One-dimensional Photonic Lattices Research Articles

A photonic thermalization gap in disordered lattices

A theoretical study looks at the interplay between disorder and chiral symmetry in the photon statistics in a one-dimensional photonic lattice, predicting that for increased disorder coherent light becomes thermal. The formation of gaps—forbidden ranges in the values of a physical parameter—is common to a variety of physical systems: from energy bandgaps of electrons in periodic lattices1 and their analogues in photonic2, phononic3 and plasmonic4 systems to pseudo-energy gaps in aperiodic quasicrystals5. Here, we predict a thermalization gap for light propagating in finite disordered structures characterized by disorder-immune chiral symmetry6—the appearance of the eigenvalues and eigenvectors in skew-symmetric pairs. In these systems, the span of sub-thermal photon statistics is inaccessible to input coherent light, which—once the steady state is reached—always emerges with super-thermal statistics no matter how small the disorder level. We formulate an independent constraint of the input field for the chiral symmetry to be activated and the gap to be observed. This unique feature enables a new form of photon-statistics interferometry: the deterministic tuning of photon statistics via controlled excitation symmetry breaking realized by sculpting the amplitude or phase of the input coherent field.

Light propagation inside ‘cavity’ formed between nonlinear defect and interface of two dissimilar one-dimensional linear photonic lattices

Light propagation through composite photonic lattice containing a cavity bounded by the interface between two structurally different linear lattices and on-site nonlinear defect in one of them is investigated numerically. We find conditions under which dynamically stable bounded cavity modes can exist. We observe various cavity localized modes such as: single-hump, multi-hump, and moving breathing modes. Light propagation obstructions are phenomenologically related to the Fano resonances. Presented numerical findings may lead to interesting applications, such as blocking, filtering, and transporting of light beams through the optical medium.

Defect states and exceptional point splitting in the band gaps of one-dimensional parity-time lattices.

We investigated defect states in band gaps of one-dimensional photonic lattices with delicate modulations of gain and loss that respect parity-time-symmetry (PT-symmetry), viz. n(z) = n*(-z). For the sake of generality, we employ not only periodic structures but also quasiperiodic structures, e.g. Fibonacci sequences, to construct aperiodic PT lattices. Differed from lossless systems for which the defect state is related to only one exceptional point (EP) of the S-matrix, we observed the splitting of one EP into a pair after the introduction of judiciously designed gain and loss in those PT systems, where the defect state enters a non-threshold broken symmetry phase bounded by the EP pair. Some interesting properties associated with defect states and EP splitting are demonstrated, such as enhanced spectral localization, double optical phase abrupt change, and wavelength sensitive reversion of unidirectional transparency.

Defect induced wave-packet dynamics in linear one-dimensional photonic lattices

We study numerically light beam propagation across uniform, linear, one-dimensional photonic lattice possessing one nonlinear defect. Depending on the strength of nonlinear defect, input beam position and phase shift, different dynamical regimes have been identified. We distinguish input parameters set for which a regime of light propagation blockade by the nonlinear defect appears. Obtained results may be useful for all-optical control of transmission of waves in interferometry.

Discrete Diffraction of Light in 1D Photonic Lattice Induced in Lithium Niobate by Means of the Pyroelectric Effect

The channel optical waveguides and one-dimensional photonic lattices have been formed in a bulk of lithium niobate sample due to the pyroelectric effect contribution. The storage time of pyroelectrically induced waveguide channels has been estimated and nonlinear regime of discrete diffraction of light within the one of photonic lattices has been demonstrated.

Tunable subwavelength photonic lattices and solitons in periodically patterned graphene monolayer.

We study linear and nonlinear mode properties in a periodically patterned graphene sheet. We demonstrate that a subwavelength one-dimensional photonic lattice can be defined across the graphene monolayer, with its modulation depth and correspondingly the associated photonic band structures being controlled rapidly, by an external gate voltage. We find the existences of graphene lattice solitons at the deep-subwavelength scales in both dimensions, thanks to the combination of graphene intrinsic self-focusing nonlinearity and the graphene plasmonic confinement effects.

Manipulation of light beam propagation in one-dimensional photonic lattices with linear refractive index profile

We use Bloch oscillations to demonstrate potential light beam propagation control in photonic lattices with linear refractive index change in transverse direction. It is qualitatively investigated how composite photonic lattice systems with varied values of refractive index gradient and nonlinearity strength along the propagation direction can be used to perform different functions, such as beam splitting and switching, in future components of all-optical networks. Additionally, we demonstrate the robustness of Bloch oscillations to nonlinearity and disorder in the proposed setup.

Propagation of light in photonic lattices with saturable nonlinearity comprising a defect

Linear and nonlinear effects accompanying the propagation of visible laser light through geometrically different one-dimensional photonic lattices made of material with a saturable nonlinearity are investigated, both theoretically and experimentally. Existence, stability and dynamics of various types of nonlinear localized modes (solitons) found to occur in lattices with a defect are explored. Additionally, the phenomenon of spontaneous symmetry breaking of a certain type of solitons is observed in symmetric lattices comprising a defect.

Propagation of nonclassical states of light through one-dimensional photonic lattices

We study the propagation of non-classical light through arrays of coupled linear photonic waveguides and introduce some sets of refractive indices and coupling parameters that provide a closed form propagator in terms of orthogonal polynomials. We present propagation examples of non-classical states of light: single photon, coherent state, path-entangled state and two-mode squeezed vacuum impinging into two-waveguide couplers and a photonic lattice producing coherent transport.

