1. 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

2. 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 105 233904 (2010) [2] Steinberg, OpEx, in press [3] Hadad, Steinberg, PRB 84 125402 (2011) [4] Mazor, Steinberg, in preparation

3. 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 105 233904 (2010) Advantages over existing one-way waveguides: Truly nano-scale transverse dimensions Much weaker magnetic fields

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Fabrication – similar structure fabricated for different application Twin twisted chains of metal cylinders 19 [5] Walavalkar, Homyk, Henry, Scherer, J. App. Phys 107, 124314 (2010) [5] Hadad, Mazor Steinberg

13. 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

14. 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

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

16. 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

17. 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

18. 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?

19. 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, 125402 (2011) Hadad, Mazor, Steinberg

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

21. 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)

22. 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