Transverse Localization Of Light Research Articles

Transverse localization of light in laser written designed disorder

Transverse Anderson localization provides the lateral confinement of electromagnetic waves in disordered systems that are invariant along the propagation direction. Here, we demonstrate a disorder induced confinement in glass microstructures where disorder is fabricated ad hoc by the femtosecond direct laser writing technique. By employing a high numerical aperture objective, we are able to write parallel arrays of tiny tubes with a refractive index higher than the surrounding glass and to arrange them in a disordered fashion in the transversal plane. We demonstrate that these paraxial scatterers are supporting transverse localization and that the confinement strength depends on the disorder properties. The proposed approach, which relies on a user-controlled positioning of individual scatterers, allows us to finely tune the structural design, maximizing the transversal confinement.

Effect of loss on transverse localization of light in 1D optical waveguide array in the presence of Kerr-type nonlinearity

In this paper we have comprehensive study on the interplay among radiation loss, transverse disorder (diagonal and off-diagonal) and Kerr-type nonlinearity on the light propagation in 1D array of optical waveguides. Our numerical results demonstrate the presence of three distinguished regimes of transverse light expansion at different propagation distances. At short propagation distance, the Kerr-type nonlinearity are dominated and results in the transverse localization of light through the self-trapping mechanism. Radiation loss, causes the light escape from the injected guides, affect the light expansion in middle distance via broadening the light beam width. At longer distance the disorder terms led to the transverse localization of light, again. Also, we compared the propagation of light in edge and middle modes in the presence of the above effects. Our results show that the propagation distance of first localized regime for edge modes is larger than the middle modes since the edge modes can exchange energy with one of the left or right waveguides, while for middle modes there are two ways for energy exchange. Therefore the discrete diffraction can be diminished the nonlinear effects in middle modes faster than the edge modes.

Defect-controlled transverse localization of light in triangular optical lattices.

We present a detailed analysis of the transverse localization of light in a triangular optical lattice with a negative defect of different depths and positions. The analysis allows us to explore some essentials of the localization behavior. We characterize the localization strength by global propagation of the signal beam and its properties on the output plane. It is demonstrated that the enhancement of the localization is dependent on the defect depth. Additionally, the calculation of the ray trace of the signal beam shows that the position of the defect has a crucial influence on the localization.

Secure information transport by transverse localization of light.

A single-photon beating with itself can produce even the most elaborate optical fringe pattern. However, the large amount of information enclosed in such a pattern is typically inaccessible, since the complete distribution can be visualized only after many detections. In fact this limitation is only true for delocalized patterns. Here we demonstrate how reconfigurable localized optical patterns allow to encode up to 6 bits of information in disorder-induced high transmission channels, even using a small number of photon counts. We developed a quantum key distribution scheme for fiber communication in which high information capacity is achieved through position and momentum complementarity.

Transverse Localization of Light in 1D Self-Focusing Parity-Time-Symmetric Optical Lattices**Supported by the National Natural Science Foundation of China under Grant Nos 11104185, 11174084, 10934011 and 11504236, the National Basic Research Program of China under Grant No 2012CB921904, the Innovation Program of Shanghai Municipal Education Commission under Grant No 11YZ118, and the Natural Science Foundation of Shanghai under Grant No 14ZR1414300.

Transverse localization of light is investigated numerically in a self-focusing Kerr medium with a complex-valued optical lattice featuring parity-time symmetry. It is demonstrated that the light localization exists below the threshold of the spatial frequency of the lattices, and is further enhanced with the decrease of the spatial frequency. The influence of defects on the transverse localization is also discussed in detail. The results show that both positive and negative defects in such a medium would enhance the localization.

Defect-controlled Anderson localization of light in photonic lattices

The transverse localization of light in a disordered photonic lattice with a central defect is analyzed numerically. The effect of different input beam widths on various regimes of Anderson localization is investigated. The inclusion of a defect enhances the localization of both narrow and broad beams, as compared to the lattice with no defect. But, in the case of a broad beam a higher disorder level is needed to reach the same localization as for a narrow input beam. It is also investigated how the transverse localization of light in such geometries depends on both the strength of disorder and the strength of nonlinearity in the system. While in the linear regime the localization is most pronounced in the lattice with the defect, in the nonlinear regime this is not the case.

