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Abstract
Material modification on plasmonic nanostructures is recognized as one of many approaches to increase optical near-field enhancement and resonance wavelength tuning. In this work, with finite-difference time-domain simulation, we showed that closed-hexagonal sub-micro disk arrays of the AgxAu1−x alloy increase electric-field enhancement in the near-infrared spectra at reduced Ag fraction in the alloy, while the arrays of pure Ag does so in the visible spectra. For the enhancement factor in the near-infrared region, the Au array is dominant around the wavelength of 800 nm, whereas the Ag0.74Au0.24 array is slightly stronger at 820 nm. Furthermore, the local confinement in the near-infrared region (800-900 nm) is strengthened by the heteromaterial array of Ag/Au sub-micro disks with alternating rows, which can boost the electric field enhancement at 1.3 and 3.9 times better than those of the pure Au and Ag arrays, respectively. The Ag, Au and Ag/Au plasmonic hexagonal arrays yield the Purcell factors of 2.42 × 105, 1.17 × 104 and 2.72 × 104, respectively, at wavelengths of 695 nm, 828 nm and 795 nm that would be suitable for spontaneous emission rate enhancement in quantum dots.
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1. Introduction
Plasmonic resonance is caused by the collective oscillation of free electric charges (plasmons) driven by optical excitation. The effects of plasmonic resonance can enhance light-matter interaction and absorbance, which has been widely beneficial in, for examples, photoluminescence [1,2], surface-enhanced Raman spectroscopy [3], infrared photodetection [4], broadband absorption [5], optical polarization converter [6], plasmonic induced transmission enhancement in waveguide [7], and second harmonic generation [8,9]. In addition to applications in sensing, especially biosensing, recently plasmonic resonance has also found applications in quantum communication technology, where optical confinement with plasmonic effects is reported to strengthen single photon brightness via plasmonic nanostructures [10–13].
Multiple factors influencing plasmonic resonance modes, and in turn the optical confinement ability, include particle size and shape [14,15], coupling distance of particles [16–19], particle arrangement [20], geometry of coupled objects [21–26], domain size of particle assembly [27], and refractive index of substrate and surrounding materials [28–30].
Plasmonic nanostructures can be fabricated in variety geometry, for examples, silver cube on flat surface [10], nanoantenna [11], nanocavity array [12], waveguide-slit [13] and metallic nanoslit array [31]. As shown in previous reports [10–13], they have been well integrated with colloidal quantum dots for suitable matching of excitation wavelength and quantum-emitter energy gap in wide range of wavelengths for spontaneous emission to improve the second-order autocorrelation $g^{2}(0)$; for examples, CdSe/ZnS (610 nm, $g^{2}(0) \approx 0.14$) [32], InP/ZnSe (629 nm, $g^{2}(0) \approx 0.03$) [33], CdSeTe/ZnS (705 nm, $g^{2}(0) \approx 0.01$) [34] and InAs/CdZnS ($\sim$ 1300 nm, $g^{2}(0) \approx 0.01$) [35]. The nanostructure of metal disks is interesting in terms of well fabrication control with mask lithography in size and inter-particle spacing.
Two-dimensional disk arrays have been used as optical confinement nanostructures which can be found in square [36–38] and hexagonal lattices [39–41]. Tuning the plasmonic resonance wavelength of a nanodisk at fixed physical parameters can be done by material mixing to modify the dielectric permittivity [42]. Combinations of materials such as alloys of Ag-Au, Au-Cu, Au-Pd, Ag-Pd, Ag-Cu have been investigated in random nanodisks [43]. The dielectric permittivity of the alloy can be estimated as a linear combination of each constituent’s permittivity via Vegard’s law [44], weighted by the fraction of the elements in the alloy. It can possibly extend to plasmonic wavelength shifts and polarizability. The plasmonic resonance of heteromaterial nanostructures have been extensively explored in dimers [45–47]; however, to our knowledge, the infinite two-dimensional arrays have been less examined.
