Mode Matching for Optical Antennas

Abstract

The emission rate of a point dipole can be strongly increased in presence of a well-designed optical antenna. Yet, optical antenna design is largely based on radio-frequency rules, ignoring e.g. ohmic losses and non-negligible field penetration in metals at optical frequencies. Here we combine reciprocity and Poynting's theorem to derive a set of optical-frequency antenna design rules for benchmarking and optimizing the performance of optical antennas driven by single quantum emitters. Based on these findings a novel plasmonic cavity antenna design is presented exhibiting a considerably improved performance compared to a reference two-wire antenna. Our work will be useful for the design of high-performance optical antennas and nanoresonators for diverse applications ranging from quantum optics to antenna-enhanced single-emitter spectroscopy and sensing.PACS numbers: 84.40. Ba, 73.20.Mf, 78.67.Bf INTRODUCTIONFocusing optical antennas (FOAs) make use of plasmonic resonances to convert propagating electromagnetic waves at visible frequencies to near-fields localized in nanoscale volumes much smaller than the diffraction limit [1,2]. In such a hot spot the local density of states (LDOS) for point-like quantum emitters (QEs) may be increased by a factor of 10 3 and possibly beyond [2][3][4], which can be applied in novel light-based technologies, e.g. quantum optics [5] and communication [6], sensing [7] as well as scanning near-field microscopy [8]. The design of FOAs, which typically consist of single or multiple particles of basic shapes [3,6,[9][10][11], is largely inspired by rules derived from the radio frequency (rf) regime. The resulting antenna structures, however, can hardly be optimal for QE-FOA coupling, since there is no comparable task in rf-technology. In addition the radiation behavior of optical antennas differs from their rf-counterparts due to ohmic losses and fields penetrating the antenna material [12]. Yet, it has been shown that the Purcell factor [13,14] Here we combine Poynting's theorem [17] with reciprocity [18] to quantify QE-FOA coupling by means of a 3D overlap integral of the QE's electric field and the antenna's mode current pattern (cf. mode matching [19,20]). Introducing a further mode-matching condition for FOA to far-field coupling allows us to identify two independent FOA mode current patterns, which both maximize antenna radiation. This enables us to understand the high performance of FOAs obtained from evolutionary optimization [21] as well as of other unusual FOA geometries, like the indented nano-cone [22] or the double hole resonator [23]. Finally, based on our new design rules, an improved plasmonic cavity antenna geometry is devised and numerically investigated. The flexibility of the presented framework opens diverse applications ranging from improved emitter-cavity coupling in quantum optics to enhanced single-emitter sensing schemes. It also provides new insights for the understanding and optimization of complex-shaped metal nano-objects as they appear in surface-enhanc...

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