DOI: 10.1007/s00339-007-4133-3 Appl. Phys. A 89, 357–362 (2007) Materials Science & Processing Applied Physics A j.-w. liaw The quantum yield of a metallic nanoantenna Department of Mechanical Engineering, Chang Gung University, 259 Wen-Hwa 1st Rd., Kwei-Shan, Tao-Yuan 333, Taiwan, R.O.C. Received: 11 December 2006/Accepted: 2 May 2007 Published online: 22 June 2007 • © Springer-Verlag 2007 ABSTRACT The local-field factor and quantum yield of a metal- lic nanoantenna are studied to identify its enhancement of an emitter’s emission within the feed gap. For simplicity, a two- dimensional model, an Au nanoantenna with an emitter at the center, is studied. The electromagnetic field is solved by a set of surface integral equations. An incident plane wave irradiat- ing the nanoantenna is modeled to simulate the excitation of the emitter by illuminating light, and the local-field factor is used to evaluate the amplification of the electric field in the feed gap of the metallic nanoantenna. Once the emitter becomes excited, a model of an electric dipole interacting with the nanoantenna is used for calculating the radiative and nonradiative powers to obtain the quantum yield of the excited emitter in the presence of the nanoantenna. The numerical results of quantum yield in- dicate that an Au nanoantenna acts as a low-pass filter for the emission of the emitter. Moreover, the smaller the feed gap, the larger the local-field factor but the less the quantum yield. PACS 78.67.-n; 33.80.-b; 33.50.-j; 42.30.-d; 42.50.Hz; 81.07.Pr 1 Introduction Recently, metallic dimers [1–3], linear nanoanten- nas (a pair of aligned nanowires [4]), and bowtie nanoanten- nas [5, 6] were proposed to enhance the local electric field within their feed gap, due to the effect of coupled surface plasmon resonance (SPR). Several experiments [4–6] have proven that these nanostructures can induce a strong local field if the polarization of the illuminating light is parallel to the axes of the structures. In addition, the metallic dimers have been applied successfully for the surface-enhanced Ra- man scattering (SERS) [2]. Another potential application of these metallic nanostructures is to enhance the spontaneous emission of an emitter, e.g. molecule fluorescence [7–9] and quantum-dot photoluminescence, when the emitter is placed within the gap. Because the lengths of the two arms of a linear nanoantenna are adjustable for different aspect ratios, it is ex- pected that a linear nanoantenna can tune the optical response more versatilely, compared with a dimer. However, so far, the quantum yield [7–10] of a metallic linear nanoantenna is not ✉ Fax: +886-3-2118050, E-mail: markliaw@mail.cgu.edu.tw well known. Therefore, we are motivated to study its quantum yield as well as local-field factor numerically by using a set of newly developed surface integral equations [11, 12]. The ad- vantage of the set of new surface integral equations is to deal with the surface components on the boundary only, and it is suitable for a problem with a multiply connected surface [12], e.g. a nanoantenna with two arms. For simplicity, a process of fluorescence is divided into two stages; the first is the excitation stage and the second is the emission stage. For the former, a model of an incident p-polarized plane wave irradiating the nanostructure is simu- lated to investigate the enhancement of the local electric field at the location of the emitter for its excitation. Throughout the paper, only a two-dimensional (2D) transverse-magnetic (TM) model is considered. At the excitation stage, a local- field factor K is used to show the enhancement of the emitter’s excitation; for one-photon excitation, the emitter’s excitation increases by a factor K 2 , and for two-photon excitation by K 4 [6, 8]. For the emission stage, an electric dipole interacting with an Au nanoantenna is used to simulate the emission of the excited emitter within the feed gap. Through this model, the radiative power [7] and nonradiative power [13] of the dipole in the presence of the metallic nanoantenna are calculated, and then the quantum yield η of the excited emitter’s emission can be obtained. Both of the two parameters, K and η, are useful to evaluate the total effect of the nanoantenna on the spontaneous emission of the emitter [9]. Since most of the energy of the SPR is confined within a thin area in the vicinity of the interface of metals and di- electrics, the surface integral equation method has an advan- tage to calculate the predominant surface components only along the boundary, rather than the whole domain field. Using the boundary element method (BEM), the surface integral equations can be solved numerically. Generally, the number of the unknowns of the BEM is less than the other methods, which need to mesh the whole domain, e.g. the finite differ- ence time domain (FDTD) method. In particular, when the gap of the metallic nanoantenna is very small (e.g. 1 nm) and an electric dipole is located at the center, a significantly large electric-field gradient is generated within the feed-gap zone of the nanoantenna. For this case, the method of surface in- tegral equations, implemented by the BEM, is particularly superior to the other domain-meshing methods by discretizing the boundary adaptively.