Au and Ag are popularly used in optical enhancement due to their biocompatibility (especially Au), photo-stability and plasmonic properties. However, they have own advanatges and disadvantages different from each other. For example, Au has more chemical stability and easier attachement to some chemical molecules, such as methylthiolate [48], on a metal surface. On the other hand, Ag has lower optical absorption in the visible light region and stronger near-field confinement ability resulted from the interband and intraband transitions [49,50] and coherent time of electrons’ oscillation [51,52]. Even though Au has weaker near-field confinement strength, this weakness can possibly be improved by mixing with Ag as alloy [53] or supporting the confinement via heteromaterial nanostructure [54], where the presence of different materials induces opposite electric charges from different material neighbors. We note that Ag has enhancement wavelengths in the visible region, while Au has less absorption in the near-infrared region. Conceivably, the Ag/Au combination can potentially shift the resonance to different wavelengths, thereby tuning it to desirable wavelength range for intended application. Therefore, it is beneficial to investigate the Au-Ag alloy and their heteromaterial arrays to evaluate and compare the optical enhancement performance in different wavelengths. The insights and deeper understanding of the plasmonic resonance can provide mechanism for tuning resonance wavelengths at far-field and modifying strength of enhancement at interested wavelengths.
To increase the spontaneous emission rate, an optical confinement system should have high quality factor $(Q)$ or small mode volume $(V)$. The high $Q$ factor is frequently achieved in photonic cavity; however, it generally has a large mode volume due to diffraction limit [55]. To reduce the mode volume, concentrating electric field with plasmonic effect is a popular choice. Although the $Q$ factor of a plasmonic nanostructure is much lower than that of the dielectric cavity, the plasmonic system generally tends to yield brighter photon emission [56]. The enhancement of spontaneous emission rate can be characterized via the Purcell factor [57], which is proportional to $Q/V$; see Eq. (6). The performance of optical enhancement has spatial dependence because the confinement of the electric field is dominant in some particular area. Thus, the $Q$ factor must be calculated at a position of interest and can be done by harmonic inversion method; see brief description in section 2.1.
In this work, we numerically investigated plasmonic resonance wavelengths focusing on the far-field absorption spectra and the optical confinement capability via near-field localization in the Ag$_{x}$Au$_{1-x}$ alloy and Ag/Au heteromaterial sub-micro disk arrays. With the modified dielectric permittivity by the alloy content, the alloy array is expected to tune the plasmonic resonance. We explored both the heteromaterial arrays of two different materials and the alloys to boost the electric field enhancement of interested wavelengths pertinent to the emission of quantum dots for potential application in quantum technology [10–13]. As such the enhancement of wavelengths 600-1200 nm is our motivation. To compare the quality of enhancement, the $Q$ factor, the Purcell factor and the wavelength shifts were calculated to evaluate the enhancement performance on the spontaneous emission rate. For similar composition of materials, we will explore whether the alloys or heteromaterial structures yield better optical enhancement.
2. Simulation model
The plasmonic resonance on the hexagonal arrays of the Ag$_{x}$Au$_{1-x}$ alloy and of the Ag/Au heterostructure sub-micro disks were numerically simulated by the MIT Electromagnetic Equation Propagation (MEEP) open-software for electromagnetic simulation with finite-difference time-domain method [58]. The alloy array has disks of uniform material, which is varied in its decomposition ($x$), whereas the Ag/Au heteromaterial structure has alternating rows of Ag and Au disks, as depicted in Figs. 1(a)-(b). Each metal disk has a diameter of 250 nm and varying thickness of 50, 100 and 150 nm. A unit cell of the interested structure was composed of a rectangle with a disk at the center and a quarter of disk at each corner, see Fig. 1(b). The unit cell has dimensions of 250 nm $\times$ $250\sqrt {3}$ nm $\times$ 400 nm, which can be meshed with square grids of width 2.5 nm. The periodic boundary condition was imposed on the $xy$-plane, while the perfectly matched layers were assumed in the vertical direction ($z$-axis) on both sides of a disk to prevent back scattering of electromagnetic waves from cell edges. The hexagonal arrays were placed on a glass substrate with the refractive index $n$ of 1.52 [59]. In the simulation process, a Gaussian-pulse source with the central frequency of 499 THz and bandwidth of 501 THz generated a plane-wave in vacuum side and was incident on the plasmonic array in the normal direction. Time-series signals were collected by defined planes for reflection and transmission at 800 nm above and below the center of a metal disk. The reflection and transmission spectra were analyzed by the Fast Fourier transform and the absorption spectra were calculated from these reflection and transmission spectra.
Fig. 1. Geometry of hexagonal sub-micro disk arrays of (a) Ag$_{x}$Au$_{1-x}$ alloy and (b) Ag/Au heteromaterial on a dielectric substrate (glass). Each sub-micro disk has diameter 250 nm and thickness 100 nm. Electromagnetic waves propagate through the array in the $k$-direction (top to bottom). (c) Real and imaginary parts of the dielectric permittivity of Au, Ag and their alloys are plotted in the wavelength range of 250-1000 nm.
