Enhancement of photothermal heat generation by metallodielectric nanoplasmonic clusters

A four-member homogenous quadrumer composed of silver core-shell nanostructures is tailored to enhance photothermal heat generation efficiency in sub-nanosecond time scale. Calculating the plasmonic and photothermal responses of metallic cluster, we show that it is possible to achieve thermal heat flux generation of 64.7 μW.cm and temperature changes in the range of ΔT = 150 K, using Fano resonant effect. Photothermal heat generation efficiency is even further enhanced by adding carbon nanospheres to the offset gap between particles and obtained thermal heat flux generation of 93.3 μW.cm and temperature increase of ΔT = 172 K. It is also shown that placement of dielectric spheres gives rise to arise collective magnetic dark plasmon modes that improves the quality of the observed Fano resonances. 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Introduction
Photothermal heat generation in metallic subwavelength structures in a short time scale has been extensively utilized in biological applications [1], photothermal cancer and tumor therapies [2][3][4], photothermal imaging [5], bubble formation for surgery [6], control of enzyme reaction [7], optoacoustic thermal therapy [8], and nanodrug delivery [9].For the noble metallic particles, localization of surface plasmon resonances (LSPRs) in nanosize structures with absorptive behavior leads to tremendous dissipation of an incident optical energy [10].This large amount of light absorption can be achieved in an extremely short time interval by the free electron gas through electron-electron scattering in a picosecond time scale at the metal-dielectric boundary, and results in photothermal heat generation [11].The photothermal responses of various shapes of nanoparticles (NPs) in different orientations have been investigated analytically and experimentally, and also, the effects of structural, optical, and environmental parameters were included in these analysis [12].Considering experimentally measured refractive index [13], dielectric constant [14], thermal conductivity [15], and specific thermal heat capacity [16] for several substances, Silver (Ag) and Aluminum (Al) have emerged as the metals of choice for light-to-heat conversion.
In the past decade, hybridization of plasmon resonances was introduced as one of the most important mechanisms in excitation and intensification of plasmon resonant modes inside and between metallic molecular NPs [17].This phenomenon can be understood by analyzing the plasmon response of simple NP assemblies such as dimers and trimers.It is verified that plasmon hybridization in a nanocomplex can be resulted by the excitation of the bonding bright and the antibonding dark resonant modes [18].In this regime, a weak and destructive interference between opposite modes might results in formation of Fano or Fano-like resonant dips [19].Fano resonance (FR) appears as a pronounced and distinct minimum at a certain frequency in the scattering spectra which strongly depends on the position and quality of dark and bright modes.Technically, at this point a high amount of optical energy accumulates in the structure and can be controlled based on application.Behaviors of hybridized and localized plasmon resonant modes and also FR mode depend on the material and geometrical properties of NPs.For instance, gold (Au) has been broadly utilized in designing molecular clusters for biochemical sensing and switching applications [19,20].Besides, Ag provides a remarkable absorption of optical energy in the visible to the near infrared region (NIR) due to ohmic losses and also the plasmon resonances excitation here depending on the complexity of the aggregate [21].On the other hand, very recently, cascaded plasmon resonant modes in simple compositional trimer clusters have been used in light to heat conversion process which resulted a significant temperature change with picoseconds relaxation time [22].Using NPs with high geometrical tunability and absorptive properties yield remarkable enhancement in photothermal response.Comparing the geometrical properties of various NPs, core-shell NPs and cavities provide unique geometrical tunability which can be employed to design highly symmetrical NP assemblies to support strong resonances [23,24].In the recent years, there have been great efforts to increase the temperature and efficiency of photothermal heat flux production in nanoplasmonic devices [12,22].However, the highest possible temperature variations that have been obtained was around ~100 K with the power flux of near to ~50 μWcm −2 .
In this context, we study the plasmon and photothermal responses for a quadrumer cluster comprises of Ag core-shell (CS) (Ag-CS) nanostructures in free space and aqueous ambiences.Using plasmon hybridization theory, we analyzed and compared the plasmon response for metallic and metallodielectric quadrumers.It is proved that a symmetric and identical four-member cluster is able to support pronounced FR mode during laser pump exposure.Determining the photothermal heat energy flux produced by the cluster, we quantified the temperature changes numerically and theoretically.Then, with the placement of carbon nanospheres (CNSs) in the offset gap space between NPs, we introduced a metallodielectric molecular assembly to enhance the photothermal efficiency.Analyzing the photothermal response of the proposed metallodielectric nanostructure, we enhanced the quality of FR mode by inducing new magnetic dark modes by tiny CNSs.It is verified that this structural modification can result in a dramatic enhancement in the temperature.

