Toward Full Spatiotemporal Control on the Nanoscale

Abstract

We introduce an approach to implement full coherent control on nanometer length scales. It is based on spatio-temporal modulation of the surface plasmon polariton (SPP) fields at the thick edge of a nanowedge. The SPP wavepackets propagating toward the sharp edge of this nanowedge are compressed and adiabatically concentrated at a nanofocus, forming an ultrashort pulse of local fields. The one-dimensional spatial profile and temporal waveform of this pulse are completely coherently controlled.PACS numbers: 71.45.Gm, 42.65.Re, 73.20.Mf Two novel areas of optics have recently attracted a great deal of attention: nanooptics and ultrafast optics. One of the most rapidly developing directions in ultrafast optics is quantum control, in which coherent superpositions of quantum states are created by excitation radiation to control the quantum dynamics and outcomes 1,2,3,4 . Of special interest are coherently controlled ultrafast phenomena on the nanoscale where the phase of the excitation waveform along with its polarization provides a functional degree of freedom to control nanoscale distribution of energy 5,6,7,8,9,10 . Spatiotemporal pulse shaping permits one to generate dynamically predefined waveforms modulated both in frequency and in space to focus ultrafast pulses in the required microscopic spatial and femtosecond temporal domains 11,12 .In this Letter, we propose and theoretically develop a method of full coherent control on the nanoscale where a spatiotemporally modulated pulse is launched in a graded nanostructured system. Its propagation and adiabatic concentration provide a possibility to focus the optical energy in nanoscale spatial and femtosecond temporal regions. The idea of adiabatic concentration 13,14 (see also Ref. 15) is based on adiabatic following by the propagating surface plasmon-polariton (SPP) wave of a plasmonic waveguide, where the phase and group velocities decrease toward a limit at which the propagating SPP wave is adiabatically transformed into a standing surface plasmon (SP) mode. This effect has been further developed theoretically 16,17 and observed experimentally. 18 To illustrate the idea of this full coherent control, consider first the adiabatic concentration of a plane SPP wave propagating along a nanowedge of silver 19 , as shown in Fig. 1(a); the theory is based on the Wentzel-KramersBrillouin (WKB) or quasiclassical approximation, also called the eikonal approximation in optics 20 as suggested in Refs. 13,14. The propagation velocity of the SPP along such a nanowedge is asymptotically proportional to its thickness. Thus when a SPP approaches the sharp edge, it slows down and asymptotically (in the ideal limit of zero thickness at the apex) stops while the local fields are increased and nano-concentrated. Now consider a family of SPP rays (WKB trajectories) propagating from the thick side of a nanowedge, as shown in Fig. 1(b). One possibility to launch such SPPs is to have nanoscale inhomogeneities (nanoparticles or nanoholes) at the thick edge of the wedge. Each of the o...

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“…Correspondingly, it is an ultra-fast, femtosecond or even subfemtosecond phenomenon, which can be coherently controlled by pulse shaping [74].…”

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