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In this paper, we report the analytic solution of the oscillating box potential. We investigate the temporal dependence of the amplitude of the ground state as a function of the system parameters. Our analysis reveals the counterintuitive behavior that the loss of the ground state is a nonmonotonic function of the oscillation frequency. On the basis of optical waveguides, we provide an experimental verification of our theoretical findings.

We present a theoretical study of the spatial Goos-H\"anchen shift occurring at the interface between two photonic graphene lattices. Numerical simulations of light propagation in such a wave-guiding system are also presented to corroborate our findings. Our results show that the combined action of the honeycomb lattice structure and the discrete nature of wave-guiding systems give rise to a giant and negative Goos-H\"anchen shift.

In contrast to plane waves, twisted or vortex beams have a complex spatial structure. Both their intensity and energy flow vary within the wave front. Beyond that, polychromatic vortex beams, such as $X$ waves, have a spatially dependent energy distribution. We propose a method to measure this (local) energy spectrum. The method is based on the measurement of the energy distribution of photoelectrons from alkali-metal atoms. On the basis of our fully relativistic calculations, we argue that even ensembles of atoms can be used to probe the local energy spectrum of short twisted pulses.

We demonstrate that superpositions of coherent and displaced Fock states, also referred to as generalized Schr\"odinger cats cats, can be created by application of a nonlinear displacement operator which is a deformed version of the Glauber displacement operator. Consequently, such generalized cat states can be formally considered as nonlinear coherent states. We then show that Glauber-Fock photonic lattices endowed with alternating positive and negative coupling coefficients give rise to classical analogs of such cat states. In addition, it is pointed out that the analytic propagator of these deformed Glauber-Fock arrays explicitly contains the Wigner operator opening the possibility to observe Wigner functions of the quantum harmonic oscillator in the classical domain., Comment: 17 pages, 5 figures

We introduce a recursive bosonic quantization technique for generating classical parity-time ($\mathcal{PT}$) photonic structures that possess hidden symmetries and higher-order exceptional points. We study light transport in these geometries and we demonstrate that perfect state transfer is possible only for certain initial conditions. Moreover, we show that for the same propagation direction, left and right coherent transports are not symmetric with field amplitudes following two different trajectories. A general scheme for identifying the conservation laws in such $\mathcal{PT}$-symmetric photonic networks is also presented.

We demonstrate that perfect transfer of path-entangled photons as well as of single-photon states is possible in a certain class of spin inspired optical systems---the so-called ${J}_{x}$ photonic lattices. In these fully integrable optical arrangements, perfect cyclic transitions from correlated states to totally anticorrelated states can naturally occur. Moreover we show that the bunching and antibunching response of path-entangled photons can be preengineered at will in such coupled optical arrangements. We elucidate these effects via pertinent examples.

We propose a versatile approach for generating multipartite $W$ states in predesigned on-chip multiport photonic lattices. It is shown that is possible to produce photon-encoded $W$ states where exactly one photon is coherently ``shared'' among $N$ optical modes by judiciously adjusting the coupling coefficients involved in one-dimensional arrays of evanescently coupled single-mode waveguides. Two-dimensional waveguide configurations are also investigated as possible avenues to produce $W$ states with equal probability amplitudes and equal relative phases.

We study Anderson localization and propagation of partially-spatially incoherent wavepackets in linear disordered potentials, motivated by the insight that interference phenomena resulting from multiple scattering are affected by the coherence of the waves. We find that localization is delayed by incoherence: the more incoherent the waves are, the longer they diffusively spread while propagating in the medium. However, if all the eigenmodes of the system are exponentially localized (as in one- and two-dimensional disordered systems), any partially-incoherent wavepacket eventually exhibits localization with exponentially-decaying tails, after sufficiently long propagation distances. Interestingly, we find that the asymptotic behavior of the incoherent beam is similar to that of a single instantaneous coherent realization of the beam., Comment: Revised version including a discussion on both spatially and temporally incoherent light beams. Revised Figs. 2 and 3 and fixed typos

We propose a classical experimental scheme for simulating quantum correlations of path-entangled biphotons, propagating in arbitrary one- or two-dimensional arrays of evanescently coupled waveguides. Our approach requires only intensity and phase measurements and can be used to characterize the evolution of the biphoton wave packet. The precision of the method and its robustness to phase fluctuations are investigated by a statistical analysis.

We present a comprehensive analysis of how the properties of two-dimensional lattice (``discrete'') solitons in a Kerr medium are influenced by their peak intensity and width. We are able to quantitatively relate the Townes solution for solitons in a two-dimensional, homogeneous media to two distinct regimes of the lattice solitons: to narrow, high-intensity, highly nonlinear solitons and to broad, low-intensity, weakly nonlinear solitons, which experience the periodic potential as an effective homogeneous medium. Both regimes, although they support a different power flow and are affected by completely different diffraction dynamics, are thus traced back to the same physical phenomenon. They are separated by a range of unstable and stable solutions, directly caused by the periodicity of the lattice.

Interference effects of photon pairs propagating through two-dimensional lattices of evanescently coupled waveguides are theoretically analyzed for input states of independent and path-entangled photons. Their correlation unveils characteristic Hong-Ou-Mandel interferences as well as more complex phenomena unique to these structures. Furthermore, purely classical states of light are used to simulate these quantum interferences in intensity correlation experiments. The results suggest that waveguide arrays can be employed as convenient devices for manipulating quantum states of light.

An electromagnetic realization of Landau-Zener (LZ) tunneling is experimentally demonstrated in femtosecond-laser written waveguide couplers with a cubically bent axis. Quantitative measurements of light evolution inside the coupler, based on fluorescence imaging, enable to trace the detailed dynamics of the LZ process. The experimental results are in good agreement with the theoretical LZ model for linear crossing of energy levels with constant coupling of finite duration.

We introduce an analytical expression for the dynamics of light propagation in a two-dimensional waveguide lattice including general long range coupling. Additionally, the diffraction properties in such general systems are investigated in detail. Using these very general results, particular geometries are discussed, including the possibility of diffraction-free propagation in the center of the Brillouin zone. Furthermore, the transition from the discrete to the continuum limit is analyzed.

We introduce an analytical formula for the dynamics of light propagation in a two-dimensional waveguide lattice including diagonal coupling. A superposition of infinite arrays created by imaginary sources is used to derive an expression for boundary reflections. It is shown analytically that for large propagation distances the propagating field reaches uniformity. Furthermore, periodic field recovery is studied and discrete anomalous refraction and diffraction are investigated in arbitrary two-dimensional lattices.