Influence of dielectric substrate on the plasmon-assisted excitation and fluorescence rates of fluorophore molecule

Simulation shows a significant influence of the dielectric substrate on the local electric field strength in the vicinity of gold nanoparticles and, consequently, on the fluorophore molecule excitation rate. The field strength and, therefore, the excitation rate fall with increasing dielectric permittivity of the substrate material and, conversely, grow with the increasing size of the nanoparticle. Such multi-vector behavior is explained, in the first case, by the increasing energy losses upon the interaction of the nanoparticle field with the substrate material while its dielectric permittivity increases. In the second case, the increase in the excitation rate as a result of increasing size of the nanoparticle prevails over the dielectric losses with a significant decrease in the excitation rate in general. It should be noted that in both cases, the significant dependence of the excitation rate on the distance between the fluorophore molecule and nanoparticle was observed, which exhibits a nonlinear behavior.

In Fig. 3.29, the distribution of electric field strength near the surface of a spherical gold nanoparticle with a radius of 20 nm in the absence of the glass substrate and in the case of its presence (f2 = 2.59) is depicted. The maximum field strength for these cases is 3.75 and 2.41, respectively; therefore, in this case the presence of a dielectric environment inhomogeneity reduces the maximum strength of the local electric field generated by a gold nanosphere under the influence of an external excitation. Obviously, the nanoparticle behaves as a classical dipole that emits light, which is consistent with the dipole approximation used in this approach.

Distribution of the electric field strength near the surface of a spherical gold nanopartide with a radius of 20 nm at an external excitation wavelength of 650 nm

Figure 3.29 Distribution of the electric field strength near the surface of a spherical gold nanopartide with a radius of 20 nm at an external excitation wavelength of 650 nm (a) without and (b) in the presence of the glass substrate (e2 = 2.59). The maximum £/£0 value in the case (a) is 3.75, and in the case (b) is 2.41. Reprinted with permission from Ref. [178], Copyright 2015, Springer Nature.

Figure 3.30 shows the dependence of the fluorophore molecule excitation rate near spherical gold nanoparticles of different sizes on the distance to the surface of the nano particle. It should be noted that with increasing gold nanoparticle size and distance from the surface of the nanoparticle, the excitation rate derivative decreases due to the exponential nature of the field distribution.

The effect of substrate on the nanostructure's local electromagnetic field is determined by the dielectric permittivity of the material from which it is made, and, like in the previous case, there is an obvious dependence of the excitation rate on the distance from the nanoparticle surface to the point of the fluorophore molecule location. The nature of this effect is shown in Fig. 3.31, which shows that in the presence of the glass substrate, the fluorophore excitation rate value is reduced by almost half compared with the case when the substrate is absent. Thus, the best way to obtain the fluorophore excitation rate enhancement is to use the substrate material with the least possible value of the dielectric permittivity.

Fluorophore molecule excitation rate change near spherical gold nanoparticles of different sizes in the absence and presence of the dielectric glass substrate

Figure 3.30 Fluorophore molecule excitation rate change near spherical gold nanoparticles of different sizes in the absence and presence of the dielectric glass substrate (e2 = 2.59). R is the spherical nanoparticle radius, and d is the distance from the nanoparticle surface to the point of fluorophore molecule location. Reprinted with permission from Ref. [178], Copyright 2015, Springer Nature.

The decrease in the fluorophore quantum yield, when it approaches the surface of a nanoparticle being in the resonant plasmon oscillations generation mode, is well known. Reduction in the quantum yield shows a gradual nonlinear decline to zero on contact of the fluorophore with the surface of the nanoparticle. Usually, to enhance the fluorescence, a separating layer of dielectric material between the nanoparticle and fluorophore is used [181]. In this study, for modeling generalized system properties, we first use the vacuum as an environment. Subsequently, to agree with experiment, simulation results for a particular case of a dielectric material that was used in the experiment will be presented. Figure 3.32 shows the typical behavior of the molecule quantum yield dependence on the distance to the surface of a gold nanoparticle. It is noticeable that the presence of the substrate generally somewhat reduces the quantum yield. The figure shows the results for a gold nanoparticle with a radius of 40 nm and a model fluorophore with the maximum initial quantum yield (without the presence of a nanoparticle), which equals to 1. Thus, we can conclude that the resulting reduction in the electric field strength near the nanoparticle in the presence of the dielectric substrate will subsequently reduce the fluorophore molecule quantum yield.

Fluorophore molecule excitation rate change near the spherical gold nanoparticle with a radius of 20 nm for different values of the substrate dielectric permittivity

Figure 3.31 Fluorophore molecule excitation rate change near the spherical gold nanoparticle with a radius of 20 nm for different values of the substrate dielectric permittivity. e2 is the substrate dielectric permittivity, and d is the distance from the nanoparticle surface to the point of the fluorophore molecule location. Reprinted with permission from Ref. [178], Copyright 2015, Springer Nature.

