Cheng, Hui-Wen;Li, Yiming, Numerical Simulation of Field Distribution of SERS Active Substrates for Rhodamine 6G Detection
In this work, we study surface enhanced Raman spectroscopy (SERS) active substrates for the detection of Rhodamine 6G. To examine the electromagnetic enhancement, we apply the finite-difference time-domain (FDTD) algorithm to analyze the structures by solving a set of coupled Maxwell’s equations (Ampere’s Law and Faraday’s Law) in differential form. The FDTD method solves Maxwell’s equations by first discretizing all equations via central differences in time and space. Then, based upon a 3D Yee’s mesh and components of the electric and magnetic fields at points, the discretized spacing in the x, y, and z directions adopted in our simulation are 0.01 um, 0.01 um and 0.01 um, where the time step is 0.0004 and the time duration T is 3 in units of femtoseconds. The discretized equations are iteratively solved in a leapfrog manner, alternating between computing the E and H fields at subsequent t/2 intervals. Notably, we employ the perfectly matched layer as the simulation domain boundaries in which both electric and magnetic conductivities are introduced in such a way that wave impedance remains constant, absorbing the energy without inducing reflections. The field enhancements are thus investigated in the visible regime with the wavelength of 633 nm. For chemical sensing, the hydrothermally roughened substrate is treated with aqueous solutions of 1E-4 M R6G. The substrate with hydrothermal treatment shows larger intensity than that without hydrothermal treatment due to the roughness on the surface. The estimation of local electric field on the substrate is carried out using three-dimensional (3D) FDTD simulation, where a directing light with the wavelength of 633 nm is considered. Without loss of generality, the effect of vertical variation of surface on the electric field enhancement is observed. The gold-coated nanoparticular structure with hydrothermal treatment has larger electrical field, due to relatively rough surfaces, than that without hydrothermal treatment. In summary, in our experimental measurement, the surface enhanced Raman scattering signals from the surface of substrates with 12-hour treatment and without treatment are performed and compared. Through the 3D FDTD calculation, we find that the hydrothermally 12-hour treated samples possess significantly vertical variations of surface and thus have relatively larger field enhancement than those without treated. Consequently, it implies a strong positive effect on the surface enhancement which is consistent with the measured intensity.
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