Vol.:(0123456789) 1 3 Applied Physics A (2018) 124:17 https://doi.org/10.1007/s00339-017-1433-0 Plasmon-enhanced optical bending and heating on V-shaped deformation of gold nanorod Jiunn‑Woei Liaw 1,2,3,4  · Cheng‑Wei Huang 5  · Mao‑Chang Huang 5  · Mao‑Kuen Kuo 5 Received: 18 July 2017 / Accepted: 22 November 2017 © Springer-Verlag GmbH Germany, part of Springer Nature 2017 Abstract The plasmon-enhanced optical bending and heating on the V-shaped deformation of a straight gold nanorod (GNR), irradiated by a linear polarized light at the longitudinal surface plasmon resonance, are studied theoretically to explain the fnding in previous experiment. Multiple multipole method is employed to calculate the optical load and heating numerically, and an elastic beam model is used to analyze the bending moment and stress in the GNR theoretically. According to our analysis, we think, frst, the plasmonic heating softens the GNR to reduce the yield strength of gold, and the non-uniform optical load induces a maximum bending moment at the middle cross section of a freestanding GNR. Then an irreversible breakpoint of the plastic hinge at the middle of GNR is developed to form a V-shaped GNR. The photothermal deformation of V-shaped GNR involving multidisciplinary interplay is worth for further investigation. 1 Introduction Plasmonic trapping, heating, deformation and printing of gold nanoparticles were studied extensively in the past decade [1–4]. In a recent paper “Bending Gold Nanorods with Light” [5], Babynina et al. showed a novel approach using light accompanied with plasmonic heating to bend gold nanorods (GNR) into V-shape using linearly polarized (LP) focused laser beam. This light–matter interaction pro- vides an insight into the plasmon-mediated manipulation on photothermally deforming GNR. They used the model of Agayan et al. [6] for the optical force calculation and Navier–Stokes equations for the hydrodynamic pressure analysis, and proposed an explanation that the optical force, the hydrodynamic pressure and the viscous drag force from surrounding fuid cause the V-shaped formation. The angle of V-shape decreases as the laser intensity increases. In this paper, we propose another viewpoint that the V-shaped GNR is mainly induced by the maximum bending moment occur- ring at the middle cross section of GNR due to the non- uniform optical load upon the freestanding GNR associated with the thermal softening of GNR inducing an inelastic deformation of V-shape, which acts like a plastic hinge. Fig- ure 1 depicts our explanation. To support our viewpoint, the analysis of the corresponding plasmonic heating, the temper- ature distribution and the optical loading on the deformation of an elastic beam are discussed in the following. 2 Theory The multiple multipole (MMP) method is used to numeri- cally analyze the electromagnetic (EM) field ( E, H) induced by a GNR suspended in water and irradiated by a LP Gaussian beam [7, 8]. In terms of the EM feld, the heating source and optical loading on GNR are numeri- cally calculated, respectively. After that, a one-dimen- sional heat conduction equation is used to theoretically estimate the temperature distribution in GNR, and a one- dimensional beam model is utilized to estimate the elas- tic/plastic deformation of GNR. The time-harmonic factor * Jiunn-Woei Liaw markliaw@mail.cgu.edu.tw * Mao-Kuen Kuo mkkuo@ntu.edu.tw 1 Department of Mechanical Engineering, Chang Gung University, Taoyuan, Taiwan 2 Institute for Radiological Research, Chang Gung University and Chang Gung Memorial Hospital, Taoyuan, Taiwan 3 Center for Advanced Molecular Imaging and Translation, Chang Gung Memorial Hospital, Linkou, Taiwan 4 Department of Mechanical Engineering, Ming Chi University of Technology, New Taipei, Taiwan 5 Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan