## PT-Symmetric Talbot Effects

Hamidreza Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, Tsampikos Kottos

We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern, has to respect specific periodicities which are dictated by the symmetries of the system. While at the spontaneous PT-symmetry breaking point, the image revivals occur at Talbot lengths governed by the characteristics of the passive lattice, at the exact phase it depends on the gain and loss parameter thus allowing one to control the imaging process.

http://arxiv.org/abs/1209.2349

Optics (physics.optics); Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)

## PT-Symmetric Electronics

J. Schindler, Z. Lin, J. M. Lee, Hamidreza Ramezani, F. M. Ellis, Tsampikos Kottos

We show both theoretically and experimentally that a pair of inductively coupled active LRC circuits (dimer), one with amplification and another with an equivalent amount of attenuation, display all the features which characterize a wide class of non-Hermitian systems which commute with the joint parity-time PT operator: typical normal modes, temporal evolution, and scattering processes. Utilizing a Liouvilian formulation, we can define an underlying PT-symmetric Hamiltonian, which provides important insight for understanding the behavior of the system. When the PT-dimer is coupled to transmission lines, the resulting scattering signal reveals novel features which reflect the PT-symmetry of the scattering target. Specifically we show that the device can show two different behaviors simultaneously, an amplifier or an absorber, depending on the direction and phase relation of the interrogating waves. Having an exact theory, and due to its relative experimental simplicity, PT-symmetric electronics offers new insights into the properties of PT-symmetric systems which are at the forefront of the research in mathematical physics and related fields.

http://arxiv.org/abs/1209.2347
Other Condensed Matter (cond-mat.other); Optics (physics.optics); Quantum Physics (quant-ph)

## Bragg solitons in nonlinear PT-symmetric periodic potentials

Mohammad-Ali Miri, Alejandro B. Aceves, Tsampikos Kottos, Vassilios Kovanis, Demetrios N. Christodoulides

It is shown that slow Bragg soliton solutions are possible in nonlinear complex parity-time (PT) symmetric periodic structures. Analysis indicates that the PT-symmetric component of the periodic optical refractive index can modify the grating band structure and hence the effective coupling between the forward and backward waves. Starting from a classical modified massive Thirring model, solitary wave solutions are obtained in closed form. The basic properties of these slow solitary waves and their dependence on their respective PT-symmetric gain/loss profile are then explored via numerical simulations.

http://arxiv.org/abs/1209.0787
Optics (physics.optics); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI); Quantum Physics (quant-ph)

## Light Transport in Random Media with PT-Symmetry

Samuel Kalish, Zin Lin, Tsampikos Kottos

The scattering properties of randomly layered optical media with $${\cal PT}$$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmitance decays exponentially as a function of the system size, with an enhanced rate $$\xi_{\gamma}(W)^{-1}=\xi_0(W)^{-1}+\xi_{\gamma} (0)^{-1}$$, where $$\xi_0(W)$$ is the localization length of the equivalent passive random medium and $$\xi_{\gamma}(0)$$ is the attenuation/amplification length of the corresponding perfect system with a $${\cal PT}$$-symmetric refraction index profile. While transmitance processes are reciprocal to left and right incident waves, the reflectance is enhanced from one side and is inversely suppressed from the other, thus allowing such $${\cal PT}$$-symmetric random media to act as unidirectional coherent absorbers.

http://arxiv.org/abs/1205.1849
Optics (physics.optics)

## Bypassing the bandwidth theorem with PT symmetry

Hamidreza Ramezani, J. Schindler, F. M. Ellis, Uwe Guenther, Tsampikos Kottos

The beat time $${\tau}_{fpt}$$ associated with the energy transfer between two coupled oscillators is dictated by the bandwidth theorem which sets a lower bound $${\tau}_{fpt}\sim 1/{\delta}{\omega}$$. We show, both experimentally and theoretically, that two coupled active LRC electrical oscillators with parity-time (PT) symmetry, bypass the lower bound imposed by the bandwidth theorem, reducing the beat time to zero while retaining a real valued spectrum and fixed eigenfrequency difference $$\delta\omega$$. Our results foster new design strategies which lead to (stable) pseudo-unitary wave evolution, and may allow for ultrafast computation, telecommunication, and signal processing.

http://arxiv.org/abs/1205.1847
Classical Physics (physics.class-ph)

## Experimental observation of the dual behavior of PT-symmetric scattering

Zin Lin, Joseph Schindler, Fred M. Ellis, Tsampikos Kottos

We investigate experimentally parity-time $${\cal PT}$$ symmetric scattering using $$LRC$$ circuits in an inductively coupled $${\cal PT}$$- symmetric pair connected to transmission line leads. In the single-lead case, the $${\cal PT}$$-symmetric circuit acts as a simple dual device – an amplifier or an absorber depending on the orientation of the lead. When a second lead is attached, the system exhibits unidirectional transparency for some characteristic frequencies. This non-reciprocal behavior is a consequence of generalized (non-unitary) conservation relations satisfied by the scattering matrix.

http://arxiv.org/abs/1205.2176
Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

## Exceptional Point Dynamics in Photonic Honeycomb Lattices with PT Symmetry

Hamidreza Ramezani, Tsampikos Kottos, Vassilios Kovanis, Demetrios N. Christodoulides

We theoretically investigate the flow of electromagnetic waves in complex honeycomb photonic lattices with local PT symmetries. Such PT structure is introduced via a judicious arrangement of gain or loss across the honeycomb lattice, characterized by a gain/loss parameter \{\gamma\}. We found a new class of conical diffraction phenomena where the formed cone is brighter and travels along the lattice with a transverse speed proportional to \{\sqrt{\gamma}\}.

http://arxiv.org/abs/1112.4734
Optics (physics.optics); Quantum Physics

## Experimental Study of Active LRC Circuits with PT-Symmetries

Joseph Schindler, Ang Li, Mei C. Zheng, F. M. Ellis, Tsampikos Kottos

Mutually coupled modes of a pair of active LRC circuits, one with amplification and another with an equivalent amount of attenuation, provide an experimental realization of a wide class of systems where gain/loss mechanisms break the Hermiticity while preserving parity-time PT symmetry. For a value PT of the gain/loss strength parameter the eigen-frequencies undergo a spontaneous phase transition from real to complex values, while the normal modes coalesce acquiring a definite chirality. The consequences of the phase-transition in the spatiotemporal energy evolution are also presented.

http://arxiv.org/abs/1109.2913
Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)

## Unidirectional Invisibility induced by PT-Symmetric Periodic Structures

Zin Lin, Hamidreza Ramezani, Toni Eichelkraut, Tsampikos Kottos, Hui Cao, Demetrios N. Christodoulides

We show that parity-time (PT) symmetric Bragg periodic structures, near the spontaneous PT – symmetry breaking point, can act as unidirectional invisible media. In this regime, the re flection from one end is diminished while it is enhanced from the other. At the same time the transmission coefficient and phase, are indistinguishable from those expected in the absence of a grating. The phenomenon is robust even in the presence of Kerr non-linearities, and it can also eff?ectively suppress optical bistabilities.

http://arxiv.org/abs/1108.2493
Optics (physics.optics)