The optical property of a material depends on its dielectric permittivity, which can be approximated by the Drude-Lorentz model [60,61]. Following Ref. [61], for an alloy A$_{x}$B$_{1-x}$, the functional form of its permittivity $\varepsilon _{\text {alloy}}(x,\omega )$ can be expressed as
Here, the subscript $\infty$ denotes the electric permittivity at ultra-high frequency; $D$ and $L$ represent the Drude and Lorentz models, respectively. The coefficients $p_{m,A}$ and $p_{n,B}$ denote the oscillation strength of each oscillator divided by the summation strength $F_{\text {A}}$ from metal A, and $F_{\text {B}}$ from metal B, respectively. Simply by combining terms and enumerating the coefficients, we can express the alloy dielectric permittivity as
In the Drude model, $\omega _{p}$ and $\Gamma _{p}$ describe plasma frequency and damping constant, respectively. In the Lorentz model, the frequency $\omega _{j}$, strength $A_{j}$ and lifetime $1/\Gamma _{j}$ depend on each oscillator, indexed by $j$, since the oscillation of electrons under the applied external electric field can be expressed generally as a summation of $k$ oscillation solutions. In our calculations, the values of the aforementioned parameters for the Ag$_{x}$Au$_{1-x}$ alloy were obtained from Ref. [60]; specifically, for the fraction $x$ of Ag, the parameter values are listed in Table 1.
Table 1. Values of parameters used in our simulation are obtained from Ref. [60]
Table 2. Calculated Purcell factor ($F_{P}$), quality factor ($Q$) and effective mode volume ($V_{\text {eff}}$) of the pure Au, Ag/Au heteromaterial and pure Ag hexagonal disk arrays at selected wavelengths.
The electric charge density $\rho$ was calculated from the Gauss’ law, $\rho =\varepsilon \nabla \cdot \textbf {E}$, where $\textbf {E}$ is the electric field vector. The Purcell factor was calculated to evaluate the optical confinement ability via Eq. (6):
To that end, the effective mode volume, given by Eq. (7), is essentially calculated in a finite domain $\mathcal {R}$ as the electric field is dominant in local confinement and rapidly tends to zero away from the confinement.
In our calculation, the integration volume $\mathcal {R}$ is performed with thickness $150$ nm centered at the point of interest. Moreover, the quality factor $Q$ was estimated by numerical calculation with the harmonic inversion method, which analyses the time-series signals with summation of sinusoidal series and decay function; see details in section below.
2.1 Harmonic inversion method
The harmonic inversion method was used to calculate the resonance frequencies, quality factors, decay constants, amplitudes and phases of concerned discrete finite-length time-series signals. This method analyzes a collection of time-series signals by a summation of exponentially decaying terms. With $N$ signal sampling points and $K$ unknowns, the frequencies $\omega _k$ and their amplitudes $d_k$, $k= 1, \ldots, K$ can be extracted from the transformation
We used the free-package harminv 1.4.1 with the filter diagonalization method (FDM) [62] to solve for resonance frequencies and the quality factor $Q$. The sampled point for calculating $Q$ was selected at coordinates (115 nm, 49 nm) in the $x$ and $y$ positions (strong localization point in the plane), where $(0,0)$ defines the center of the middle disk of a unit cell, and 5 nm above the substrate. Generally, $Q$ depends on the spatial coordinates, and we have selected the above point because it yields the maximum electric field intensity.
