those results to the results obtained with an SGN [Fig. 8(a-c)]. It is very clear fromFig. 8 (a-c) that the average strength and also the spread of the plasmonic fields are enhanced tremendously with increasing cavity size. It is also clear that the enhancement in the local electric-fields is solely due to

Figure 8. Electric field distributions (in log scale) calculated at the respective LSPR maxima for (a) an SGN (b) an HGN with 32 nm cavity, and (c) an HGN with 48 nm cavity. All the nanoprisms are 10 nm thick and have side length of 100 nm.

an increased proximity of the inner and outer surfaces with increasing cavity size, i.e., with decreasing intersurface gap and increasing aspect ratio. Such inter-surface distance dependent increase in local electric fields with increase in cavity size explains the aspect ratio dependency of the RI-sensitivity as shown in Fig. 7(d). Moreover, all these results suggest that the local electric-field and consequently the RI-sensitivity of any given HGN can be maximized by placing the cavity surface at the closest possible distance from the outer surface. This can be achieved most easily and efficiently by shifting the cavity toward the tip (i.e., adopting and maintaining a C2v geometry), similar to what we have shown in Fig 6 (c-d). Such shifting enhances the RI-sensitivity of an HGN exponentially (see SI). An investigation into the RI dependence of the dipolar LSPR peak of an HGN (L=100 nm, T=4 nm, 2r=48 nm) whose cavity-centre is shifted by 6 nm from the centre of mass toward the tip, yields a sensitivity value of 1062 nmRIU-1(See SI). Note that for the HGN with the same L, T, and r values but the cavity placed at centre of mass of the prism yielded a sensitivity of 812 nmRIU-1 (see SI). To our knowledge, the observed RI-sensitivity value of 1062 nmRIU-1 for a gold nanostructure of such a small volume (~ 10000 nm3) is unprecedented. Based on our results, we emphasise that it is possible to tune the sensitivity to even larger values by controllably tuning the structural parameters (e.g., thickness; reduction of thickness steeply increases RI-sensitivity for HGNs; see SI) of the nanoprisms and the sensing wavelength range can go well beyond near infrared. As a matter of fact, the RIsensing ability of the HGNs, studied in this work, spans a wide range of wavelength, from visible to near infrared (592 nm - 2312 nm). It is interesting to note that both the factors namely, reduction in thickness and the shifting of the cavity of an HGN toward the nanoprism's tip, enhances the RI-sensitivity but the enhancement is linear in the former case but exponential in the latter case. Therefore, it is pretty obvious that the RI sensitivities of HGNs are

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much more sensitive to the position of cavity than the thickness of nanoprism. In the preceding sections we have demonstrated that the RIsensitivity of HGNs can be tremendously enhanced by the judicious optimization of the structural parameters. However, it is known that certain structural defects such as, cornerrounding and corner-snipping lowers the RI-sensitivity of 27 solid nanoprisms. Unfortunately, some amount of rounding or snipping of the corners (tips) is almost inevitable in case of colloidal metal nanoprisms, be it solid or hollow. Therefore, we studied the effect of such structural defects on the RI-sensitivities of HGNs and compared the results to those obtained for SGNs. The studied nanoprisms were 10 nm thick and had side-lengths of 100 nm before the incorporation of any rounding or snipping. Next, more and more rounding/snipping were introduced at the corners of the nanoprisms. Note that we considered only the tips of the nanoprisms as corners in this study. The cavity diameter in the case of HGN was 32 nm. The results are shown in Fig. 9. We see from Fig. 9 (a and b) that RI-sensitivity decreases for both SGN as well as HGN with increasing snipping or rounding of the corners. However, the most interesting point to observe here is that the loss of sensitivity for HGN, upon rounding/snipping the corners, is far less than that determined for the SGN. This is a very important and interesting

Figure 9. Effect of (a) snipping and (b) rounding of corners of the HGNs and SGNs (T=10 nm, L= 100 nm, 2r = 32 nm) on their RI sensitivities. It is evident that snipping and corner rounding reduces the sensitivities but the reduction is less in HGN than SGN. Electric field distributions for HGNs [(c) and (d)] and SGNs [(e) and (f)] with and without corner rounding.