Results and discussion
To calculate the spectral response for the proposed structures, finite-difference time-domain (FDTD) method was used (Lumerical FDTD Solutions package), with the following parameters: The spatial cell sizes (mesh sizes) were set to d x = d y = d z = 0.5nm, and 128 perfectly matched layers (PMLs) were the boundaries.Also, considering numerical stability for the employed subwavelength components, simulation time step was set to the 0.02 fs according to the Courant stability.The light source was a Gaussian pulse with a pulse length of 2.6533 fs, the offset time of 7.5231 fs, the waist radius of the incident beam is 600nm, and the divergence angle was set to 9.04°.The default intensity of the incoming electric field was set to 1 × 10 −3 W.μm −2 .However, we also analyzed the photothermal heat production for different incident light intensities.Figs.1(a)-1(c) exhibit schematic diagrams for an Ag-CS NP with the description of geometrical parameters inside and also, the quadrumer cluster in both metallic and metallodielectric regimes, respectively is shown here.To examine the optical properties of the quadrumer cluster, we used a modified version of Drude model for Ag-CSs particles [24]: where ε ∞ is the permittivity for the high-frequency response ε ∞ = 4.9.For the present study the other model parameters are: the bulk plasma frequency ω p = 1.3736 × 10 16 rad/s, and the damping frequency γ = 2.7335 × 10 15 Hz.Locating four identical Ag-CSs with the dimensions of r a /r b /r c /h = 60/105/140/85 nm next to each other with an offset distance of D 4q = 15nm (see the inset in Fig. 1(d)).We calculated the scattering and absorption profiles for the quadrumer cluster in free space and water which are shown Figs.1(d) and 1(e), respectively.For the free space (n = 1), a noticeable FR mode is induced at the visible spectrum (λ = 0.690 μm), while for the fluid system (n = 1.33) like biological mechanisms, the FR is red-shifted to the longer spectra (λ = 0.760 μm) and also becomes deeper due to high amount of energy accumulation at this position [25,26].This red-shift in the position of FR mode includes a noticeable field intensification at the resonance frequency (ω LSPR ).In addition, a huge amount of power dissipation is recorded at the resonance wavelength.Noticing in the numerically obtained Efield maps as two-dimensional snapshots for each profile (see Figs. 1(f) and 1(g)), the plasmon resonance enhancement in the aqueous ambience is superior and the excitation of plasmon resonances in all of the NP members is achieved.Also, in this system, the EM energy is localized in the offset gaps between Ag-CS particles and in the space between the core and shell parts.This strong localization of plasmon modes can lead to large amount of heat energy production.In this regime, we expect an enhanced photothermal power generation at sub-nanosecond time scale according to the incident Gaussian pulse length (~2.65 fs).The amount of power dissipation and heat generation can be analyzed in nanoscale dimensions considering all the parameters for the structural and environmental characteristics using the following equation [22,27]: where C abs is the, absorption coefficient φ is the optical flux of the incident light source (Jm −2 ), c CS is the specific heat capacity of the Ag-CS (JKg −1 K −1 ) NPs, ΔT is the temperature variations in a specific time scale (K), ρ cs is the density of the Ag-CS (Kgm −3 ) NPs, and V CS is the volume of the entire nanocluster (m 3 ).Practically, the mechanism of photothermal heat generation and transfer in nanoscale is a nonequilibrium process.Hence, we assume that the phonons interact with the Ag-CS cluster as a hot object, with the aqueous medium as a cool object and travel in this ambience [22].Considering the amount of absorbed power and environmental properties, the absorption coefficient at ω LSPR is given by: where P LSPR is the optical power loss density per volume that is absorbed by NPs based on ohmic losses of Ag-CS units at ω LSPR , n m is the refractive index of the surrounding medium, 0 ε and 0 μ are the permittivity and permeability of the free space, respectively, and exc E  is the amplitude of the incident transverse electric field.Here, we put into the account, the amount of energy that was absorbed at ω LSPR , and then, we determined the photothermal heat generated in a very short time scale by setting the relevant simulation parameters in picoseconds.Figure 2(a) shows the total generated heat flux (Q h ) by the Ag-CS quadrumer cluster in the water medium, which can be quantified at ω LSPR by using the equation: ( ) proposed by Baffou et al. [12].More than the distinct extreme that is appeared for the position of FR minimum, we also observed a couple of shoulders at the visible (~0.580 μm) and NIR (~1.1 μm) spectra which are correlated with small amount of optical power absorption at the bonding and antibonding resonant modes positions, respectively.For the considered setting above, we calculated the temperature changes as ΔT = 150 K for a metallic quadrumer cluster composed of Ag-CS particle units with the optical fluence of the incident pulse of 20 Jm −2 .The energy dissipation inside the metallic quadrumer cluster at ω LSPR is shown in Fig. 2(b) as heat power map.It should be underlined that such a high temperature is obtained in a sub-nanoscale time duration due to high dissipation of optical power inside the Ag-CS quadrumer cluster.However, this performance of the proposed nanocluster can be further enhanced by utilizing plasmon transmutation effect [28,29].To this end, we modified the plasmon response of the quadrumer cluster with the placement of CNSs to the offset junctions between proximal NPs (Ag-C-Ag).For the CNSs, we employed carbon particles with the experimentally determined complex permittivity as ε = 2.25 + i0.0215, and absorption coefficient, α = 1531.5cm −1 [30].The plasmon transmuting in a four-member subwavelength cluster includes inducing collective antibonding magnetic plasmon resonant modes which leads to intensifying the energy of the