λ1λ1 λ2λ2 2λ22λ2 λ1λ1 λ2λ2 2λ22λ2 Enhancement of Second-Harmonic Generation through Plasmon Resonances in Silver Nanorods Nicholas Wang 1, Patrick McAvoy 2, Isaak Mayergoyz 2, Oded Rabin 1,3 1. Department of Materials Science and Engineering, University of Maryland, College Park, MD Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD Abstract Goal Methods Second-Harmonic Generation (SHG) is an optical process in which incident radiation interacts with a nonlinear medium, producing photons with twice the energy. SHG can be useful for PV and IR imaging. Enhanced SHG may be achieved by coupling the radiation to surface plasmons in metallic nano-objects. We report a theoretical study of enhanced second-harmonic generation through the calculation of plasmon resonances for 3-D nano-objects with cylindrical symmetry. Our algorithms calculate the resonant wavelengths characteristic to silver nanostructures in vacuum. Focusing on axial dipole plasmon modes, the criteria for enhanced second- harmonic generation are met when the wavelength of the first resonance mode is twice that of the second resonance mode. Enhanced second-harmonic generation is predicted in nanorods of aspect ratios of 7, 8, and 9 with varying concentric hole depths and various degrees of edge rounding. The enhancement is most effective when the excitation is at 980 nm. Determine cylinder geometries suitable for the enhancement of second-harmonic generation 1.Create cylinder model using Blender® 3-D software and export mesh coordinates 2.Run eigenvalue algorithms (MATLAB®) to identify the axial dipole plasmon resonances of the input geometry using the metal dielectric function. The outputs for each resonance mode are: ε* – resonance permittivity, λ – resonance wavelength, and a surface charge density distribution. 3.Reiterate the process with a new cylinder geometry until λ 1stmode / λ 2ndmode = 2. Effects of Cylinder Edge Rounding Conclusions  For cylinders of aspect ratio 7, 8, and 9 with varying concentric hole depths, we observe ratios of λ 1stmode /λ 2ndmode close to 2, which meet the criteria of enhancement of second-harmonic generation.  The effects of rounding are negligible at high aspect ratios. Future Work  Calculate the electric field around the cylinders for the 1 st and 2 nd axial dipole modes at resonance to determine the extent of electric field overlap between the two modes.  Calculate plasmon resonances for Au nanorods We studied the effects of cylinder edge rounding on the resonance wavelength for the 1 st and 2 nd axial dipole plasmon modes.  Aspect Ratio = cylinder length:diameter  The above plots show the calculated values of resonance wavelength for the 1 st axial mode, 2 nd axial mode, and twice the 2 nd axial mode vs. cylinder aspect ratio for a solid nanorod (left) and a nanotube (right).  We observe that the criteria for enhanced second-harmonic generation (λ 1 /λ 2 = 2) is met for cylinder aspect ratio value of 8 for solid rods and 7 for tubes.  Hole depth is defined to be the length of a concentric hole introduced both in the top and bottom faces of the cylinder, as seen in the wire view above. The unit (hole depth*2)/cylinder length is used for normalization among different AR cylinders.  Above is a plot of the ratio of resonance wavelengths of the 1 st and 2 nd modes for cylinders of various aspect ratios vs. concentric hole depth. The values vary monotonically with aspect ratio but not with hole depth.  The criteria of enhanced second-harmonic generation can be met only by cylinders of aspect ratio 7 ≤ AR ≤ 9. Results Eigenvalue algorithm in MATLAB® Blender® model ε* and λ of plasmon resonances Charge distribution 3-D view 2-D view No SmoothingBevel Smoothing  The above plots show the shift in wavelength due to edge rounding for cylinders of aspect ratio 1 (left) and 9 (right). Edge rounding affects small aspect ratio structures more prominently. In these structures, evanescent electric fields are more concentrated along the edges. 1 st mode 2 nd mode Plasmonic Spectra for Cylinders – Varying Aspect Ratio (AR) Plasmonic Spectra for Cylinders with Concentric Holes λ 1 / λ 2 Δλ