Optical waveguide arrays: quantum effects and PT symmetry breaking

Abstract

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.

Wave transport and statistical properties of an open non-Hermitian quantum dot with parity-time symmetry

“…Here we may mention especially inelastic quantum scattering and transport by complex potentials V [20][21][22][23][24][25][26] and optical waveguides [27][28][29] that are all examples of applied NHQM. Eigenvalues of a non-Hermitian Hamiltonian are generally complex.…”

“…Examples of PT quantum mechanics are found in Refs. [27][28][29] for optical wires. It seems, however, that PT invariance has received less or no attention in conventional condensed matter physics and nanodevices as here.…”

PT-breaking threshold in spatially asymmetric Aubry-André and Harper models: Hidden symmetry and topological states

“…The emergence of complex-conjugate eigenvalues at the exceptional point γ = γ PT is called PT -symmetry breaking [26,27]. When γ > γ PT , the eigenfunctions with complex eigenvalues become increasingly asymmetrical [28].…”

“…These lattice models initially arose in the condensed-matter physics where the model parameters-the lattice constant, the on-site potential, the tunneling amplitudes, and the type and the strength of disorder-are primarily determined by Coulomb interaction and thus cannot be varied beyond a few percent. However, the lattice realizations in coupled waveguide arrays are far more protean [27], and thus, recent studies have focused on experimental realizations of AAH models in such settings.…”

Revisiting the Optical PT-Symmetric Dimer

“…The second one dealt with composite systems, where a mature mode coupling theory produced a theory of coupled optical P T -symmetric structures [9]. In the ten years following those first proposals for an optical realization of P T -symmetry, work has been reported on slab waveguides [10,11], Bragg scatterers [12][13][14][15][16][17], as well as linear [18][19][20][21][22][23][24][25][26] and nonlinear [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] coupled waveguides, to mention just a few. Research in this field is slowly getting to information technologies applications with recent proposals of all-optical P T -symmetric logic gates [46] and amplitude-to-phase converters [47].…”