We analyze the impact of loss in lattices of coupled optical waveguides and find that in such case, the hopping between adjacent waveguides is necessarily complex. This results not only in a transition of the light spreading from ballistic to diffusive, but also in a new kind of diffraction that is caused by loss dispersion. We prove our theoretical results with experimental observations. PACS numbers: PACS numbers: 42.25. Bs, 42.79.Gn, 72.10.Bg, 73.23.Ad Absorption is an intrinsic feature of photonic systems, arising due to the laws of causality [1]. It results in decoherence and, hence, in a considerable change in the dynamics of optical waves. However, it is generally agreed that in the particular case of homogeneous and isotropic loss the impact on the amplitude distribution in the system vanishes, besides a global decay of the integrated power [1]. A very prominent photonic system is arrays of evanescently coupled waveguides [2], where a tailored absorption (or absorption/gain) distribution is the basis for a multitude of unexpected physical phenomena, such as exceptional points [3], unusual beam dynamics [4], spontaneous PT -symmetry breaking [5], non-reciprocal Bloch oscillations [6] and dynamic localization [7], unidirectional cloaking [8], and even tachyonic transport [9]. Owing to the intuition described above, if all lattice sites exhibit exactly the same absorption, its impact vanishes in the evolution equations of these systems. In a more mathematical language, in this case absorption adds to the Hamiltonian as a pure diagonal matrix with identical elements, which can be removed by normalization.In our work we show that absorption in coupled waveguide systems does always impact the light dynamics, even if it is homogeneous and isotropic in all lattice sites. Due to the imaginary part of the dielectric function (that describes the absorption) imaginary off-diagonal elements in the Hamiltonian appear that cannot be removed by normalization, causing significant deviations in the light dynamics compared to the Hermitian case. However, our theory holds for all Schrödinger type systems that can be mapped onto a tight binding lattice, e.g., paraxial waves in optics or mechanics as well as quantum dynamics in spin chains, population transfer in multi-level systems and graphene. Our theory supplements the knowledge about the influence of non-Hermiticity to all these systems in general including the effect of PT symmetry.In order to study the impact of absorption in such systems, we consider a one-dimensional array of N identical single mode optical waveguides with width 2w, inter-site spacing d, and the complex relative electric permittivity + i at the positions x n (n = 1, 2, ..., N ), which is surrounded by a bulk material (with 0 + i 0 ). A sketch of this system is shown in Fig. 1.The dynamics of wave propagating through this system is governed by the Helmholtz wave equationwhere ψ(x, z) is the electric field amplitude, k 0 = ω c is the propagation constant in free space, and ε(x) is relative electric ...
We propose an exactly solvable waveguide lattice incorporating inhomogeneous coupling coefficient. This structure provides a classical analogues to the squeezed number and squeezed coherent intensity distribution in quantum optics where the propagation length plays the role of squeezed amplitude. The intensity pattern is obtained in a closed form for an arbitrary distribution of the initial beam profile. We have also investigated the phase transition to the spatial Bloch-like oscillations by adding a linear gradient to the propagation constant of each waveguides (α). Our analytical results show that the Bloch-like oscillations appear above a critical value for the linear gradient of propagation constant (α > αc). The phase transition (in the propagation properties of the waveguide) is a result of competition between discrete and Bragg diffraction. Moreover, the light intensity decay algebraically along each waveguide at the critical point while it falls off exponentially below the critical point (α < αc).
We numerically investigate the vacuum electron acceleration by a high-intensity linearly polarized twisted laser pulse. It is shown that the inherent spiral structure of a Laguerre-Gaussian laser pulse leads to improvement in trapping and acceleration of an electron to energies of the order of GeV in the off-axis case. Also, it is demonstrated that by employing a proper choice of initial injection parameters, the high-energetic electrons with very small scattering angles can be produced. V C 2015 AIP Publishing LLC. [http://dx.
We investigate numerically the effect of long-range interaction on the transverse localization of light. To this end, nonlinear zigzag optical waveguide lattices are applied, which allows precise tuning of the second-order coupling. We find that localization is hindered by coupling between next-nearest lattice sites. Additionally, (focusing) nonlinearity facilitates localization with increasing disorder, as long as the nonlinearity is sufficiently weak. However, for strong nonlinearities, increasing disorder results in weaker localization. The threshold nonlinearity, above which this anomalous result is observed grows with increasing second-order coupling.
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