Effect of long-range correlated disorder on the transverse localization of light in 1D array of optical waveguides

In this paper, the effects of the long-range correlated diagonal disordered optical waveguide arrays in the presence and absence of the positive Kerr nonlinearity are analyzed numerically. The calculated inverse localization length shows that the long-range correlation in a disordered system causes a decrease in the transverse localization in linear optical waveguide arrays. In the presence of positive Kerr nonlinearity, the inverse localization length is increased by increasing the nonlinear parameters in long-range correlated disordered systems in comparison with the uniform distribution disordered systems. This means that the long range correlation causes an enhancement of transverse localization in nonlinear waveguides in contrast with linear waveguide arrays. The calculated participation ratio and effective beamwidth confirm these results for linear and nonlinear systems.

Interface localization of light in disordered photonic lattices

The Anderson localization of light at the interface separating square and hexagonal photonic lattices is demonstrated numerically. The influence of varying lattice intensities and disorder level on the transverse localization of light is discussed. Both suppression and enhancement of light localization in the presence of the interface, depending on the difference in the lattice intensity in both regions, and the position of the excited lattice site are demonstrated. Such localization is compared to the cases with no interfaces. Also, it is analysed how the presence of a phase-slip defect modifies the phenomenon of Anderson localization of light at the interface.

Transverse localization in nonlinear photonic lattices with second-order coupling

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.

Effect of Kerr nonlinearity on the transverse localization of light in 1D array of optical waveguides with off-diagonal disorder

In this paper a simulation of the transverse localization of light in 1D array of optical waveguides in the presence of off-diagonal disorder is presented. Effects of self-focusing and self-defocusing Kerr nonlinearity on the transverse localization of surface and bulk modes of the disordered waveguides array are taken into consideration. The simulation shows that in the off-diagonal disordered array at low nonlinear parameters, the transverse localization of light becomes more than that of the corresponding diagonal disordered array. However by increasing the nonlinear parameters the diagonal disordered array is localized more than the associated off-diagonal disordered array for both surface and bulk modes. It is also found that the surface modes become more localized than the bulk modes by increasing the nonlinear parameter. The calculated effective beam width versus propagation distance for off-diagonal disordered arrays confirms these results.

Anderson localization of light in PT-symmetric optical lattices

Anderson localization (AL) of light is investigated numerically in a disordered parity-time (PT)-symmetric potential, in the form of an optical lattice. The lattice is recorded in a nonlinear medium with Kerr nonlinearity. We demonstrate enhancement of light localization in a PT-symmetric lattice, as compared to the localization in the corresponding real lattice. The effect of strength of the gain-loss component in the PT lattice on various regimes of AL is also discussed. It is found that the localization exists and is further enhanced above the threshold strength of the imaginary part of the potential. The influence of nonlinearity and disorder level on the transverse localization of light in such a complex-valued potential is addressed.

Transverse localization of light and its dependence on the phase front curvature of the input beam in a disordered optical waveguide lattice

We investigate the influence of the phase front curvature of an input light beam on the transverse localization of light, choosing an evanescently coupled disordered one-dimensional semi-infinite waveguide lattice as an example. Our numerical study reveals that a finite phase front curvature of the input beam does indeed play an important role and it could degrade the quality of light localization in a disordered dielectric structure. More specifically, a faster transition from the ballistic mode of beam propagation due to diffraction to a characteristic localized state is observed in the case of a continuous wave (CW) beam whose phase front is plane, as compared to one having a curved phase front.

Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice

In a numerical study, we observe Anderson localization of surface modes at the interface between a linear and a nonlinear dielectric medium, containing an optically induced disordered photonic lattice. We discover the threshold for the existence of such localized modes. The influence of Kerr nonlinearity and disorder levels on the transverse localization of light at such an interface is discussed. We demonstrate the suppression of localization for lower disorder levels, as compared to both completely linear and completely nonlinear medium. We also reveal Anderson localization at the linear-nonlinear interface in the presence of a phase-slip defect, and demonstrate the suppression of localization in that case as well.

Role of optical nonlinearity on transverse localization of light in a disordered one-dimensional optical waveguide lattice

We report a detailed numerical investigation on transverse localization of light in a 1D disordered lattice consisting of a large array of coupled waveguides in the presence of nonlinearity in the medium. Our study reveals that the presence of a focusing type of nonlinearity favors faster localization of light while a defocusing type of nonlinearity degrades the quality of localization. It is shown that presence of either of these could over-shadow localization of light unless the strength of disorder is sufficiently strong. Influence of the input beam width on propagation of light in such a disordered nonlinear medium has also been discussed. The present study should be useful in potential applications, in which one could exploit dominance of focusing nonlinearity on transverse localization of light in a disordered medium.