3. Results and discussion
The far-field absorption spectra of the hexagonal arrays of sub-micro disks of the Ag$_{x}$Au$_{1-x}$ alloy were numerically studied with incident polarized waves, denoted by E$_{x}$ and E$_{y}$ for $x$ and $y$ polarization, respectively. For both polarization incidences, a broadband absorption peak of the pure Au array at the wavelength 500 nm induced by an interband transition shifts to a shorter wavelength. This shift is larger at higher fraction $x$ of Ag; see Fig. 2. We note that the interband transitions (e.g., $d$ to $s$ orbitals) of Au and Ag were at wavelength of 539 nm (2.3 eV) and 335 nm (3.7 eV), respectively [49]. In Fig. 2(a), with the E$_{x}$ incidence, the plasmonic resonance peaks of the first and second orders, here respectively denoted by $\lambda _{ex1}$ and $\lambda _{ex2}$, have larger blue shifts at higher Ag content $x$ in the alloy. We found that $\lambda _{ex1}$ and $\lambda _{ex2}$ lie in the ranges of 762-837 nm and 613-699 nm, respectively, as $x$ decreases from 1.00 to 0.00. Additional peaks besides $\lambda _{ex1}$ and $\lambda _{ex2}$ are clearly visible at wavelengths of 564 nm and 703 nm in the pure Ag array. The observed multiple peaks come from the higher resonance order and are more dominant when particles are closer [24]. From our investigation, these additional Ag peaks disappear when there is an open gap between the particles. For plasmonic resonance modes responding to the E$_{y}$ incidence, see Fig. 2(b), the first order of resonance, $\lambda _{ey1}$, also has a blue shift and lies in the wavelength range of 697-774 nm. When the lattice axis is aligned with the external polarization, it yields higher energy of a resonance mode and results in wavelength $\lambda _{ey1}$ shorter than $\lambda _{ex1}$. Moreover, the resonance peak from the E$_{y}$ incidence is less distinguishable because it merges with the nearest peaks from more multi-coupling directions other than that of E$_{x}$.
Fig. 2. Absorbance spectra of the hexagonal Ag$_{x}$Au$_{1-x}$ alloy array in (a) E$_{x}$ and (b) E$_{y}$ polarizations at different Ag fraction $x$.
The relation between the plasmonic resonance wavelength and the change of dielectric permittivity is approximately linear; see Fig. 3. We remark that the dielectric permittivity of the Ag$_{x}$Au$_{1-x}$ alloys is not directly proportional to the Ag fraction. In case of the E$_{x}$ polarization incident on the Ag$_{x}$Au$_{1-x}$ alloy array, the resonance wavelength shifts are found to obey $\lambda _{ex1}=-69.5x+833$ nm and $\lambda _{ex2}=-81.5x+695$ nm with $R^{2}$ estimates of 0.97 and 0.98, respectively. That $\lambda _{ex2}$ shows higher sensitivity to $x$ than $\lambda _{ex1}$ is due to being a higher resonance mode. Similarly, the plasmonic resonance wavelength $\lambda _{ey1}$ for the E$_{y}$ incidence follows $\lambda _{ey1}=-71.9x+769$ nm with R$^{2} \approx 0.97$. Under the plasmonic resonance condition without coupling to other particles, the resonance appears at the strongest polarizability when the dielectric permittivity $\varepsilon _{m}$ of the metal and that of its surrounding media $\varepsilon _{d}$ satisfy the condition $\varepsilon _{m}=-2\varepsilon _{d}$. At a fixed wavelength, as the Ag fraction $x$ increases, the dielectric permittivity of Ag$_{x}$Au$_{1-x}$ shifts to a more negative value in the real part and maintains its highly dispersive curve. This implies that the resonance mode has a shorter wavelength at higher Ag fraction in the alloy.
Fig. 3. Resonance wavelengths of the hexagonal Ag$_{x}$Au$_{1-x}$ alloy sub-micro disk array under variation of the Ag fraction in the first order ($\lambda _{ex1}$), the second order ($\lambda _{ex2}$) in the $x$-polarization, and the first order ($\lambda _{ey1}$) in the $y$-polarization. Linear fits are shown in solid linear lines. The resonance wavelengths plotted as a function of the averaged real part of the dielectric permittivity are presented in the inset.
The optical confinement ability of the hexagonal alloy disk array depends on the dielectric permittivity of the sub-micro disks, so it is material dependent. In this case, it also spatially varies. In Fig. 4, the electric field intensity enhancement $(|E|/|E_{0}|)^{2}$ is calculated on the top and bottom cut planes in both E$_{x}$ and E$_{y}$ polarizations. The cut planes are chosen near the top and bottom edges of a sub-micro disk, so that the enhancement factor can be investigated for its spatial dependence. In Fig. 4(a), the enhancement factors of the pure Au hexagonal array at wavelength 837 nm in the E$_{x}$ polarization are 39.78 and 38.34 on the top and bottom planes, respectively. We observed that the electric field is mainly localized at nanogaps near the disk-disk contact point, and the plasmonic coupling between the metal particles induces opposite electric charges on the nearest particles; see Fig. 4(b). Moreover, the distribution of electric charge density indicates that the plasmonic coupling occurs mainly on the sub-micro disks along $30^{\circ }$ and $-30^{\circ }$ directions with respect to the $x$-axis. Considering the vertical direction, the electric charge density of each disk has the same sign due to its thickness of less than $\lambda /2$. For the E$_{y}$ polarization, the electric field confinement similarly appears in small spaces between the particles, but it is coupled to neighboring particles in all directions, as shown in Fig. 4(c). The enhancement factors were estimated to be 11.77 and 17.95 on the top and bottom planes, respectively. With the charge density spanning to couple in more directions, this results in lower density of the electric charge and weaker electric field confinement; see Fig. 4(d). These results are consistent with the previous report by Ref. [20] that the electric field confinement becomes weaker when there are multiple coupling directions, and particle alignment deviates from the polarization direction.
