An Analytic Approach to Nanofocusing with Pyramidal Horn Antennas

Horn antenna is one of the simplest even widely used antennas in the RF and microwave regimes. However, few systematic investigations on pyramidal horn antennas are found at optical frequency while optical antennas are extensively studied in various applications. Here, we investigate the feature of pyramidal horn nanoantennas and explore the mechanism of nanofocusing. Although the dimensions of antenna can be optimized through numerical simulations for the applications, it is inefficient due to the large degree of freedom of a horn antenna. Firstly, we analyze both the scattering loss and the dissipative loss during compressing electromagnetic waves in the horn antennas while the dimensions gradually decrease. Then, we establish an analytic and simple approach of mode matching, which is based on the effective index method, to efficiently squeeze light into arbitrarily small 3D nanospots. We numerically demonstrate that a nanofocusing spot of pi lambda (2)/1200 at the wavelength of 785 nm with 1.2 dB losses is achieved by a pyramidal horn nanoantenna with the analytically determined dimensions. The intensity enhancement is further increased to more than 6000 times by introducing surface plasmon coupling at the input interface.