Objective Port wine stain is a congenital skin disease mainly in the face and neck, which seriously affects the physical and mental health of patients. aiming to thermally damage the malformed capillaries through laser energy absorption by hemoglobin, pulse dye laser and alexandrite laser with wavelengths of 585/595 and 755 nm, respectively, are used to treat port wine stains clinically. However, there is competitive absorption of laser energy between epidermal melanin and dermal hemoglobin, which limits the increase of laser energy with a wavelength of 585/595 nm and the alexandrite laser with 755 nm for Asians. The core -shell Au nanoparticle (NP) can be used to enhance the laser energy absorption by blood due to its adjustable absorption peak to a specific wavelength by changing its structural parameters and distinctive photothermal absorption. In this work, the effects of the structural parameters ( particle radius, the thickness of the gold shell, and interparticle distance) on the photothermal properties of a single particle and the dimer were studied theoretically under 585 nm and 755 nm wavelengths, which could provide theoretical guidance in the laser surgery of vascular dermatosis in a clinic. Methods The core -shell Au NP is immersed in water for nanoscale heating. The simulation calculations of the electromagnetic field propagation and the heat transfer among different media are resolved by the finite element method ( FEM). For the electromagnetic simulation, first, the basic properties of each domain, including the perfectly matched layer (PML) and scattering boundary condition, are strictly defined. Then, the properties of the electromagnetic waves in the domain are set, including the incident direction and intensity. The electric field vector solution of the core-shell NPs mediated by the plane wave is obtained by solving the Helmholtz equation of Si020-3Au core-shell NP. Based on the solved electric field vector solution, we could analyze the influence of structural parameter changes on the local electric field distribution. The light energy absorbed by NPs was converted into heat energy by the Joule heating effect. For the heat transfer simulation, by solving the three-dimensional steady-state heat conduction equation with the heat source supplied by light energy absorption under the third thermal boundary condition, we could obtain the effect of structural parameter changes on the temperature-rise distribution. Before calculation, the solved domains are meshed. Results and Discussions For the single NP, when the particle radius r is constant under A = 585 nm, with an increase in the thickness of the Au shell s, the maximum electric field intensity E/E,,,, and the temperature-rise AT, _, which are mainly affected by the number of internal free electrons and the average-free path, increase first and then decrease (Fig. 3); When the thickness of Au shell s is constant under A = 585 nm, as particle radius r increases, E/E,,,, and AT, _ which is mainly affected by the phase delay effect and the number of effective free electrons have no obvious regular pattern. Meanwhile, for A = 585 nm, when r = 32.5 nm, s = 12 nm, and AT, _ are 12.4 and 106.5 K, respectively. For A = 755 nm, when r = 35 nm, s = 5 nm, E/E,,,, and AT, _ are 1.93 and 1.32 times of the corresponding value of the A = 585 nm case, respectively ( Fig. 5). In addition, compared with the corresponding value of the A = 585 nm case, when the thickness of the Au shell is thinner, the photothermal properties of the particle are better. The effects of interparticle distance / = 0-100 nm on the electric field intensity E/E0 and temperature-rise field AT distribution of the dimer are studied when A = 585 nm (setting each single particle as follows: r = 32.5 nm, s =12 nm). When / = 0 nm, E/E,,,, and AT, _ are in the central point, whereas for 1 = 60 nm, E/E0 h, and AT, _ are in a single particle surface and interior, respectively (Figs. 6 and 7). Besides, / has different effects on E/E,,,, and AT, _ of the dimer. When l<10 nm, E/E0 decreases sharply with the increase in 1. When 1>60 nm, as the optical properties of the dimer are similar to that of single NPs, E/E0 stops changing. For the temperature-rise field, when 1<10 nm, owing to the decrease of the thermal coupling effect and the local electric field intensity E/E0,, with the increase in 1, the absorption thermal power density Q, and AT, _ decrease rapidly. When 1>10 nm, although E/E0, decreases, the isobaric coupling effect of a single particle increases gradually, so AT,, increases continuously. When 1> 60 nm, the temperature-rise distribution is similar to that of a single particle and becomes stable (Fig. 8). Conclusions For a single core-shell Au NP, when the particle radius r is fixed under A = 585 nm, as the thickness of the gold shell increases, E/E0,, and AT,, increase first and then decrease. In addition, for A = 585 nm, when r = 32.5 nm and s =12 nm, E/E0,,, and AT,, are 12.4 and 106.5 K, respectively. For A = 755 nm, when r = 35 nm and s = 5 nm, E/E0,, and AT,, are 1.93 and 1.32 times of the corresponding value of the A = 585 nm case, respectively. Besides, compared to the corresponding value of the A = 585 nm case, when the shell thickness is thinner, the photothermal properties of the particle are better. While for the dimer, / has different effects on E/E0,, and AT,,; when l<10 nm, E/E0,, and AT,, decrease, while for l>10 nm, although E/ E0 decreases, AT,, increases continuously and finally becomes stable.
