Transverse Localization Research Articles

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.

Producing acoustic frozen waves: simulated experiments

In this paper, we show how appropriate superpositions of Bessel beams can be successfully used to obtain arbitrary longitudinal intensity patterns of nondiffracting ultrasonic wave fields with very high transverse localization. More precisely, the method here described allows generation of longitudinal acoustic pressure fields whose longitudinal intensity patterns can assume, in principle, any desired shape within a freely chosen interval 0 ≤ z ≤ L of the propagation axis, and that can be endowed in particular with a static envelope (within which only the carrier wave propagates). Indeed, it is here demonstrated by computer evaluations that these very special beams of nonattenuated ultrasonic field can be generated in water-like media by means of annular transducers. Such fields at rest have been called by us acoustic frozen waves (FWs). The paper presents various cases of FWs in water, and investigates their aperture characteristics, such as minimum required size and ring dimensioning, as well as the influence they have on the proper generation of the desired FW patterns. The FWs are particular localized solutions to the wave equation that can be used in many applications, such as new kinds of devices, e.g., acoustic tweezers or scalpels, and especially in various ultrasound medical apparatus.

Nematicons and Their Electro-Optic Control: Light Localization and Signal Readdressing via Reorientation in Liquid Crystals

Liquid crystals in the nematic phase exhibit substantial reorientation when the molecules are driven by electric fields of any frequencies. Exploiting such a response at optical frequencies, self-focusing supports transverse localization of light and the propagation of self-confined beams and waveguides, namely “nematicons”. Nematicons can guide other light signals and interact with inhomogeneities and other beams. Moreover, they can be effectively deviated by using the electro-optic response of the medium, leading to several strategies for voltage-controlled reconfiguration of light-induced guided-wave circuits and signal readdressing. Hereby, we outline the main features of nematicons and review the outstanding progress achieved in the last twelve years on beam self-trapping and electro-optic readdressing.

Transverse localization in disordered lattices containing left-handed metamaterials

A numerical study is reported of the propagation of an initially localized wave in a one-dimensional disordered lattice composed of left-handed metamaterials. We first consider the structure made of right-handed and left-handed materials arranged periodically. By allowing disorder in the refractive index of the right-handed materials, the injected wave becomes localized as propagating through the disordered lattice. Then, we consider another photonic lattice comprising only left-handed metamaterials. It is found that the inclusion of disorder in the negative refractive index of the constituents of the system leads to transverse Anderson localization. We also investigate the dispersion effect of metamaterials on the localization behavior. It is demonstrated that inclusion of a dispersive metamaterial in the disordered photonic lattices causes the quality of transverse localization to enhance with increasing wavelength.

Transverse localization of sound

Transverse localization of sound

Optical waveguide arrays: quantum effects and PT symmetry breaking

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 ($\mathcal{PT}$) 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 $\mathcal{PT}$-symmetric Hamiltonians and the transition from a purely real energy spectrum to a spectrum with complex conjugate eigenvalues that occurs in them.

Fabrication and characterization of disordered polymer optical fibers for transverse Anderson localization of light.

We develop and characterize a disordered polymer optical fiber that uses transverse Anderson localization as a novel waveguiding mechanism. The developed polymer optical fiber is composed of 80,000 strands of poly (methyl methacrylate) (PMMA) and polystyrene (PS) that are randomly mixed and drawn into a square cross section optical fiber with a side width of 250 μm. Initially, each strand is 200 μm in diameter and 8-inches long. During the mixing process of the original fiber strands, the fibers cross over each other; however, a large draw ratio guarantees that the refractive index profile is invariant along the length of the fiber for several tens of centimeters. The large refractive index difference of 0.1 between the disordered sites results in a small localized beam radius that is comparable to the beam radius of conventional optical fibers. The input light is launched from a standard single mode optical fiber using the butt-coupling method and the near-field output beam from the disordered fiber is imaged using a 40X objective and a CCD camera. The output beam diameter agrees well with the expected results from the numerical simulations. The disordered optical fiber presented in this work is the first device-level implementation of 2D Anderson localization, and can potentially be used for image transport and short-haul optical communication systems.

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

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.

Anderson localization of light in the presence of weak longitudinal modulation of the refractive index in 1D disordered waveguide lattices

We report an enhancement of the effect of transverse localization of light (TL) in the presence of a weak longitudinal modulation of the refractive index in disordered waveguide lattices. In our chosen lattices, tunneling inhibition along the length favors diffraction-free propagation along with the simultaneous presence of transverse disorder. Our results will be useful for tuning the threshold value of disorder to achieve localized light.

