One-dimensional Photonic Lattices Research Articles

Two-color solitons in chirped photonic lattices

We address the properties of two-color localized nonlinear modes supported by one-dimensional chirped photonic lattices imprinted in quadratic media. The impacts of chirp rate and phase mismatch on the two-color solitons are investigated. Various families of two-color soliton solutions are found. In contrast to the unchirped lattices, chirped lattices can enhance the stability of two-color solitons. Odd solitons can be completely stable provided that the chirp rate exceeds a critical value, even for varying phase mismatches. We also study the excitation, unpacking, and oscillation of two-color solitons in chirped lattices. Our results may enrich the potential applications of two-color solitons in all-optical communications.

Observation of linear and nonlinear strongly localized modes at phase-slip defects in one-dimensional photonic lattices

We investigate light localization at a single phase-slip defect in one-dimensional photonic lattices, both numerically and experimentally. We demonstrate the existence of various robust linear and nonlinear localized modes in lithium niobate waveguide arrays exhibiting saturable defocusing nonlinearity.

Counterpropagating solitons at boundary of photonic lattices

We study numerically the interaction of two counterpropagating (CP) optical beams near the boundary of a truncated one-dimensional photonic lattice. We demonstrate that the mutual coupling of beams suppresses the effective repulsion from the lattice edge, resulting in the formation of CP surface solitons. Such localized beams may propagate in the same, as well as in neighboring, waveguides. We also reveal that the lattice disorder reduces substantially the threshold power for the formation of CP surface states.

Glauber–Fock photonic lattices

We show that classical analogs to quantum coherent and displaced Fock states can emerge in one-dimensional semi-infinite photonic lattices having a square root law for the coupling coefficients. Beam dynamics in these fully integrable structures is described in closed form, irrespective of the site of excitation. The trajectories of these beams are closely examined, and pertinent examples are provided for their realization.

Waveguide arrays in selectively infiltrated photonic crystal fibres

The periodic array of air holes in the cladding of a photonic crystal fibre (PCF) provides a convenient scaffold for the introduction of an infiltrating liquid. In this paper we demonstrate a novel platform of one-dimensional tuneable nonlinear photonic lattices produced by selectively infiltrating a row of holes in a PCF. Such structures have been realised by blocking individual holes on one end of a PCF, leaving the desired infiltration pattern unblocked. Unblocked holes are then infiltrated by immersing the unblocked end of the fibre in a reservoir of the infiltrating liquid, allowing for the realisation of a wide variety of periodic structures. Such structures are studied for traditional linear and nonlinear effects in periodic systems.

Optically-induced defect states in photonic lattices: formation of defect channels, directional couplers, and disordered lattices leading to Anderson-like light localization

Formation of defect states by optical induction in one-dimensional photonic lattices fabricated in photorefractive lithium niobate is investigated experimentally. First, by using a moving narrow laser beam for defect recording, we investigate light propagation in samples containing single line defects and adjacent channel defects forming directional couplers. Then, these results are used to create lattices with randomly distributed defects, resembling a disordered optical potential. In such lattices, wave propagation is found to change from ballistic transport to transverse Anderson-like light localization as a function of induced disorder.

Spatial Frequency Combs and Supercontinuum Generation in One-Dimensional Photonic Lattices

We experimentally demonstrate the formation of spatial supercontinuum and of spatial frequency combs in nonlinear photonic lattices. This process results from multiple four-wave mixing initiated by launching two Floquet-Bloch modes into a one-dimensional lattice. The dynamics of the waves is sensitively dependent on the transverse momentum difference between the two initial modes: when this momentum difference is commensurable with the lattice momentum the waves evolve into a frequency comb, whereas when it is incommensurable the waves evolve into a supercontinuum of spatial frequencies.

Experimental control of pattern formation by photonic lattices

We study the control of modulational instability and pattern formation in a nonlinear dissipative feedback system with a periodic modulation of the material refractive index. We use a one-dimensional photonic lattice in a single-mirror feedback configuration and identify three mechanisms for pattern control: bandgap suppression of instability modes, periodicity induced pattern modes, and orientational pattern control.

Higher-band gap soliton formation in defocusing photonic lattices

We report on the experimental observation of higher-band gap solitons in a one-dimensional photonic lattice possessing a defocusing saturable nonlinearity. Pure Floquet-Bloch modes of the first three bands are excited using a prism-coupler setup, and spatial gap solitons of different width are formed, the latter property being related to the increasing anomalous diffraction in the three bands and the fixed value of the nonlinearity in our lithium niobate sample.

Surface defect linear modes in one-dimensional photonic lattices

We report on the existence of surface defect linear modes at an interface between the defect of one-dimensional photonic lattices and the uniform media. The interface defect can significantly affect the properties of linear modes. Such new type of modes exists in the first bandgap for positive defects; while they exist in the second bandgap for negative defects. Particularly, when a Gaussian beam, which is similar to the linear mode, is launched at the defect site, we find that the Gaussian beam can be strongly confined at defect site and robustness along longitudinal direction for a long distance. When launched at a small angle into the defect site, the Gaussian beam exhibits stable snake propagation.

