Thin elongated rod antennas with a diameter smaller than the skin depth exhibit surface plasmon polariton modes that can propagate along the antenna while being reflected at the antenna ends. In the line-current model, a current is associated with these modes in order to approximate the optical properties of the antennas. We find that it is crucial to correctly derive the reflection of the surface plasmon polariton modes at the antenna ends for predicting the resonance position and shape accurately. Thus, the line-current model allows for deriving the wavelength scaling behavior of plasmonic near fields as well as the emitted third-harmonic intensity efficiently. Neglecting the frequency dependence of the nonlinear susceptibility, we find that the third-harmonic intensity of such metallic rod antennas scales as the fourth power of the frequency, whereas it decreases with the twelfth power within the limit of the generalized Miller’s rule.
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