The theoretical approach using Green's function, which is applied in this study, for the first time allowed us to estimate the fluorescence rate enhancement for fluorophores with different quantum yield in the presence of a spherical gold nanoparticle located on a dielectric substrate (Fig. 3.33). In confirmation of the results of Ref. [177], the dependence of fluorescence rate enhancement factor on the distance between the fluorophore and surface of the nanoparticle exhibits a non-monotonic character and expresses a maximum depending on several factors. Known nonlinear dependence on the initial fluorophore quantum yield, nanoparticle size and the distance between the fluorophore and nanoparticle is supplemented in our case with the influence of the presence of the dielectric substrate. It is evident from Fig. 3.33 that the presence of the dielectric substrate slightly reduces the amount of fluorescence rate enhancement in equidistant point, which increases in proportion to the size of the gold nanoparticle.

Fluorophore molecule

Figure 3.32 Fluorophore molecule (q° = 1) quantum yield Q depending on the distance to the surface of the spherical gold nanoparticle with a radius of 40 nm in the absence (solid line) and in the presence (dashed line) of the glass substrate with e2 = 2.59. d is the distance from the molecule to the nanoparticle surface. Reprinted with permission from Ref. [178], Copyright 2015, Springer Nature.

It is known that the value of the molecule initial quantum yield significantly affects their emission enhancement factor [182, 183]. Since the enhancement factor is inversely proportional to q°, the smaller the value, the more significant enhancement of emission can be obtained (Fig. 3.34). Simulation results show that the dependence of the fluorescence rate enhancement factor on the value of the initial quantum yield is pronouncedly nonlinear. In particular, in the case of the fluorophore molecule with q° = 0.1, located near the gold nanoparticle with a radius of 80 nm, simulation revealed that the maximum yem/y°m value is 22.5 in the absence of substrate and 16.1 in the presence of the glass substrate (£2 = 2.59). An important result of the simulation obtained is to find the existence of an optimal distance between the fluorophore and nanoparticle depending on the size of the initial quantum yield.

As shown in Fig. 3.34 (inset), the optimal distance for a maximum fluorescence rate enhancement factor is markedly different in the case of low and high values of the fluorophore quantum yield. For example, for = 0.1 the optimal distance is 12 nm, and for = 1, it is 18 nm. Significant differences in enhancement values, which are introduced by the presence of the dielectric substrate, indicate the need to consider the impact of this factor in the design of plasmonic nanochips and optimization of dimensional parameters of nanostructures depending on the dielectric characteristics of the substrate. Factor of the substrate becomes even more important in further consideration of the fluorescence enhancement mechanism depending on the wavelength resonance positions of the fluorophore molecule and nanoparticle.

Dependence of the fluorescence rate enhancement factor for a fluorophore molecule

Figure 3.33 Dependence of the fluorescence rate enhancement factor for a fluorophore molecule (q° = 1) on the distance from the surface of the spherical gold nanoparticle of different radii, d is the distance from the molecule to the nanoparticle surface. Reprinted with permission from Ref. [178], Copyright 2015, Springer Nature.

Fluorescence rate enhancement factor for fluorophores with different initial quantum yield near the surface of a spherical gold nanoparticle with a radius of 80 nm

Figure 3.34 Fluorescence rate enhancement factor for fluorophores with different initial quantum yield near the surface of a spherical gold nanoparticle with a radius of 80 nm (a) in the absence and (b) in the presence of the glass substrate with e2 = 2.59. d is the distance from the molecule to the nanoparticle surface. Insets: dependences of the optimal distance between the fluorophore and nanoparticle on the initial quantum yield value. Reprinted with permission from Ref. [178], Copyright 2015, Springer Nature.

Thus, for the first time, the influence of the dielectric substrate on the amplification of a local electromagnetic field near the metal nanostructure and, consequently, on the emission of fluorophore molecules near its surface, was considered. Calculations have shown that the local electric field strength values and the fluorophore quantum yield decrease with increasing value of the dielectric permittivity of the substrate. Simulation of the fluorophore molecule fluorescence rate enhancement Jem him revealed that the yem him value increases with the size of the spherical gold nanoparticle and the presence of the substrate slightly reduces its value. The results obtained have also confirmed the known fact that the emission of molecules with low initial quantum yield is amplified in the presence of gold nanostructures much better than for molecules that are characterized by a high value. The developed theoretical approach and the obtained results can be used in the development of new plasmonic nanochips based on gold and silver nanostructures for applications as sensor elements of fluorescent sensors and other devices operating on the basis of the localized surface plasmon resonance phenomenon.

 
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