Wave Tunneling and Hysteresis in Nonlinear Junctions

Abstract

We consider the nonlinear tunneling of a plane wave through a small barrier potential in a medium with self-defocusing, or repulsive, interactions. We show that nonlinearity can either suppress or enhance transmission rates, determined by whether the initial kinetic energy is above or below the barrier height. Associated with this threshold is the appearance of two distinct hysteresis loops, going clockwise or counterclockwise, respectively. Spatial dynamics upon reflection and transmission reveals the formation of dispersive shock waves (dark soliton trains) due to phase jumps at the interfaces and wave steepening during propagation. The results are demonstrated experimentally for optical wave tunneling through a refractive index defect but will hold for any Schrödinger system that contains a nonlinear junction.

Superfluid light in bulk nonlinear media

“…In experiments, a wide variety of δ (r ⊥ , z) profiles can be generated either in a static way by microstructuring the physical and chemical properties of the crystal or by dynamically inducing a refractive index modulation with a strong additional laser beam via the optical nonlinearity of the medium, e.g. the photo-refractive one [8]: the power and flexibility of femtosecond laser writing techniques to realize a rich variety of three-dimensional structures is reviewed in [14] and exemplified in [15]. Rich structures such as rotating waveguide arrays can also be generated taking advantage of the complex propagation dynamics of the strong additional laser driving the photo-refractive nonlinearity [16].…”

Observation of surface dispersive shock waves in a self-defocusing medium

“…In nonlinear optics, DSWs were initially studied in optical fibers in the temporal domain [13,14]. Recently, DSWs with a laser beam as an initial input have been the subject of intense study in many optical systems, including photorefractive media [15][16][17], thermal media [18][19][20][21][22][23][24], nematic liquid crystals [25], nonlinear arrays [26], quadratic media [27], disordered media [28], and nonlinear junctions [29]. Here, diffractions result in spatial dispersion that regularizes the shock front through the onset of fast oscillations in an expanding region after the wave-breaking points.…”

Propagation of a quantum fluid of light in a cavityless nonlinear optical medium: General theory and response to quantum quenches

“…This framework has been used in a number of theoretical works where laser-physics problems have been reformulated in the hydrodynamics language [16], including, e.g., the investigation of superfluid-like behaviors in the flow of a photon fluid [17][18][19][20][21], of nonlinear phenomena with light waves [22][23][24][25], and of the so-called acoustic Hawking radiation [26][27][28][29]. From the experimental point of view, numerous works have been devoted to the study of nonlinear features that may appear in these systems, with a special attention dedicated to their relation to hydrodynamics and superfluidity aspects [30][31][32][33][34][35][36]. A major first step in the very quantum direction of realizing a gas of strongly interacting photons in a propagating geometry has been recently reported using an optically dressed atom gas in the Rydberg-EIT regime as a bulk nonlinear medium: This has allowed for the experimental observation of strongly repulsing photons [37] and, soon after, of two-photon molecular bound states [38].…”