Local Capacitor Model for Plasmonic Electric Field Enhancement J. H. Kang, 1 D. S. Kim, 2 and Q-Han Park 1, * 1 Department of Physics, Korea University, Seoul, 136-701, Korea 2 Center for Subwavelength Optics and Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea (Received 24 October 2008; revised manuscript received 5 January 2009; published 6 March 2009) We present a local capacitor model that enables a simple yet quantitatively accurate description of lightning rod effect in nanoplasmonics. A notion of -zone capacitance is proposed and applied to predict the strongly induced electric field by a light source near nanoscale metal edges such as metal tip or metal gap. The enhancement factor, calculated from the local capacitor model, shows excellent agreement with more rigorous results. The -zone capacitor allows a blockwise treatment of nano-optical devices and constitutes a basic element of optical nanocircuits. DOI: 10.1103/PhysRevLett.102.093906 PACS numbers: 41.20.Jb, 73.20.Mf, 78.67.n, 84.40.Ba The lightning rod induces strong electric field near the tip as charge tends to accumulate at a sharper edge. This lightning rod effect has received great interest recently in the study of nanoscale structures of metal with applications to diverse areas including near field spectroscopy [1,2], surface plasmons [3–5], optical antenna [6,7], surface en- hanced Raman spectroscopy [8], biomedical science, and other applications [9]. When excited by light, the enhanced electric field near metal edges is generally accompanied by a surface charge oscillation and also called local plasmon. The plasmonic enhancement of electric field increases if metal edges form a gap as can be seen in a bow-tie antenna [7] or in a nanoparticle dimer [10]. This is expected since the gap structure is supposed to increase the ‘‘capacitance’’ of the system and subsequently the induced electric field. The meaning of capacitance in a plasmonic configuration is dubious, however, as the conventional concept of static capacitance fails to apply. Thus the quantitative account of plasmonic local field enhancement based on a capacitor concept so far has been lacking. If possible, the capability of controlling enhancement through capacitance would play a key role in nanoscale optical devices and also in the development of recently emerging optical nanocircuit concepts [11]. In this Letter, we introduce the concept of ‘‘-zone’’ capacitance for plasmonic systems and apply it to predict the strong enhancement of electric fields near subwave- length metal structures. The -zone capacitance, defined as a static local capacitance restricted to a wavelength- confined region, is evaluated explicitly for two typical cases of subwavelength metal structures: (1) metal slit with a narrow gap and (2) a metal tip near a metal surface or, equivalently, two metal tips forming a gap. We show that the plasmonic enhancement of electric field mainly comes from the local charging of the -zone capacitor where charging is done by the light-induced surface current flowing in to or out of the  zone. The enhancement factor, calculated for two cases varying parameters such as gap size or metal thickness, shows an excellent agreement with rigorous finite difference time domain (FDTD) calcula- tions. They are also consistent with the experimental result on the field enhancement in a metal slit [12]. More im- portantly, the -zone capacitor approach allows a block- wise treatment of nano-optical devices and constitutes a basic element of optical nanocircuits. The validity of the local capacitor model for metal structures at the skin-depth scale is also discussed. When an electromagnetic wave impinges upon a metal, current is induced due to the high conductivity of metal. The current density resides mostly near the surface within the skin-depth region and can be replaced by an effective surface current ~ K eff ¼ ~ n  ~ H k [13]. Here, ~ n is the unit vector normal to the surface and ~ H k is the tangential magnetic field just outside the surface. For simplicity, we assume metal to be a perfect conductor and address the effect of finite conductivity and skin-depth later. For a plane wave normally incident on a thick metal surface with magnetic field strength ~ H 0 , we have ~ K eff ¼ ~ n  2 ~ H 0 . This surface current, when blocked by a tip end or a discontinuous gap as shown in Fig. 1, accumulates charge at the edge through the charge conservation law: ~ r ~ K eff þ @ t  S ¼ 0. Since the light-induced surface cur- rent flowing into the edge region is an alternating current, surface current responsible for charging the metal edge region is in fact restricted within a region of length scale the wavelength . This is our main observation leading to the definition of local capacitance. Henceforth we call the local region of surface contained within a distance  from the edge ‘‘the  zone,’’ as illustrated in Fig. 1(a). More specifically, we measure the distance from the edge in the direction of transverse electric field of incoming light and consider a volume that encloses the metal edge within the distance  [shaded cylinder in Fig. 1(a)]. The  zone is then the metal surface surrounding the edge that stays inside the volume. The induced charge Q ind by the surface current ~ K eff flowing into the  zone is Q ind ¼ Z Z  S dA ¼ 1 iw Z @Z ~ K eff  ^ ndl; (1) PRL 102, 093906 (2009) PHYSICAL REVIEW LETTERS week ending 6 MARCH 2009 0031-9007= 09=102(9)=093906(4) 093906-1 Ó 2009 The American Physical Society