Bloch dynamics of light waves in helical optical waveguide arrays

Propagation of light waves in one-dimensional and two-dimensional photonic lattices made of uniformly twisted (helical) arrays of evanescently coupled optical waveguides is theoretically investigated and shown to provide a classic wave optics analog of the quantum dynamics of a Bloch particle in an electromagnetic field. For a one-dimensional waveguide array, it is demonstrated that the behavior of discretized light in the array exactly mimics the wave packet dynamics of a quantum harmonic oscillator on a lattice, with the existence of quasiharmonic and quasi-Bloch oscillations. For a two-dimensional twisted waveguide array, it is shown that propagation of discretized light exactly mimics the quantum motion of an electron in a two-dimensional crystalline potential subjected to a uniform magnetic field, orthogonal to the crystal plane, combined with a repulsive harmonic electrostatic force.

Lattice-cavity solitons in a degenerate optical parametric oscillator

We predict the existence of lattice-cavity solitons for a quadratic nonlinear cavity, where the linear losses are compensated for by the optical pump at second harmonic (degenerate optical parametric oscillator), and which is endowed with a one-dimensional photonic lattice. In the limit of strong discreteness (weak coupling) this kind of soliton solution contains as the subclass the quadratic discrete cavity solitons. The nonlinear coupling between the Bloch waves of different photonics bands allows for the formation of a reach variety of localized solutions. In particular, different types of multiband lattice-cavity solitons can be identified. Most types of lattice-cavity solitons do not have counterparts, neither in conventional planar microresonators nor in genuine discrete systems as an array of weakly coupled cavities. We show that these solitons may destabilize as a consequence of the competition between Bloch waves of different photonic bands.

Saturable discrete vector solitons in one-dimensional photonic lattices

Localized vectorial modes, with equal frequencies and mutually orthogonal polarizations, are investigated both analytically and experimentally in a one-dimensional photonic lattice with saturable nonlinearity. It is shown that these modes may span over many lattice elements and that energy transfer among the two components is both phase and intensity dependent. The transverse electrically polarized mode exhibits a single-hump structure and spreads in cascades in saturation, while the transverse magnetically polarized mode exhibits splitting into a two-hump structure. Experimentally such discrete vector solitons are observed in lithium niobate lattices for both coherent and mutually incoherent excitations.

Light propagation in double-periodic nonlinear photonic lattices in lithium niobate

Single- and double-periodic one-dimensional photonic lattices are formed in lithium niobate using both titanium in-diffusion and holographic grating recording. We investigate linear band structures and diffraction properties of such superlattices and observe a decrease of discrete diffraction with increasing modulation depth of the second superimposed lattice. In weakly modulated superlattices with tailored diffraction properties, our results demonstrate the formation of discrete solitons having a propagation constant inside the extra mini-gap formed inside the Brillouin zone.

“Incoherent” generation of spatial gap solitons within one-dimensional photorefractive photonic lattices in lithium niobate

The effect of the formation of spatial gap solitons within one-dimensional optically induced photo-refractive photonic lattices in iron-doped lithium niobate is experimentally investigated. Mutually incoherent Bragg-matched beams with optical powers in the microwatt range from two different He-Ne lasers are used to generate immobile spatial gap solitons within the lattice with a spatial period of 15 μm.

Light induced angular steering via Floquet-Bloch band-tunnelling in one-dimensional liquid crystalline photonic lattices

AbstractWe investigate all-optical Zener tunnelling in electro-optically tunable arrays of identical channel waveguides in undoped nematic liquid crystals. By all-optically inducing a refractive acceleration, we demonstrate a novel technique for band-to-band tunnelling, as well as a novel approach to light controlled steering and readdressing.

Higher-band modulational instability in photonic lattices

Propagation of extended Floquet-Bloch modes in the first three bands of a one-dimensional photonic lattice possessing a self-defocusing saturable nonlinearity is studied experimentally and numerically on the example of waveguide arrays in lithium niobate. Discrete modulation instability is observed in all bands in the region of anomalous diffraction, whereas modes propagate stable in the normal diffraction regime.

Defect solitons in optically induced one-dimensional photonic lattices in LiNbO3:Fe crystal

We observe experimentally defect solitons with the odd and the even symmetry in one-dimensional optically induced nonlinear photonic lattices in self-defocusing LiNbO3:Fe crystal when a Gaussian probe beam is launched at normal incidence. We find that the odd symmetric defect soliton is stable while the even symmetric defect soliton is unstable.

Two-dimensional solitons in saturable media with a quasi-one-dimensional lattice potential

We study families of solitons in a two-dimensional model of the light transmission through a photorefractive medium equipped with a (quasi-)one-dimensional photonic lattice. The soliton families are bounded from below by finite minimum values of the peak and total power. Narrow solitons have a single maximum, while broader ones feature side lobes. Stability of the solitons is checked by direct simulations. The solitons can be set in motion across the lattice (actually, made tilted in the spatial domain), provided that the respective boost parameter does not exceed a critical value. Collisions between moving solitons are studied too. Collisions destroy the solitons, unless their velocities are sufficiently small. In the latter case, the colliding solitons merge into a single stable pulse.

Defect solitons in photonic lattices

Nonlinear defect modes (defect solitons) and their stability in one-dimensional photonic lattices with focusing saturable nonlinearity are investigated. It is shown that defect solitons bifurcate out from every infinitesimal linear defect mode. Low-power defect solitons are linearly stable in lower bandgaps but unstable in higher bandgaps. At higher powers, defect solitons become unstable in attractive defects, but can remain stable in repulsive defects. Furthermore, for high-power solitons in attractive defects, we found a type of Vakhitov-Kolokolov (VK) instability which is different from the usual VK instability based on the sign of the slope in the power curve. Lastly, we demonstrate that in each bandgap, in addition to defect solitons which bifurcate from linear defect modes, there is also an infinite family of other defect solitons which can be stable in certain parameter regimes.