Fig. 4. (a, c) Time-averaged electric field intensity $(|E|/|E_{0}|)^{2}$, and (b, d) the corresponding charge density distributions in the E$_{x}$ and E$_{y}$ polarizations. The field and charge densities are plotted in the Au array at wavelengths (a, b) 836 and (c, d) 775 nm.
The spectral profile of the maximum enhancement factor was studied from near-field localization on the top and bottom planes. This profile differs from that of the far-field absorption spectrum because of its spatial dependence. The proposed plasmonic structure has large effective radius per wavelength and narrow nanogaps near a contact point. With these parameters, it can be treated as a sub-wavelength grating. Yoon et al. [31] argued that the optical reflection and transmission could comprise plasmonic and non-plasmonic parts, where the former is introduced by the surface plasmon resonance, while the latter is caused by the structural interface. They demonstrated that the wavelengths of the surface plasmon resonance and reflection peaks are different.
The maximum enhancement factors of the Ag$_{x}$Au$_{1-x}$ hexagonal array on the top and bottom planes are presented in Fig. 5. Notably, on the top plane, the variation of the maximum enhancement factors as a function of wavelength has minima around 700 and 800 nm; see Fig. 5(a). Because the two lowest enhancement factors appear in all metals, it possibly results from the disk geometry. On the bottom plane, the pure Ag hexagonal array has larger deviation from the shared lowest point; see Fig. 5(b). The maximum and minimum of the enhancement factors shown in Fig. 5 are switched between the top and bottom planes. This suggests that the plasmonic resonance mode has a cyclic shift from these two parts. To verify the assumption that the disk thickness affects the shared lowest point on the top plane, the pure Au sub-micro disks of the closed hexagonal arrays are changed in height to 50 nm and 150 nm. In Fig. 6(a), the lowest values of the maximum enhancement factors corresponding to the thicknesses of 50 nm and 150 nm obviously deviate from those of the thickness 100 nm in the wavelength range of 750-800 nm. This is caused by the resonance interference from the top and bottom sharp edges. From Fig. 7(a), in the visible light region, the Ag$_{0.74}$Au$_{0.26}$ and Ag arrays have high enhancement factors at wavelength 600 nm, while the pure Au and Ag$_{0.24}$Au$_{0.76}$ arrays have stronger enhancement at 650 nm. In the near-infrared region, at wavelength of 800 nm, the maximum enhancement factor on the bottom plane tends to be stronger for the pure Au and alloy arrays (than for the pure Ag); see Fig. 7(b). In this case, the Au array still gives the strongest enhancement factor than the alloy array.
Fig. 5. Maximum enhancement factors of the Ag$_{x}$Au$_{1-x}$ alloy sub-micro disk arrays shown at (a) top and (b) bottom planes.
Fig. 6. Maximum enhancement factors of the Au sub-micro disk arrays shown at (a) top and (b) bottom planes with varying disk thickness at 50, 100 and 150 nm.
Fig. 7. Maximum enhancement factor at interested wavelengths on (a) top and (b) bottom cut planes shown as a function of the Ag fraction $x$ in Ag$_{x}$Au$_{1-x}$ alloy sub-micro disk arrays.
The hexagonal heteromaterial arrays of sub-micro disks were also investigated in the far-field spectra as shown in Fig. 8. With the E$_{x}$ polarization incidence, see Fig. 8(a), the absorption peak of the heteromaterial array lies between its alloy counterparts. For example, the wavelength of 779 nm found in the Ag/Ag$_{0.48}$Au$_{0.52}$ heteromaterial hexagonal array was at the middle of 761 nm from the pure Ag array and 796 nm from the Ag$_{0.48}$Au$_{0.52}$ alloy array, respectively. This suggests that the induced resonance in the heteromaterial array has averaged energy from its constituents. On the other hand, the first-order resonances in the E$_{y}$ incidence exhibits weaker linear fitting than that in the E$_{x}$ case. This is because the plasmonic coupling with the same material has stronger effects.
