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Enhanced Non-Reciprocity by Rotations Interplay: One-Way Plasmonic Chains and Perfectly Matched Nano-Antennas 1 Ben Z. Steinberg Yakir Hadad Yarden Mazor Ben Z. Steinberg

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Particles based plasmonic nano-structures –Particle arrays, clusters, arrays of clusters, etc.. Symmetry breaking effects [1,4] –Non-reciprocal waveguides, one-way guiding effects Gain and SHG in plasmonic chains [2] –Non-linear effects based on Lorentz force – gain and SHG –Chain & particles design to achieve phase-matching conditions between chain modes Rigorous spectral analysis & Green’s function theories [3] –New wave constituents –Edge effects (finite, semi-infinite chains) –better understanding of the above, etc.. Activity Overview Hadad, Mazor, Steinberg [1] Hadad, Steinberg, PRL (2010) [2] Steinberg, OpEx, in press [3] Hadad, Steinberg, PRB (2011) [4] Mazor, Steinberg, in preparation

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Strongly non-reciprocal nano-scale Plasmonic chains –Enhanced non-reciprocity by interplay of two-type rotations Two NANO SCALE one-way waveguides: –First: Spiral structure (Chirality) Longitudinal Magnetization leads to Faraday Rotation Structural chirality –Second: New type of “longitudinal rotation” + “longitudinal chirality” Use as perfectly matched Nano-Antenna Talk Overview Hadad, Mazor, Steinberg 3 [1] Hadad, Steinberg, PRL (2010) Advantages over existing one-way waveguides: Truly nano-scale transverse dimensions Much weaker magnetic fields

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Linear array of closely spaced (plasmonic) particles –Particles are much smaller than Single particle dynamics: well described by its polarizability – -th particle excitation: dipole moment –Entire chain dynamics: Sub-Diffraction Chain (SDC) 4 Field in the absence of the particle Hadad, Mazor, Steinberg

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Chain modes One longitudinal (z), two transverse (x,y) (trans. are degenerate if particles are spheres) “trapped” (guided) modes: Inter-particle distance Guided modes transverse width (if ) Radiation modes (or leaky waves) Traditional solution: substitute into the chain equation With conventional plasmonic particles: reciprocal solution (even in, etc…) 5 Sub-Diffraction Chain (SDC) Hadad, Mazor, Steinberg

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Conventional SDC’s (Cont.) Dispersion curves for guided modes spherical particles, –even in –Longitudinal modes bandwidth is larger by –T and L modes have the same central frequency 6 Transverse (x,y) polarization Longitudinal (z) polarization Light-line modes Very close to light-line, down to origin (no cutoff) Very week interaction with chain Poor confinement Hardly excited (can be proved rigorously) Hadad, Mazor, Steinberg

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Non Reciprocal Chains Goal: A truly nano-scale one-way waveguide General approach: –Start with a SDC –Add longitudinal magnetic field; Faraday rotation is created (as always with magnetized plasma) – a “slight” non-reciprocity –Break spherical symmetry of plasmonic particles (e.g. use ellipsoids) –Add chirality – let the ellipsoids rotate, so a spiral is created –Interplay of two-type rotations: strong non-reciprocity, one-way guiding »Clear physical interpretation ? Y! a needle = polarizer 7 Hadad, Mazor, Steinberg

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Analysis Reference particle polarizability –(blue ellipsoid at the origin) –Where –and where = plasma frequency, = cyclotron frequency 8 that of a magnetized plasma Hadad, Mazor, Steinberg

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Analysis – Chain dynamics Polarizability of the n-th ellipsoid –Hence chain dynamics is governed by use matrix properties –Shift invariant difference equation for. The solution is where 9 Depends only on n-m Hadad, Mazor, Steinberg

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Results A chain of plasmonic prolate ellipsoids with Dispersions –Prolates have two different major axes – two different operation bands –Upper band 10 Hadad, Mazor, Steinberg

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Results (Cont.) The one-way behavior –A chain of 801 particles –Central particle (at origin) is excited 11 Lower band Upper band Hadad, Mazor, Steinberg

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Fabrication – similar structure fabricated for different application Twin twisted chains of metal cylinders 19 [5] Walavalkar, Homyk, Henry, Scherer, J. App. Phys 107, (2010) [5] Hadad, Mazor Steinberg

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Yet another one (easier to fabricate, difficult to analyze) –Start with a SDC –Add transverse magnetic field: It couples the previously independent (x,z) polarizations a “slight” non-reciprocity: Longitudinal rotation of dipoles (rotate in a plane parallel to chain) –Break spherical symmetry of plasmonic particles (e.g. use ellipsoids) –Add longitudinal chirality – let the ellipsoids rotate, in a plane parallel to the chain A new kind of structure Non-Bravais lattice, or clustered chain Can be fabricated by printing –Interplay of two-type rotations: strong non-reciprocity, one-way guiding 13 Hadad, Mazor, Steinberg

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The heart of the matter – a longitudinally rotating wave Already at the level of spherical particles with transverse H: –Longitudinal rotation – polarization rotates in a plane parallel to chain 14 Hadad, Mazor, Steinberg

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Add longitudinal rotation of geometry 15 Response to excitation of central dipole:

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Analysis – Chain dynamics Polarizability of the n-th ellipsoid –Chain dynamics is governed by –Rotation and propagation now do not commute: Formulation is NOT shift-invariant –Need to develop and apply a theory for clustered chain (non-Bravais lattices). 16 Hadad, Mazor, Steinberg

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New antenna concept –Terminated one-way waveguide –Back reflections cannot occur –Trapped mode in the “permitted” direction is converted to radiation with nearly 100% efficiency TL in the “permitted” direction Leaky Wave antenna in the “forbidden” direction (but broadside and not endfire) Perfectly matched nano-antenna 15 In/Output port Leaky wave Ant. Hadad, Mazor, Steinberg

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Input powerReturn Loss One way bandwidth 10 Matching results Input port Hadad, Mazor, Steinberg How well is the port matched to chain? How well is the antenna matched?

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Radiation Patterns - Tx and Rx Gain – with respect to a Single Dipole (First chain’s element) –Tx mode –Rx mode –For the non-reciprocal case Tx and Rx patterns are different 11 Main lobe One-way Two-way Two way: [3] Trapped Trapped One way: Trapped Leaky At the chain termination [3] Hadad, Steinberg, Phys Rev B 84, (2011) Hadad, Mazor, Steinberg

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Beam scanning 18% variation of - –Doesn't change the one-way property –Yields turn of main lobe 12 TX RX Hadad, Mazor, Steinberg

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Chiral non-reciprocal surfaces 21 One-side plate One-quadrant plate ? Array of magnetized spiral chains..and if shifted: Spiral rotation chains in x (one-way) Longitudinal in y (also one-way)

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Conclusions Nano-scale one-way guiding : interaction between electromagnetic and geometric rotations Nano-antennas based on these structures are: –Perfectly matched to a remote source –Non-reciprocal (different Tx Rx patterns) –Dynamically tunable (by change of magnetic field) 22 Advantages over existing one-way waveguides: Truly nano-scale transverse dimensions Much weaker magnetic fields

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