One of the fundamental axioms of quantum mechanics is associated with the Hermiticity of physical observables 1 . In the case of the Hamiltonian operator, this requirement not only implies real eigenenergies but also guarantees probability conservation. Interestingly, a wide class of non-Hermitian Hamiltonians can still show entirely real spectra. Among these are Hamiltonians respecting parity-time (PT) symmetry 2-7 . Even though the Hermiticity of quantum observables was never in doubt, such concepts have motivated discussions on several fronts in physics, including quantum field theories 8 , nonHermitian Anderson models 9 and open quantum systems 10,11 , to mention a few. Although the impact of PT symmetry in these fields is still debated, it has been recently realized that optics can provide a fertile ground where PT-related notions can be implemented and experimentally investigated [12][13][14][15] . In this letter we report the first observation of the behaviour of a PT optical coupled system that judiciously involves a complex index potential. We observe both spontaneous PT symmetry breaking and power oscillations violating left-right symmetry. Our results may pave the way towards a new class of PT-synthetic materials with intriguing and unexpected properties that rely on non-reciprocal light propagation and tailored transverse energy flow.Before we introduce the concept of spacetime reflection in optics, we first briefly outline some of the basic aspects of this symmetry within the context of quantum mechanics. In general, a HamiltonianĤ =p 2 /2m + V (x) (wherex andp are position and momentum operators respectively, m is mass and V is the potential) is considered to be PT symmetric, PTĤ =Ĥ PT , provided that it shares common eigenfunctions with the PT operator 1,[16][17][18][19][20][21] . This condition corresponds to an exact or unbroken PT symmetry, as opposed to that of broken PT symmetry, where, even though PTĤ =Ĥ PT is still valid,Ĥ and PT (or any other antilinear operator) possess different eigenvectors 22 . For the case considered here, given that the action of the parity P and time T operators is defined asp → −p,x → −x andp → −p,x →x, i → −i, respectively, it then follows that a necessary (but not sufficient) condition for a Hamiltonian to be PT symmetric is V (x) = V * (−x). In other words, PT symmetry requires that the real part of the potential V is an even function of position x, whereas the imaginary part is odd; that is, the Hamiltonian must have the formĤ =p 2 /2m + V R (x) + iεV I (x), where V R,I are the symmetric and antisymmetric components of V , respectively 12-14 . Clearly, if ε = 0, this Hamiltonian is Hermitian. It turns out that, even if the antisymmetric imaginary component is finite, this class of potentials can still allow for both bound and radiation states, all with entirely real spectra. This is possible as long as ε is below some threshold, ε < ε th . If, on the other hand, this limit is crossed (ε > ε th ), the spectrum ceases to be real and starts to involve imaginary ei...

We investigate, experimentally and theoretically, light propagation in one-dimensional waveguide arrays exhibiting a saturable self-defocusing nonlinearity. We demonstrate low-intensity "discrete diffraction", and the high-intensity formation of spatial gap solitons arising from the first band of the transmission spectrum. The waveguide arrays are fabricated by titanium in-diffusion in a photorefractive copper-doped lithium niobate crystal, and the optical nonlinearity arises from the bulk photovoltaic effect.

The observation of nonlinear staggered surface states at the interface between a substrate and a one-dimensional self-defocusing nonlinear waveguide array is reported. Launching of staggered input beams of different power in the first channel of the array results in formation of localized structures in different channels. Our experimental results are confirmed numerically.

We demonstrate spatial Rabi oscillations in optical waveguide arrays. Adiabatic transitions between extended Floquet-Bloch modes associated with different bands are stimulated by periodic modulation of the photonic lattice in the propagation direction. When the stimulating modulation also carries transverse momentum, the transition becomes indirect, equivalent to phonon-assisted Rabi oscillations. In solid state physics such indirect Rabi oscillations necessitate coherent phonons and hence they have never been observed. Our experiments suggest that phonon-assisted Rabi oscillations are observable also with Bose-Einstein condensates, as well as with other wave systems-where coherence can be maintained for at least one period of the Rabi oscillation.

We report on the fabrication and characterization of ridge waveguides in lithium niobate thin films by diamond blade dicing. The lithium niobate thin films with a thickness of 1 µm were fabricated by bonding a He-implanted lithium niobate wafer to a SiO(2)-coated lithium niobate wafer and crystal ion slicing. Propagation losses of 1.2 dB/cm for TE and 2.8 dB/cm for TM polarization were measured at 1550 nm for a 9.28 mm long and 2.1 µm wide waveguide using the Fabry-Perot method.