Discrete Talbot Effect Research Articles

Discrete Talbot effect in modulated lattices with PT symmetric perturbations

We demonstrate both theoretically and numerically that the periodic self-imaging phenomenon of light patterns with certain input periods can be effectively realized in a three-layered optical lattice with parity–time symmetric modulations, which can introduce a modulation phase to the lattice structure. By varying the ratio of coupling coefficients, the Talbot distance can be engineered, which can be further tuned by adjusting the modulation phase. The Talbot effect occurs only if the modulation phase belongs to a specific set: {±π/3,±π/2,±2π/3,±π}.

Discrete Talbot effect in reciprocal and nonreciprocal dimer lattices

We investigate the Talbot self-imaging in one-dimensional discrete dimer lattices, where the source of non-Hermiticity derives not from gain and loss but from anisotropic couplings. The conditions that guarantee the existence of the Talbot effect in discrete dimer lattices are defined. It is shown that the Talbot self-imaging effect is possible in both reciprocal (Hermitian) and nonreciprocal (non-Hermitian) dimer lattices when the period of the input pattern is chosen as a finite set of periodicities ( N = 1 , 2, 3, 4 for reciprocal lattice and N = 1 , 2 for nonreciprocal lattice). Unlike the Talbot effect in reciprocal lattices, where the self-imaging with conserved total energy of the central part of the model occurs during propagation, here the total energy of the field exhibits oscillatory behavior in the Talbot process for nonreciprocal dimer lattices. The Talbot distance can be controlled by adjusting the lattice coupling and anisotropic coupling coefficients. Our results can be extended to other photonic superlattices with an arbitrary number of sites in each unit cell.

Controllable discrete Talbot self-imaging effect in Hermitian and non-Hermitian Floquet superlattices.

We investigate the discrete Talbot self-imaging effect in Floquet superlattices based on a mesh of directional couplers with periodically varying separation between waveguides, both theoretically and numerically. The modulated discreteness of the lattices sets strong constraints to ensure the Talbot effect generation. We show that discrete Talbot effect occurs only if the incident periods are N = 1, 2, and 4 in dispersive regimes of the Hermitian superlattices. In both dynamic localized and rectification regimes, self-imaging effect can occur for arbitrary input period N. For the rectification case, Talbot distance equals the input period. In the regime of dynamical localization, the Talbot distance remains unchanged irrespective of the pattern period. For non-Hermitian Floquet superlattices, due to the non-zero imaginary part of quasi-energy spectrum arising at the center of the Brillouin zone, where the mode degeneracy occurs, Talbot revival is not preserved when the input period is an even number, and exists only as N = 1 in the dispersive regime. The theoretical calculations and numerical simulations verify each other completely.

Frequency diffraction management through arbitrary engineering of photonic band structures

It is of fundamental interest to control light diffraction in discrete optical systems. However, photon hopping in discrete systems is dominated by the nearest-neighbor coupling, limiting the realization of nonlocal diffraction phenomena. Here, we generalize the discrete diffraction from spatial to the frequency domain using optical phase modulators. By inducing long-rang couplings in the frequency lattice through periodic modulation signals, we find the lattice band structure can be artificially engineered, giving rise to the realization of arbitrary frequency diffraction. Particularly, we create linear, bilinear and semicircular band structures using sawtooth, triangular and semicircular modulation waveforms and realize the directional, bidirectional, omnidirectional frequency diffraction as well as the spectral "superlens". We also revisit frequency discrete Talbot effect and generalize the allowed incident period to arbitrary integers through band structure engineering. Moreover, as the frequency transition also carries a wave vector mismatch, an effective electric field will emerge, through which we can realize frequency Bloch oscillations that manifest the effects of arbitrary spectral routing and self-imaging. The study paves a promising way towards versatile spectrum management for both optical communications and signal processing.

Spectral photonic lattices with complex long-range coupling

We suggest and experimentally realize a spectral photonic lattice - a signal can hop between discrete frequency channels, driven by nonlinear interaction with stronger pump lasers. By controlling the complex envelope and frequency separations of multiple pumps, it is possible to introduce non- local hopping and to break time-reversal symmetry, which opens up new possibilities for photonic quantum simulation. As two examples, we observe a spectral quantum walk and demonstrate the discrete Talbot effect in the spectral domain, where we find novel instances containing asymmetry and periodicities not possible in spatial lattices.

Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays

We theoretically predict and numerically simulate the discrete plasmonic Talbot effect in dielectric graphene plasmonic waveguide (DGPW) arrays at THz wavelengths. The super-modes in DGPW arrays are analyzed by using super-mode theory and the field intensity distributions in the designed DGPW arrays are explained by the superposition of different super-modes and simulated by using commercial software (COMSOL) based on finite element method (FEM). The discrete plasmonic Talbot effect is realized by superposition of different super-modes. The Talbot distance can be actively tuned by varying the Fermi energy of graphene and it decreases monotonically with increasing Fermi energy. In addition, it is found that the Talbot distance increases with the period of the DGPW arrays. Simulation results show a good agreement with the theoretical analysis.

Discrete Talbot effect in two-dimensional waveguide arrays.

We theoretically study discrete Talbot self-imaging in hexagonal, square, and irregular two-dimensional waveguide arrays. Different from its counterpart in a continuous system, the periods of the input fields must belong to {1, 2, 3, 4, 6} for Talbot self-imaging. Also, the combinations of the input periods cannot be 3 & 4, or 4 & 6 along two different directions, which distinguishes itself from the one-dimensional discrete Talbot effect.

Discrete plasmonic Talbot effect in subwavelength metal waveguide arrays

Discrete plasmonic Talbot effect in the subwavelength metal waveguide arrays (SMWAS) is theoretically analyzed and numerically simulated. Based on the finite-difference time-domain technique, we discuss the influence of the structural parameters on the Talbot distance. By carefully choosing the geometry parameters, the Talbot distance decreases to about one third of the incident wavelength. The numerical simulation results agree with the theory of the discrete Talbot effect in the SMWAS.

Tunable discrete Talbot effect in inhomogeneous photonic lattices

We discuss the discrete Talbot effect in one- and two-dimensional waveguide lattices under the influence of an external potential. It is shown that the field recovery can be precisely tuned by changing the gradient of the potential. In a two-dimensional configuration, the diagonal coupling does not affect the period of recovery.