induced FR dip.To show the effect of CNSs placement to the metallic quadrumer cluster, we calculated the photothermal response for the metallodielectric nanocomplex with breaking the symmetry of the cluster due to the presence of the nanospheres.It should be noted that due to the concentration of hybridized plasmon resonant modes at the edge-to-edge distances (gaps) between Ag-CS units, we expect more heat generation in these regions.The placement of the carbon nanospheres in the gaps accompanied by the formation of strong collective magnetic modes results in large plasmon resonance energy accumulation at these gaps.Figures 3(a) and 3(b) exhibit the scattering and absorption cross-sectional profiles for the metallodielectric assembly, respectively.It is observed that placement of two CNSs with the radii of 14nm in the junction between Ag-CS NPs makes corresponding FR dip deeper, meanwhile its position red-shifts to the longer wavelengths due to symmetry cancellation caused by addition of CNSs.Considering the plasmon resonance hybridization mechanism, with the placement of one or two CNSs at the left side of the quadrumer, collective magnetic subradiant modes could be induced, while a symmetry breaking can be performed as a result of this metal-dielectric contribution.Formation of collective magnetic dark modes can result in a deeper Fano minimum.However, comparing the effect of symmetry breaking and the CNS deposition, the role of dark modes induced by CNSs in Fano minimum intensification is significant.Hence, increasing the number of CNSs at the offset gaps between Ag-CSs leads to formation of enhanced subradiant modes.Therefore, for the quadrumer cluster with four CNSs, a sharper dip appears at λ = 0.950 μm, corresponding to the strong hotspots.Note that in the depicted scattering spectra in Fig. 3(a), increasing the number of the deposited CNSs at the gaps, red-shifts the FR mode and leads to narrower and deeper dips.The inset in Fig. 3(a) shows a schematic for the examined quadrumer with the placement of CNSs, while the illumination and polarization directions are indicated by arrows.Figure 3(c) displays the field distribution and E-field map for the plasmon resonance hybridization and excitation inside a metallodielectric quadrumer with two CNSs in the left side of the quadrumer (the location of dielectric spheres are indicated by the arrows).For the metallodielectric quadrumer with four CNSs, analyzing the photothermal response of the latest nanocomplex immersed in the aqueous ambience (see Emap profile depicted in Fig. 3(d)), we found a significant improvement in the electric field enhancement in comparison to the fully metallic quadrumer and a cluster with two CNSs.In order to show the behavior of quadrumer at the position of bright and dark modes, we plotted electric field distribution diagram for both of the modes, as shown in Figs.3(e) and 3(f), respectively.Noticing in the depicted arrows, in Fig. 3(e) all of the dipolar plasmons oscillate in-phase and in the same direction in all of the Ag-CS units.On the other hand, considering Fig. 3(d), the dipolar moments of two units are in the opposite direction of the other units, which is in complete agreement with the plasmon hybridization theory.Figure 4(a) shows the internal electric field enhancement factor (|E in |/|E exc |) which is the ratio of the overall localized field in the NPs gaps and in the space between cores and shells to the incoming electric field for the clusters in all the examined structural alterations.This field enhancement is calculated at the FR position.Comparing this parameter for both metallic and metallodielectric (with four CNSs) clusters, a significant enhancement in the electric field intensity for the metallodielectric structure with four CNSs is observed.Figure 4(b) shows numerically computed photothermal heat flux where the peak of power is red-shifted to the longer spectra by increasing the number of CNSs.For the cluster with four CNSs, the photothermal heat power flux is calculated as 93.3 μW.cm −2 .Figure 4(c) exhibits the absorbed power loss density by NPs as a two-dimensional snapshot.Employing the method described above, temperature variation in the metallodielectric nanocomplex is estimated as ΔT = 172 K.  Finally, we examined the effect of variations in the intensity of the incident laser power on the photothermal heal temperature production as shown in Fig. 4(d) for both metallic and metallodielectric quadrumer clusters.Using the proposed method by Fang et al. [31] that was proposed for plasmonic particles immersed in water medium, the temperature variations in the proposed nanoscale structure can be plotted as a function of incident laser source power.According to depicted I-T curve, increasing the intensity of light up to 1.5 mW.μm −2 leads to minor enhancements in the produced photothermal heat temperature, while for higher intensities (I>1.5 mW.μm −2 ) temperature variation is very small and negligible, due to limited geometrical capacity of the quadrumer nanostructure in supporting high energies.For instance, for I = 2 mW.μm −2 , change in the temperature due to generated thermal heat could not reach above ΔT~180 K (saturating condition).Also, it should be underlined that for practical applications, such a high power can result in destructive effects such as defects in the geometries of the cluster.
Carbon nanotubes and graphene sheets [32] and more recently plasmonic nanoshells and nanomatryushkas [33] have been employed in bio-medical applications such as tumor and cancer therapies.Here, we proposed a numerical method to analyze the behavior of a nanoplasmonic structure with the contribution of carbon nanospheres.Comparing the performance of the proposed nanostructure with the analogous ones that have been reported in the literature [32,33], the plasmon response of the proposed structure is superior,Therefore, with their improved characteristics, we expect that the proposed metallodielectric nanostructures will make a great contribution to various bio-medical and photothermal spectroscopy applications.