Controlling the transverse localization of THz waves in an InSb based disordered waveguide array using temperature

We propose that the transverse localization in a semiconductor-based disordered waveguide array can be made controllable in the terahertz (THz) regime by changing the ambient temperature. The standard scalar Helmholtz equation is used to describe THz wave propagation through the waveguide array. It is assumed that the waveguides are fabricated from the indium-antimonide (InSb) semiconductor, while the spacing between them is a dielectric. Disorder is introduced in the system by the random refractive index of the spacing medium. Our results demonstrate that the transverse width of the output intensity increases when increasing the temperature. This effect is attributed to the temperature-dependent electric permittivity of the used semiconductor. Then, the waveguides are composed of a dielectric and the spacing between them is filled with the InSb semiconductor. For this case, to introduce disorder, we assumed that the refractive indices of the waveguides are randomized. It is found that the output intensity becomes more localized with increasing temperature. However, further increasing the temperature leads to the delocalization of output intensity. The effect of spacing between adjacent waveguides on the threshold degree of disorder has also been investigated.

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.

Modal perspective on the transverse Anderson localization of light in disordered optical lattices

We frame the transverse Anderson localization of light in a one-dimensional disordered optical lattice in the language of localized propagating eigenmodes. The modal analysis allows us to explore localization behavior of a disordered lattice independent of the properties of the external excitation. Various localization-related phenomena, such as the periodic revival of a propagating Anderson-localized beam are easily explained in modal language. We characterize the localization strength by the average width of the guided modes and carry out a detailed analysis of localization behavior as a function of the optical and geometrical parameters of the disordered lattice. We also show that in order to obtain a minimum average mode width, the average width of the individual random sites in the disordered lattice must be larger than the wavelength of the light by approximately a factor of two or more, and the optimum site width for the maximum localization depends on the design parameters of the disordered lattice.

Effective theory for the propagation of a wave packet in a disordered and nonlinear medium

The propagation of a wave packet in a nonlinear disordered medium exhibits interesting dynamics. Here, we present an analysis based on the nonlinear Schr\"odinger equation (Gross-Pitaevskii equation). This problem is directly connected to experiments on expanding Bose gases and to studies of transverse localization in nonlinear optical media. In a nonlinear medium, the energy of the wave packet is stored both in the kinetic and potential parts, and details of its propagation are to a large extent determined by the transfer from one form of energy to the other. A theory describing the evolution of the wave packet has been formulated [Schwiete and Finkel'stein, Phys. Rev. Lett. 104, 103904 (2010)] in terms of a nonlinear kinetic equation. In this paper, we present details of the derivation of the kinetic equation and of its analysis. As an important new ingredient, we study interparticle collisions induced by the nonlinearity and derive the corresponding collision integral. We restrict ourselves to the weakly nonlinear limit, for which disorder scattering is the dominant scattering mechanism. We find that in the special case of a white-noise impurity potential, the mean-squared radius in a two-dimensional system scales linearly with $t$. This result has previously been obtained in the collisionless limit, but it also holds in the presence of collisions. Finally, we indicate different mechanisms through which the nonlinearity may influence localization of the expanding wave packet.

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.

Defect-controlled transverse localization of light in disordered photonic lattices

We study numerically Anderson localization of light in a disordered photonic lattice containing vacancy defects of different length. The influence of Kerr nonlinearity and disorder level on the transverse localization of light in different triangular lattice geometries is discussed. We demonstrate both suppression and enhancement of light localization in the presence of defects of different size, depending on the disorder level and the strength of the nonlinearity. We find that, in the linear regime, localization is more pronounced in the lattice with the simplest defect type—the single vacancy. In a strongly focusing nonlinear regime, the presence of all defect kinds enhances localization, as compared to the case with no defects. In the defocusing nonlinear regime, a suppression of localization in the presence of all defect types is demonstrated, as compared to the localization in the lattice without defects. In the end, the effect of input beam width on various regimes of Anderson localization is discussed.

On Hokusai's Great wave off Kanagawa : localization, linearity and a rogue wave in sub-Antarctic waters

The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc. 63, 119–135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave. In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut.

Transverse localization of light in the disordered one-dimensional waveguide arrays in the linear and nonlinear regimes

Transverse Anderson localization of light in one-dimensional waveguide arrays with both width and position disorders of individual waveguide has been studied and characterized quantitatively in the viewpoint of transverse localization of eigen modes of the disordered arrays. With the increase in the disorder of the waveguide arrays, more and more eigen modes become localized near the band edges of the finite-sized waveguide arrays in the linear regime. Such a disorder-induced light localization is more effective in waveguide arrays with the width disorder than those with the position disorder. It is shown that, a self-focusing nonlinearity results in an increase of the inverse participation ratio of the nonlinear disordered modes originating from Anderson modes near the edge of the semi-infinite bandgap, therefore, tends to enhance the transverse localization of light. On the other hand, with the increase of the self-defocusing nonlinearity, the inverse participation ratio first increases to a maximum and then decreases for the nonlinear disordered modes originating from Anderson modes near the edge of the first bandgap. The delocalization effect in the self-defocusing case is mainly the result of the joint effects of the normal diffraction near the second band edge and the resonant interaction between the nonlinear disordered modes and the eigen modes in the second band of the waveguide array.

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.

Image transport quality can be improved in disordered waveguides

We show that the quality of image transport can be improved in disordered waveguides compared with periodic waveguides such as coherent fiber optic bundles that are commonly used for imaging applications. The improvement is due to the transverse Anderson localization phenomenon that creates localized transport channels with finite radii through the disordered imaging waveguide.