Enhanced NonReciprocity by Rotations Interplay OneWay Plasmonic Chains

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

Activity Overview • 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. . [1] Hadad , Steinberg, PRL 105 233904 (2010) [2] Steinberg, Op. Ex, in press [3] Hadad , Steinberg, PRB 84 125402 (2011) Hadad, Mazor, Steinberg [4] Mazor, Steinberg, in preparation

Talk Overview • 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) Advantages over existing one-way waveguides: • Truly nano-scale transverse dimensions • Much weaker magnetic fields Ø Longitudinal Magnetization leads to Faraday Rotation Ø Structural chirality – Second: New type of “longitudinal rotation” + “longitudinal chirality” • Use as perfectly matched Nano-Antenna [1] Hadad , Steinberg, PRL 105 233904 (2010) 3 Hadad, Mazor, Steinberg

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

Sub-Diffraction Chain (SDC) • 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 • Radiation modes (or leaky waves) • Traditional solution: substitute Ø (if ) into the chain equation With conventional plasmonic particles: reciprocal solution (even in , etc…) 5 Hadad, Mazor, Steinberg

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 Transverse (x, y) 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) Longitudinal (z) polarization 6 Hadad, Mazor, Steinberg

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

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

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

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

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

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

Yet another one (easier to fabricate, difficult to analyze) – Start with a SDC – Add transverse magnetic field: Ø It couples the previously independent (x, z) polarizations Ø 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 Ø A new kind of structure Ø Non-Bravais lattice, or clustered chain Ø Can be fabricated by printing – Interplay of two-type rotations: strong non-reciprocity, one-way guiding 13 Hadad, Mazor, Steinberg

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

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

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

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

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

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 Main lobe Ø Tx and Rx patterns are different One-way Two-way At the chain termination Two way: Trapped [3] Trapped One way: Trapped Leaky 11 [3] Hadad, Steinberg, Phys Rev B 84, 125402 (2011) Hadad, Mazor, Steinberg

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

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

Conclusions • Nano-scale one-way guiding : interaction between electromagnetic and geometric rotations Advantages over existing one-way waveguides: • Truly nano-scale transverse dimensions • Much weaker magnetic fields • 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