Transverse localization of light in nonlinear photonic lattices with dimensionality crossover

In a numerical study, we demonstrate the dimensionality crossover in Anderson localization of light. We consider crossover from the two-dimensional (2D) to the one-dimensional (1D) lattice, optically induced in both linear and nonlinear dielectric media. The joint influence of nonlinearity and disorder on Anderson localization in such systems is discussed in some detail. We find that, in the linear regime, the localization is more pronounced in two dimensions than in one dimension. We also find that the localization in the intermediate cases of crossover is less pronounced than in both the pure 1D and 2D cases in the linear regime, whereas in the nonlinear regime this depends on the strength of the nonlinearity. There exist strongly nonlinear regimes in which 1D localization is more pronounced than the 2D localization, opposite to the case of the linear regime. We find that the dimensionality crossover is characterized by two different localization lengths, whose behavior is different along different transverse directions.

Localization of light in evanescently coupled disordered waveguide lattices: Dependence on the input beam profile

We investigate how the transverse localization of light in evanescently coupled, disordered, lossless waveguide lattices depends on the shape and size of an input beam. Our detailed numerical study not only reveals waveguide-like propagation of the localized state inside such a disordered discrete medium but also shows that a specific localized state is independent of the spatial profile of the input beam. Dependence of the localized state on input beam parameters and lattice parameters is also reported. Our results should be of interest for engineering light propagation with discrete diffractive optics in practical optical geometries (e.g., microstructured arrays of optical waveguides, fiber arrays, etc.) and for realizing waveguide-like (without any diffractive spread) propagation even in the presence of structural disorders and refractive index perturbations.

Transport and Anderson localization in disordered two-dimensional photonic lattices

One of the most interesting phenomena in solid-state physics is Anderson localization, which predicts that an electron may become immobile when placed in a disordered lattice. The origin of localization is interference between multiple scatterings of the electron by random defects in the potential, altering the eigenmodes from being extended (Bloch waves) to exponentially localized. As a result, the material is transformed from a conductor to an insulator. Anderson's work dates back to 1958, yet strong localization has never been observed in atomic crystals, because localization occurs only if the potential (the periodic lattice and the fluctuations superimposed on it) is time-independent. However, in atomic crystals important deviations from the Anderson model always occur, because of thermally excited phonons and electron-electron interactions. Realizing that Anderson localization is a wave phenomenon relying on interference, these concepts were extended to optics. Indeed, both weak and strong localization effects were experimentally demonstrated, traditionally by studying the transmission properties of randomly distributed optical scatterers (typically suspensions or powders of dielectric materials). However, in these studies the potential was fully random, rather than being 'frozen' fluctuations on a periodic potential, as the Anderson model assumes. Here we report the experimental observation of Anderson localization in a perturbed periodic potential: the transverse localization of light caused by random fluctuations on a two-dimensional photonic lattice. We demonstrate how ballistic transport becomes diffusive in the presence of disorder, and that crossover to Anderson localization occurs at a higher level of disorder. Finally, we study how nonlinearities affect Anderson localization. As Anderson localization is a universal phenomenon, the ideas presented here could also be implemented in other systems (for example, matter waves), thereby making it feasible to explore experimentally long-sought fundamental concepts, and bringing up a variety of intriguing questions related to the interplay between disorder and nonlinearity.

Spatial optical simultons in nonlinearly coupled planar waveguides.

With second-harmonic generation in surface and buried planar waveguides achieved by direct and reverse proton exchange in lithium niobate, we demonstrate a novel kind of quadratic spatial simulton: The transverse-electric fundamental input and the transverse-magnetic second-harmonic waves nonlinearly couple two superimposed planar waveguides, permitting transverse localization of light at room temperature and at excitations as low as 340 nJ in 20-ps pulses.

Weak transverse localization of light scattered incoherently from a one-dimensional random metal surface

We consider the incoherent scattering of light from a one-dimensional, random, metal surface when the plane of incidence is parallel to the generators of the surface and perpendicular to the mean surface. The incoherent component of the scattered light is then confined to a conical region whose axis of rotation is the intersection of the plane of incidence with the mean surface. Scattering anomalies associated with weak localization are observed in both copolarized and cross-polarized scattering. Results are presented for the scattering of visible light from both silver and gold surfaces.