Faucet for wave transmission through rotation of waveguide

Faucet for wave transmission through rotation of waveguide Artem Pilipchuk and Alina Lyapina Kirensky Institute of Physics, Federal Research Center KSC SB RAS, 660036 Krasnoyarsk, Russia

Thomas Young speaking on 24 November 1803, to the Royal Society of London, began his description of the historic experiment on double -slit interference. His talk was published in the following year's Philosophical Transactions, and was destined to become a classic, still reprinted and read today. The Bakerian Lecture: Experiments and Calculations Relative to Physical Optics Thomas Young Philosophical Transactions of the Royal Society of London Vol. 94 (1804), pp. 1 -16

Milestones of wave interference (by chronology) 1. J. von Neumann and E. Wigner, Z. Phys (1929) Bound states in the continuum (BSC) H. Friedrich and D. Wintgen, "Interferring resonances and bound states in the continuum, “ PRA (1985). Phys. Rev. (1959)

3. Fano asymmetric resonance

4. Topological singularities or vortices

Rotation of waveguide unites all these phase features

Effective non-Hermitian Hamiltonian l l l l U. Fano, Phys. Rev. 124, 1866 (1961). H. Feshbach, Ann. Phys. (New York) (1958) ; (1962). C. Mahaux, H. A. Weidenmuller, Shell-Model Approach to Nuclear Reactions, North-Holland, Amsterdam, 1969. I. Rotter, Rep. Prog. Phys. , 54, 635 (1991). H. -J. Stockmann and Petr Seba, JPA (1998). H. -J. Stockmann, Quantum Chaos (1999). K. Pichugin, H. Schanz, and Petr Seba, Phys. Rev. E (2001). Sadreev and I. Rotter, JPA (2002). W is matrix Nx. M where N is the number of eigen states of closed quantum system, M is the number of continua (channels)

Albeverio, Kurasov, Kus, and Petr Seba, J. Math. Phys. (1966): Fyodorov and Sommers, J. Math. Phys. 38, 1918 (1997) l. Pichugin, Schanz, and Petr Seba, Phys. Rev. E (2001).

How to tune transmission spectra (Fano resonances) ? 1. Change of eigenvalues

2. Vary the coupling strength S. Rotter, F. Libisch, J. Burgoffer, U. Kuhl, and H. -J. Stockmann, "Tunable Fano resonances in transport through microwave billiards“, PRE (2004).

3. Make the coupling strengths complex by rotation of waveguide The continua of waveguides The Neumann BC z Resonator

Effective non-Hermitian Hamiltonian

Phase transformation of continua

Transmittance in the first channel p=0, q=1

Wave faucet

l. I. Rotter, Rep. Prog. Phys. , 54, 635 (1991) l Okolowicz, Ploszajczak, and I. Rotter, Phys. Rep. (2003) l. Sadreev and I. Rotter, JPA (2003)

Numerous events of zero resonant widths, bound states in the continuum Symmetry protected BSCs

BSC 1

Coupling with evanescent modes of channels p=+/- 1, q=1 Coupling with propagating modes of the channel p=0, q=1

Hermitian anti-Hermitian Shifted waveguides lift a degeneracy of cylindrical Resonator relative to +- m

It is easy to find the symmetry protected

Bound state in the continuums due to interference of states 211, -211, 112, and -112

Twisted BSCs

Spinning bound states in the continuum R. Parker, "Acoustic resonances and blade vibration in axial flow compressors", J. Sound and Vibration (1984). Y. Duan and M. Mc. Iver, "Rotational acoustic resonances in cylindrical waveguides", Wave Motion (2004). No spinning currents because evanescent modes of shifted waveguides lift a degeneracy +- m Phase of the scattering function at z=L/2

Eigenlevel 012 crosses eigenlevel +-2 11 Eigenlevel 013 crosses eigenlevel +-2 11

conclusions 1. Rotation of input or output waveguide in respect to resonator attributes 2. phase factors into the coupling matrix elements 2. That in turn strongly effects Fano resonances and respectively wave transmittance. Wave faucet. 3. There is discrete set of the rotation angles at which wave localizes inside the resonator, bound states in the continuum of both waveguides, left and rotated right ones. Trapping of sound waves. Collapse of Fano resonance, when unit transmittance coalesces with zero transmittance. 4. Evanesvcent modes of rotated waveguide gives rise to modification of Hamiltonian of cylindrical resonator whose eigenvalues dependent on the rotation angle and lift the degeneracy relative to the azimuthal quantum number. Analogue with magnetic flux.