Conclusions
In this study, we proposed a method to improve photothermal heat generation in both fully metallic and metallodielectric quadrumer cluster composed of Ag-CSs and CNSs.Analyzing the spectral response of the metallic assembly, we determined the generated photothermal heat power flux numerically.Then, with the placement of CNSs in the offset gap distance between proximal NPs, we induced collective magnetic plasmon resonant (dark) modes in the cluster that resulted in pronounced FR mode in the extinction profile which is correlated with the high power absorption at the NIR.Using photothermal spectroscopy, we analyzed and compared generated thermal heat flux for quadrumers with subnanosecond relaxation time.

Fig. 1 .
Fig.1.a, b, c) Schematic diagrams for an Ag-CS nanoparticle and a four-member quadrumer composed of CS NPs in both metallic and metallodielectric regimes, respectively, d, e) scattering and absorption profiles for the metallic quadrumer in the free space and aqueous ambiences under transverse polarization excitation (E exc ).The insets show the gap distance between Ag-CS units and E-field illumination direction, f, g) E-field profiles during plasmon resonance excitations coupling in the metallic quadrumer in free space and liquid systems.

Fig. 2 .
Fig. 2. a) Thermal heat power flux (Q h ) profile for a metallic nanoassembly during laser pump exposure in a liquid system, b) dissipated power density mapping in a metallic quadrumer at the peak of absorption.

Fig. 3 .
Fig. 3. a, b) Scattering and absorption spectra for Ag-CS quadrumer cluster with the carbon nanospheres with different quantities in an aqueous system, c, d) electric field profile |E| showing the hybridization and enhancement in metallodielectric quadrumer clusters with two and four CNSs, respectively, e, f) electric field distribution diagram inside the metallodielectric quadrumer with four CNSs at FR position for bright and dark modes.

Fig. 4 .
Fig. 4. a) Field enhancement factor (|E in |/|E exc |) over the photon energy for both metallic and metallodielectric (with four CNSs) clusters in an aqueous ambience, b) photothermal heat power flux (Q h ) spectra at the interparticle junction for a metallodielectric assembly with CNSs, c) photothermal heat density in quadrumer with four CNSs, d) photothermal heat temperature variations over the laser pulse intensity for both metallic and metallodielectric plasmonic clusters.