Effect of spatially nonlocal versus local optical response of a gold nanorod on modification of the spontaneous emission

The spontaneous emission rate of a two-level quantum emitter(QE) near a gold nanorod is numerically investigated.Three different optical response models for the free-electron gas are adopted, including the classical Drude local response approximation, the nonlocal hydrodynamic model, and the generalized nonlocal optical response model. Nonlocal optical response leads to a blueshift and a reduction in the enhancement of the spontaneous emission rate. Within all the three models, the resonance frequency is largely determined by the aspect ratio(the ratio of the nanorod length to the radius) and increases sharply with decreasing aspect ratio. For nanorod with a fixed length, it is found that the larger the radius is, the higher the resonance frequency is, and the smaller the enhancement is. However, if the length of the nanorod increases, the peak frequency falls sharply, while the spontaneous emission enhancement grows rapidly. For nanorod with a fixed aspect ratio, the peak frequency decreases slowly with increasing nanorod size. Larger nanorod shows smaller nonlocal effect. At a certain frequency, there is an optimal size to maximize the enhancement of the spontaneous emission rate. Higher order modes are more affected by the nonlocal smearing of the induced charges, leading to larger blueshift and greater reduction in the enhancement. These results should be significant for investigating the spontaneous emission rate of a QE around a gold nanorod.