# Optimization of Nonspherical Gold Nanoparticles for Photothermal Therapy
## 1 Introduction  
Gold nanoparticles can strongly absorb the incident light at the resonance wavelength. Almost all of the absorbed light is converted to heat via a series of nonradiative processes [1]. Moreover, gold nanoparticles are biocompatible and nontoxic. Therefore, they can easily penetrate a tumor upon systemic delivery and can be easily conjugated to cancer cells. Based on the above-mentioned properties, gold nanoparticles can be used as an effective therapeutic agent for the photothermal therapy (PTT) of cancer [1; 2; 3; 4]. The enhancement of the light absorption ability of gold nanoparticles reduces the dosage of gold, shortens the illumination time, and decreases the damage of healthy cells. The light absorption ability of gold nanoparticles with a fixed shape is strongly dependent on the particle size [5; 6; 7]. Therefore, it is necessary to find the optimal size of gold nanoparticles by maximizing their light absorption ability at the excitation wavelength.  
It is well known that experimental investigations on PTT are limited with respect to the prepared samples. Some of the samples can strongly absorb light at the target laser wavelength without ensuring their maximum light absorption ability. In order to find the optimal size of gold nanoparticles forPTT, some numerical optimizations were performed on gold nanoparticles [8; 9; 10; 11; 12]. However, to the best of our knowledge, we found two issues which led to inaccurate optimization results. Firstly, it is unreasonable to use the absorption efficiency \(Q_{abs}\) as an objective function in optimization. The \(Q_{abs}\) is defined as \(C_{abs}/S\), where \(C_{abs}\) is the absorption cross-section which represents the light absorption energy by a single particle, and \(S\) is the particle cross-sectional area projected onto a plane perpendicular to the incident light [13]. Assuming that a fixed volume of bulk gold is used to prepare nanoparticles, the appropriate size of the nanoparticles which can most effectively absorb light of a given wavelength should then be selected. Clearly, \(C_{abs}/V\) (\(V\) is the particle volume) should be computed as a function of size rather than of \(Q_{abs}\)[14], in order to fulfill the above-mentioned criteria. Secondly, the random orientation of nonspherical particles, which is an important parameter affecting their light absorption abilities, is not considered in optimization. [PERSON] and [PERSON] [10] considered the circular polarization of incident light to take into account the random orientation, but it was a conceptual mistake [13]. In this study, the above-mentioned two issues were solved and accurate optimal size parameters of three typical nonspherical gold nanoparticles (nanospheroid, nanocylinder, and nanorod) were obtained for PTT.  
The remainder of this paper is organized as follows: Section 2 describes the calculation of light absorption by nonspherical gold nanoparticles. Section 3 presents the method for obtaining the optimal size of gold nanoparticles at typical laser wavelengths used in PTT. The effects of the laser wavelength and the refractive index of tissue on the optimization results are discussed. Moreover, the ranges of size parameters that keep the volume absorption coefficient greater than a threshold are computed. Finally, Section 4 concludes the paper.