Comprehensive Surface-Wave Description for the Nano-scale Energy Concentration with Resonant Dipole Antennas

Abstract

Resonant optical dipole nano-antennas allow giant field enhancement within nano-gaps. To show how the energy of external illumination waves is delivered and concentrated in nano-gaps, we build up a model by considering the dynamical launching and multiple scattering processes of surface plasmon polaritions (SPPs) on both antenna arms. The model captures the main feature of the antenna resonance as evidenced by comparison of the model prediction with fully vectorial numerical results and provides an intuitive picture that the energy of external wave is initially transferred into SPP and is then coupled into the nano-gap. The enhanced field in the nano-gap oscillates quasi-periodically with the increase of the antenna-arm length, and the resonance peaks can be predicted with a phase-matching condition derived from the model, showing that antenna resonance is due to a constructive interference of the multiple-scattered SPPs. Analytical equation for determining the complex resonance wavelength and the quality factor of the resonant modes is obtained. The model however exhibits observable deviation from fully vectorial numerical results for the lowest resonance order (for antenna with the shortest arms), evidencing that, for this case, surface waves other than SPPs contribute to the antenna resonance.The present results are helpful for clarifying the underlying physics for the energy concentration with resonant dipole antennas and may provide recipes for intuitive design of antenna devices, such as those used for optical nonlinearity enhancement and biochemical sensing.

Remote two-dimensional nanometric localization of molecules by the analysis of fluorescence coupled to guided surface plasmons

“…β + i ( i = 1, 2) can be obtained using the reciprocity theorem:In eqn (3), [ E ± i , H ± i ] can be calculated using FEM or aperiodic Fourier modal method (a-FMM). 43–45 Compared with another calculation method of β + i using the mode orthogonality theorem, 46 the advantages of using eqn (3) is that when the location r 0 or polarization direction p of the point source is changed, there is no need to repeatedly solve Maxwell's equations once [ E ± i , H ± i ] is obtained because of the analyticity of the equation. Besides, eqn (3) can also provide physical intuition for the analysis of β + i .…”

Understanding localized surface plasmon resonance with propagative surface plasmon polaritons in optical nanogap antennas

“…5[denoted by gk 0;c ] at a certain frequency, in view that ρ, τ, r, n eff , and thus gk 0;c are slowly varying functions of k 0;c . The accuracy of this evaluation can be further improved with the iteration formula k m 0;c gk m−1 0;c [11]. To seek the solution of Eqs.…”

“…For solving the QNM with the full-wave a-FMM, a point emitter with complex frequency is placed in the vicinity of the antenna. In view of the divergence of the excited field Fω as the emitter frequency ω approaches the eigenfrequency of QNMs, the QNMs can be obtained by solving a nonlinear equation 1∕Fω 0 (with the linear interpolation method) [11,56]. The solution of 1∕Fω 0 is commonly not unique and depends sensitively on the initial value, which causes difficulty in finding all QNMs within the wavelength range of interest.…”

“…Resonant optical antennas are important devices that can efficiently accelerate the radiation of emitters such as molecules or quantum dots placed nearby [1][2][3][4][5][6] or, reciprocally, allow giant enhancement of the near field under far-field illumination [7][8][9][10][11][12]. By controlling the geometrical parameters to fulfill resonance conditions, optical antennas can be widely used in nonlinear optics [13,14], white light supercontinuum generation [7], single-emitter fluorescence enhancement [1,3], and surface enhanced Raman scattering [15][16][17].…”

“…SPP Fabry-Perot models have been developed for antennas composed of a single wire, in which SPPs are bouncing back and forth between the arm facets that act as mirrors [41][42][43][44]. Recently, the Fabry-Perot model has been extended to nanogap antennas with two arms by including the SPP hopping from one arm to the other and the SPP reflection at the gap [5,11]. The extended model, which relies on the ab initio calculation of a few elementary SPP scattering coefficients, has been shown to comprehensively and accurately reproduce many antenna characteristics, for example, scattering cross section, near-field enhancement factor, Purcell factor, and far-field radiation pattern.…”