Abstract. Over the last two decades, advances in fabrication have led to significant progress in creating patterned heterostructures that support either carriers, such as electrons or holes, with specific band structure or electromagnetic waves with a given mode structure and dispersion. In this article, we review the properties of light in coupled optical waveguides that support specific energy spectra, with or without the effects of disorder, that are well-described by a Hermitian tight-binding model. We show that with a judicious choice of the initial wave packet, this system displays the characteristics of a quantum particle, including transverse photonic transport and localization, and that of a classical particle. We extend the analysis to non-Hermitian, parity and time-reversal (PT ) symmetric Hamiltonians which physically represent waveguide arrays with spatially separated, balanced absorption or amplification. We show that coupled waveguides are an ideal candidate to simulate PT -symmetric Hamiltonians and the transition from a purely real energy spectrum to a spectrum with complex conjugate eigenvalues that occurs in them.

We investigate the single-particle time evolution and two-particle quantum correlations in a one-dimensional N -site lattice with a site-dependent nearest-neighbor tunneling function t α (k) = t 0 [k(N − k)] α/2 . Since the bandwidth and the energy-level spacings for such a lattice both depend upon α, we show that the observable properties of a wave packet, such as its spread and the relative phases of its constituents, vary dramatically as α is varied from positive to negative values. We also find that the quantum correlations are exquisitely sensitive to the form of the tunneling function. Our results suggest that arrays of waveguides with position-dependent evanescent couplings will show rich dynamics with no counterpart in present-day, traditional systems.

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A theoretical proposal for photonic transport in an array of waveguides is presented. By coupling phase-displaced inputs into adjacent waveguides, and calculating the expectation value of the position space operator, we demonstrate directed motion in this system. The one way photonic transport arises from interferences due to the phase differences in the inputs to the waveguides.2

We investigate the effects of disorder on single particle time-evolution and two-particle correlations in an array of evanescently coupled waveguides with position-dependent tunneling rates.In the clean limit, the energy spectrum of such an array is widely tunable. In the presence of a Hermitian on-site or tunneling disorder, we find that the localization of a wave packet is highly sensitive to this energy spectrum. In particular, for an input confined to a single waveguide, we show that the fraction of light localized to the original waveguide depends on the tunneling profile.We compare the two-particle intensity correlations in the presence of Hermitian, tunneling disorder and non-Hermitian, parity-and-time-reversal (PT ) symmetric, on-site potential disorder. We show the two-particle correlation function in both cases is qualitatively similar, since both disorders preserve the particle-hole symmetric nature of the energy spectrum.