Fig. 8. Absorbance spectra of the hexagonal heteromaterial array in (a) E$_{x}$ and (b) E$_{y}$ incident polarizations.
The maximum enhancement factor of the heteromaterial array also depends on a pair of coupled materials. On the bottom plane, see Fig. 9(b), the Ag/Au array shows the strongest enhancement factor of 100, while the factor of 130 at wavelength of 700 nm is attained in the Ag/Ag$_{0.48}$Au$_{0.52}$ array. It should be pointed out that the heteromaterial array has stronger enhancement in the wavelength range of 800-850 nm, which corresponds to a single-material array where Au is dominant. The Ag/Au heteromaterial array boosts the enhancement factor in the range of 800-850 nm due to strongly induced opposite charges, while the optical strength around 700 nm is suppressed. Comparing the Ag/Au heteromaterial array and Ag$_{0.48}$Au$_{0.52}$ alloy array on the bottom plane, although the material percentages in both arrays are comparable, it shows that arrangement of different materials affects the optical confinement ability. In this case, the Ag/Au heteromaterial array provides the enhancement factor approximately 1.7 times greater than that of the Ag$_{0.48}$Au$_{0.52}$. On the top plane, the maximum enhancement factor has local minimum points at 700 nm and 800 nm, similar to a homogeneous material (i.e., not heterostructure) array.
Fig. 9. Maximum enhancement factor of heteromaterial sub-micro-disk array at thickness of 100 nm shown in (a) top and (b) bottom planes.
The enhancement performance on the spontaneous emission rate of the hexagonal sub-micro disk arrays of pure Ag, pure Au and Ag/Au heteromaterial were estimated by the Purcell factor, see Table 2. The pure Au and Ag/Au heteromaterial arrays were chosen in the calculation because they have high enhancement factor in the near-infrared region (800-850 nm), while the pure Ag array was selected to investigate the lowest bound in such region. The respective values of the alloy arrays lie between these values. We note that the pure Ag array has a very large Purcell factor at $2.42{\times }10^{5}$ ($Q \approx 86.68$, $V_{\text {eff}} \approx 9.14{\times }10^{3}$ nm$^3$) at wavelength 695 nm. The Ag/Au heteromaterial disk array still yields high Purcell factor of $2.72{\times }10^{4}$ ($Q \approx 8.44$, $V_{\text {eff}} \approx 1.19{\times }10^{4}$ nm$^3$) at wavelength of 795 nm. Hence, the Purcell factors of the proposed sub-micro disk arrays in order of $10^{4}-10^{5}$ is comparable to that from Ag nanoparticles of diameter around 10 nm [57]. Finally, we remark that, these hexagonal sub-micro disk arrays would be suitable excitation for infrared quantum dots such as InAs/CdZnS which operated in telecommunication O-band (1300 nm emission).
4. Conclusion
The plasmonic hexagonal sub-micro disk arrays of pure Ag, pure Au and their alloys show wavelength shifts in the far-field absorption spectra due to the variation of the alloy dielectric permittivity. The far-field spectra for the $x$-polarized incident waves have more distinguishable absorption peaks than those for the $y$-polarized waves, as the latter has more plasmonic coupling directions. The heteromaterial array yields far-field resonance wavelengths corresponding to the averaged dielectric permittivity of the metals in the array, and the enhancement factor of near-field localization in the heteromaterial array in the near-infrared region (800-830 nm) is significantly stronger than those in the pure Ag, pure Au and alloy arrays. Additionally, the Purcell factor, used to evaluate the enhancement ability on the spontaneous emission rate, of the heteromaterial is greater than those from the pure Ag and pure Au arrays by a factor of approximately 2.3 for both metals in near-infrared wavelength. The high Purcell factor of the Ag/Au heteromaterial array, approximately by four orders of magnitude, is potentially beneficial for the enhancement of quantum dot emission.
Funding
King Mongkut’s University of Technology Thonburi’s Post-doctoral Fellowship; NSRF via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation (B05F640051).
Acknowledgements
This research was supported by King Mongkut’s University of Technology Thonburi’s Post-doctoral Fellowship. SS, WP, YI, EK, RB and TD acknowledge funding support from the NSRF via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation (grant number B05F640051).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper may be requested from the corresponding author.
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