Observation of accelerating Wannier–Stark beams in optically induced photonic lattices

We generate optical beams analogous to the Wannier-Stark states in semiconductor superlattices and observe that the two main lobes of the WS beams self-bend (accelerate) along two opposite trajectories in a uniform one-dimensional photonic lattice. Such self-accelerating features exist only in the presence of the lattice and are not observed in a homogenous medium. Under the action of nonlinearity, however, the beam structure and acceleration cannot be preserved. Our experimental observations are in qualitative agreement with theoretical predictions.

Control of light propagation in one-dimensional quasi-periodic nonlinear photonic lattices

We investigate light localization in quasi-periodic nonlinear photonic lattices (PLs) composed of two periodic component lattices of equal lattice potential strength and incommensurate spatial periods. By including the system parameters from the experimentally realizable setup, we confirm that the light localization is a threshold determined phenomenon in a limit of negligible nonlinearity. In addition, we show that self-trapping can affect the localized light in the established setup only in the presence of strong nonlinearity. Guided by these findings we consider the possibility of governing light propagation by proposing a composite lattice system comprising alternating quasi-periodic parts with different potential depths and nonlinearity strengths.

Beam control in tri-core photonic lattices

We report on theoretical investigations of beam control in one-dimensional tri-core photonic lattices (PLs). Linear splitting is illustrated in tri-core PLs; the effect of defect strength on the splitting is discussed in depth for single-wavelength light. We reveal that splitting disappears when the defect strength trends to zero, while reoccurring under nonlinearity. Multi-color splitting and active control are also proposed in such photonic structures.

Anomalous refraction in disordered one-dimensional photonic lattices

We study the light refraction behavior at the entrance surface of the width-disordered one-dimensional waveguide array. As compared to the case in a uniform periodic waveguide array, anomalous refraction behavior is observed for the eigenmodes in the first band of the disordered waveguide array. The transverse propagation velocities of the eigenmodes in the first band are dramatically suppressed and the light is tightly confined around and propagates along the initially exciting waveguides. This may provide an effective method for beam coupling and collimation in the disordered photonic lattices.

Dynamics of dark solitons localized at structural defect in one-dimensional photonic lattices with defocusing saturable nonlinearity

We investigated the influence of the structural defect placed inside uniform photonic lattice on existence and dynamics of dark spatially localized defect modes. Depending on the strength of the defect and considering the lattice with defocusing saturable nonlinearity, we found two different types of dark solutions to exist. Their stability and dynamical properties are shown to be affected by the defect as well.

Spontaneous symmetry breaking of gap solitons in defect-loaded uniform one-dimensional photonic lattices

We observe theoretically and experimentally the phenomenon of spontaneous symmetry breaking of strongly localized nonlinear optical modes at the microwatt level in a one-dimensional photonic lattice with a single coupling defect.

Light propagation management by disorder and nonlinearity in one-dimensional photonic lattices

We study managing of light beam propagation by competing disorder and nonlinearity in one-dimensional disordered, nonlinear photonic lattices (PLs). The system is modeled by a paraxial time-independent Helmholtz equation, which includes the nonlinear saturable self-interacting term and the quenched or nonquenched disordered PL potential. Diverse PL structures with alternating length of the regular and disordered parts are investigated showing the possibility to change the light propagation from ballistic to the propagation of the transversely localized structures originating from the Anderson-like localization or self-trapping mechanism. Dynamical calculations indicate the possibility of guiding light through the lattice by proper lattice management.

Dynamics of gap solitons in one-dimensional binary lattices with saturable self-defocusing nonlinearity and alternating spacing

The existence and stability of spatial solitons in one-dimensional binary photonic lattices with alternating spacing and a saturable defocusing type of nonlinearity are investigated. Five types of nonlinear localized structures are found to exist: two in the mini-gap in the energy spectrum and others in the regular gap. It is proved that some of them are stable in certain ranges of the system parameters. Interactions between two identical localized structures propagating parallel to each other are investigated, too. It is shown that this interaction leads to formation of different localized patterns, such as solitons, breather-like modes, and breather complexes. The interaction output depends on the power and type of interacting identical solitons, the separation between them, the width of the mini-gap, and the phase relation between the tails of interacting solitons.

Elimination of transverse instability in stripe solitons by one-dimensional lattices

We demonstrate theoretically and experimentally that the transverse instability of coherent soliton stripes can be greatly suppressed or totally eliminated when the soliton stripes propagate in a one-dimensional photonic lattice under self-defocusing nonlinearity.

Disorder-induced localization of light in one- and two-dimensional photonic lattices

We study Anderson localization of light in one-dimensional (1D) and 2D photonic lattices. The influence of nonlinearity and disorder on Anderson localization in both systems is studied numerically. A sharp difference between localization in the linear and the nonlinear regimes is observed. Localization in the linear regime is more pronounced in the 2D lattice than in the 1D lattice. In the nonlinear regime, the coexistence of nonlinearity and disorder leads us to different conclusions. There are different nonlinear regimes in which 1D localization is more pronounced than 2D localization.

Mobility of high-power solitons in saturable nonlinear photonic lattices

We theoretically study the properties of one-dimensional nonlinear saturable photonic lattices exhibiting multiple mobility windows for stationary solutions. The effective energy barrier decreases to a minimum in those power regions where a new intermediate stationary solution appears. As an application, we investigate the dynamics of high-power Gaussian-like beams finding several regions where the light transport is enhanced.