Parity-time (PT) symmetric periodic structures, near the spontaneous PT-symmetry breaking point, can act as unidirectional invisible media. In this regime, the reflection from one end is diminished while it is enhanced from the other. Furthermore, 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 nonlinearities, and it can also effectively suppress optical bistabilities.

We show that non-linear optical structures involving a balanced gain-loss profile, can act as unidirectional optical valves. This is made possible by exploiting the interplay between the fundamental symmetries of parity (P) and time (T ), with optical nonlinear effects. This novel unidirectional dynamics is specifically demonstrated for the case of an integrable PT -symmetric nonlinear system.

We introduce here the concept of acoustic parity-time (PT ) symmetry and demonstrate the extraordinary scattering characteristics of the acoustic PT medium. On the basis of exact calculations, we show how an acoustic PT -symmetric medium can become unidirectionally transparent at given frequencies. Combining such a PT -symmetric medium with transformation acoustics, we design two-dimensional symmetric acoustic cloaks that are unidirectionally invisible in a prescribed direction. Our results open new possibilities for designing functional acoustic devices with directional responses.

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.

A mechanism for asymmetric transport based on the interplay between the fundamental symmetries of parity (P) and time (T ) with nonlinearity is presented. We experimentally demonstrate and theoretically analyze the phenomenon using a pair of coupled van der Pol oscillators, as a reference system, one with anharmonic gain and the other with complementary anharmonic loss; connected to two transmission lines. An increase of the gain/loss strength or the number of PT -symmetric nonlinear dimers in a chain, can increase both the asymmetry and transmittance intensities.PACS numbers: 42.25.Bs, 11.30.Er Directed transport is at the heart of many fundamental problems in physics. Furthermore it is of great relevance to engineering where the challenge is to design on-chip integrated devices that control energy and/or mass flows in different spatial directions. Along these lines, the creation of novel classes of integrated photonic, electronic, acoustic or thermal diodes is of great interest. Unidirectional elements constitute the basic building blocks for a variety of transport-based devices such as rectifiers, pumps, molecular switches and transistors.The idea was originally implemented in the electronics framework, with the construction of electrical diodes that were able to rectify the current flux. This significant revolution motivated researchers to investigate the possibility of implementing this idea of "diode action" to other areas. For example, a proposal for the creation of a thermal diode, capable of transmitting heat asymmetrically between two temperature sources, was suggested in Ref.[1]. Another domain of application was the propagation of acoustic pulses in granular systems [2].A related issue concerns the possibility of devising an optical diode which transmits light differently along opposite propagation directions. Currently, such unidirectional elements rely almost exclusively on the Faraday effect, where external magnetic fields are used to break space-time symmetry. Generally this requires materials with appreciable Verdet constants and/or large size non-reciprocal devices -typically not compatible with on-chip integration schemes or light-emitting wafers [3]. To address these problems, alternative proposals for the creation of optical diodes have been suggested recently. Examples include optical diodes based on second harmonic generation in asymmetric waveguides [4] and nonlinear photonic crystals [5], photonic quasi-crystals and molecules [6], or asymmetric nonlinear structures [7]. Most of these schemes, however, suffer from serious drawbacks making them unsuitable for commercial or smallscale applications. Relatively large physical sizes are often needed while absorption or direct reflection dramatically affects the functionality leading to an inadequate balance between figures of merit and optical intensities. In other cases, cumbersome structural designs are necessary to provide structural asymmetry, or the transmitted signal has different characteristics than the incident one.In this Letter ...