property of the HGNs which makes them superior candidate than SGNs in practical sensing applications. However, the question that we ask at this point is: why does HGNs suffer less loss of sensitivity compared to SGNs? In order to find the answer, we performed comparative analyses of the electric-field distributions in hollow and solid gold nanoprisms with various degrees of corner-rounding or snipping. Four representative images of electric-field distribution corresponding to HGN and SGN with sharp and rounded tips are shown in Fig. 9 (c-f). From the plotted field profiles it is obvious that the main reason behind the drop in RI-sensitivity is a decrease in local electricfield intensity (which in turn results in sizeable amount blue shifting of the dipolar LSPR peaks) and its average decay length upon rounding of the corners. The loss in the field intensity and its average decay length upon corner rounding is much more for solid nanoprism compared to HGN. Nanoparticles with sharp tips show extremely high concentration and enhancement of electric-field at Page 6 of 9

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the tips. This effect is also known as lightning rod effect. Any rounding or snipping of the sharp tip drastically reduces the lightning-rod effect leading to a reduction in the electric-field intensity and a spectral blue shift. This is exactly what happens in case of the SGNs as, for SGN, the electric-field hotspot is generated only within a small volume around the tips. On the other hand, the scenario is quite different for HGNs. Unlike SGN, the lightning rod effect is not the only cause behind the concentration and enhancement of electric field in HGNs. Plasmon hybridization in HGN leads to the concentration of a large quantity of additional electric-fields and that too, over a large volume. This additional electric-field originating from plasmon hybridization does not get affected much due to a rounding or snipping of the tips. Therefore, a corner rounding or snipping cannot diminish the overall electric field intensity and its spread from the surface in HGNs by the same extent as it does for SGNs. The overall findings of this work unequivocally suggest that, due to their extremely large RI-sensitivities and a better immunity against shape defects, HGNs are much better suited as nanosensors in the visible-NIR region than any other plasmonic nanostructure of comparable volume

gion than any other plasmonic nanostructure of comparable volume.

ASSOCIATED CONTENT Supporting Information: It contains polarization dependence of the LSPR spectra, electric-field distribution for quadrupolar mode, E-field dependence of RI sensitivity, thickness and cavity-position dependence of RI sensitivity. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author Manabendra Chandra. Email- [email protected]

ACKNOWLEDGMENT This work was supported by the Council of Scientific and Industrial Research, Govt. of India (Project No- CSIR/CHM/ 2015220). The authors thank Vijay Ganesh for his help in plotting electric-field and charge-distribution data using IGOR.

ABBREVIATIONS

CONCLUSIONS In this study, we have determined the structure-specific plasmon resonances, the associated local electric-fields and the sensitivity factors of various different structures of hollow gold nanoprisms using finite-difference timedomain technique. The LSPR peak positions, the plasmonic fields and the RI sensitivities of the HGNs are highly tunable and structure-specific and are sensitive to the thickness, cavity size and especially, to the cavityposition. The RI sensitivities of HGNs are much larger than those of solid gold nanoprisms of similar dimensions. This is due to the fact that HGNs have larger sensing volumes with strong plasmonic E-fields resulting from the plasmon hybridization, as evident from the E-field and charge-density distributions. Our results show that the sensitivity factor scales almost linearly with the aspect ratio of the HGNs. Interestingly, the sensitivity factor of HGN increases exponentially when the cavity is moved toward the tip of the prism. For a 4 nm thick HGN, with 48 nm cavity and 100 nm side length, whose cavity-center is 52 nm away from the tip, shows a sensitivity factor of 1062 nmRIU-1. This is the largest RI-sensitivity value ever measured or calculated for any plasmonic nanostructures with similar volume. Moreover, the RI sensing ability of the HGNs, studied in this work, spans a wide range of wavelength, from visible to near infrared (592 nm-2372 nm). Another interesting observation is that the loss in RI-sensitivity due to very commonly occurring shapedefects such as corner rounding or snipping is much less in HGNs compared to solid gold nanoprisms. Overall, it turns out from this comprehensive study that HGNs are much better suited as nanosensors in the visible-NIR re-

HGN, Hollow gold nanoprism; SGN, Solid gold nanoprism; LSPR, Locallized surface plasmon resonance; FDTD, Finitedifference time-domain; RI, Refractive index.

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