Whirling Plasmons: Angular Momentum Selection Rule

Abstract

P lasmonic systems have been shown to be resonantly excited when the linear momentum selection rule is fulfi lled.1 However, conservation of total angular momentum (AM) in a closed physical system results in additional selection rules. e AM of an optical beam comprises the intrinsic component—the spin, associated with the handedness of the circular polarization—and the extrinsic component— orbital AM (OAM), associated with a spiral phase front.2 Here, we demonstrate a plasmonic nanostructure that exhibits a crucial role of an AM selection rule in a lightsurface plasmon scattering process. In our experiment, the intrinsic AM of the incident radiation was coupled to the extrinsic momentum of the surface plasmons via spin-orbit interaction, which was manifested by a geometric Berry phase.3 Due to this eff ect, we achieved a symmetry breaking that resulted in a spin-dependent enhanced transmission through coaxial nanoapertures, even in rotationally symmetric structures.4 In an optical paraxial beam with a spiral phase distribution (= –l, where  is the azimuthal angle in polar coordinates, and the integer number l is the topological charge), the total AM per photon, in units of h– (normalized AM), was shown to be j=(+l), where =1 is the right-handed circular polarization and =–1 is the left-handed circular polarization.2 In accordance with fundamental physical principles, resonant excitation of the nanoaperture eigenmode requires that the exciting wave match the excited mode, both with its linear and angular momentum. is matching imposes restrictions, or selection rules, on the excitation process. e coaxial nanoaperture was milled by a focused ion beam into a 200-nmthick gold fi lm evaporated onto a glass wafer. e inner and the outer radii of the ring slit were 250 and 350 nm, respectively. e aperture was designed to be a single mode system—in other words, to possess a single allowed excitation with OAM of lGM=±1. e aperture was surrounded by an annular coupling grating with a period of 500 nm. is element was illuminated by a green laser light (532 nm) whose phase was modulated by a spatial light modulator to achieve a spiral phase corresponding to an OAM of lext=0, ±2. e incident spin (in=±1) induced a spiral phase of the excited surface plasmons via spinorbit interaction, and, therefore, was converted to the OAM.5 e surface mode then acquired OAM of lSM= in+ lext. e best overlapping of the surface mode and guided modes was obtained when lSM= lGM, i.e. (a) Mechanism of the nanoaperture’s excitation controlled by AM selection rules. Incident beam bears the intrinsic AM of in and the extrinsic AM of lext. Excited surface mode acquires the OAM of lSM as a result of spin-orbit interaction. Guided mode with lGM is excited only if selection rule is satis ed. (Inset) Scanning electron microscope image of the structure. (b) Intensity distribution cross-sections for different lext. Blue dashed lines correspond to in=1 and red solid lines to in=–1. Intensity was normalized by the transmission measured via coaxial aperture without the surrounding corrugation. (Horizontal dimension was scaled according to the optical magni cation.) (a)