Optical Waveguide Arrays Research Articles

Self-trapping threshold in disordered nonlinear photonic lattices

We investigate numerically and experimentally the influence of coupling disorder on the self-trapping dynamics in nonlinear one-dimensional optical waveguide arrays. The existence of a lower and upper bound of the effective average propagation constant allows for a generalized definition of the threshold power for the onset of soliton localization. When compared to perfectly ordered systems, this threshold is found to decrease in the presence of coupling disorder.

Phase-dependent reversible nonreciprocity in complex metamolecules

Nonreciprocity of complex metamolecules based on the collapse of parity-time symmetry is investigated through an application to an optical waveguide array, demonstrating the strong dependency on the phase of eigenspectra. Contrary to the intuitive expectation, we reveal that more rapid and tunable nonreciprocal dynamics is achieved in the regime where the real and complex phases coexist and, furthermore, with the benefit of significantly reduced gain. It is shown that this paradoxical behavior originates from the effect of ``spatial trapping modes,'' which hinder the energy transfer within the metamolecule due to decreased effective coupling between waveguides. As an application, we demonstrate the novel phenomenon of ``reversible nonreciprocity,'' based on the manipulation of a single trapping mode.

Quantum simulation of the Riemann-Hurwitzζfunction

We propose a simple realization of a quantum simulator of the Riemann-Hurwitz (RH) $\ensuremath{\zeta}$ function based on a truncation of its Dirichlet representation. We synthesize a nearest-neighbor-interaction Hamiltonian, satisfying the property that the temporal evolution of the autocorrelation function of an initial bare state of the Hamiltonian reproduces the RH function along the line $\ensuremath{\sigma}+i\ensuremath{\omega}t$ of the complex plane, with $\ensuremath{\sigma}>1$. The tight-binding Hamiltonian with engineered hopping rates and site energies can be implemented in a variety of physical systems, including trapped-ion systems and optical waveguide arrays. The proposed method is scalable, which means that the simulation can be, in principle, arbitrarily accurate. Practical limitations of the suggested scheme, arising from a finite number of lattice sites $N$ and from decoherence, are briefly discussed.

Bandstructure measurement in nonlinear optical waveguide arrays

We demonstrate a technique for measuring the linear bandstructure of periodic systems with quadratic nonlinearity. The phase-matching constraints of parametric optical frequency mixing are employed to probe the longitudinal wavevectors of the eigenmodes. The method is verified experimentally by measuring the diffraction relation of eigenmodes in periodically poled titanium-indiffused lithium niobate waveguide arrays with second-harmonic generation.

Discrete breathers and negative-temperature states

We explore the statistical behaviour of the discrete nonlinear Schrödinger equation as a test bed for the observation of negative-temperature (i.e. above infinite temperature) states in Bose–Einstein condensates in optical lattices and arrays of optical waveguides. By monitoring the microcanonical temperature, we show that there exists a parameter region where the system evolves towards a state characterized by a finite density of discrete breathers and a negative temperature. Such a state persists over very long (astronomical) times since the convergence to equilibrium becomes increasingly slower as a consequence of a coarsening process. We also discuss two possible mechanisms for the generation of negative-temperature states in experimental setups, namely, the introduction of boundary dissipations and the free expansion of wavepackets initially in equilibrium at a positive temperature.

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.

Effects of initial states on continuous-time quantum walk in the optical waveguide array

Continuous-time quantum random walk is constructed when photons propagate passing the branches of the waveguide array. It is possible to make quantum simulator, based on the quantum walk in waveguides, on a commercial scale firstly, but there are still some problems such as input state, the structure and boundary of the waveguides that should be treated at present. A nearest-neighbor coupling model is used to deal with the question of coupled waveguides and an explicit analytical solution can be derived. Using the analytical solution, we analyze the effects of input state on particle number probability distribution function and the second-order coherence degree of the quantum walk process in periodic waveguides. The results show that the symmetry properties of the input state would influence the distribution of second-order coherence degree, but have little effect on the probability distribution function.

Integrated optical waveguide and photodetector arrays based on comb-like ZnO structures

On-chip integrations of photonic waveguides and high-performance electrically-driven devices, by combining different active or passive optical components, are imperative towards the advancement of nanophotonic circuitry systems. We experimentally demonstrate the collective optical functionalities of ZnO microstructures towards designing an integrated photonic system by combining the optical waveguiding and detection properties. Comb-like microstructures composed of periodic arrays of smooth, single-crystalline ZnO nanowires are synthesized for these purposes. We demonstrate that ZnO comb structures could be used as optical waveguides, which can manipulate the blue, green, and red laser beams to an interconnected waveguide array. These results are substantiated by extensive investigation of waveguiding properties of single, stacked or crossbar nanowires, and different branched microstructures. These waveguide arrays can be successfully coupled with another ZnO comb-based photodetector and the collective performances of the integrated optical micro-device units are investigated in detail. This study shows that ZnO comb-based optical waveguide arrays have the great potential to be used as a bottom-up strategy for the construction of various miniaturized photonic demultiplexer systems.

Scattering of the discrete solitons on the -symmetric defects

We study the propagation of linear waves and solitons in an array of optical waveguides with an embedded defect created by a pair of waveguides with gain and loss satisfying the so-called parity-time () symmetry condition. We demonstrate that in the case of small soliton amplitudes, the linear theory describes the scattering of solitons with a good accuracy. We find that the incident high-amplitude solitons can excite the mode localized at the -symmetric defect. We also show that by exciting the localized mode of a large amplitude, it is possible to perform phase-sensitive control of soliton scattering and amplification or damping of the localized mode.

Negative refraction and spatial echo in optical waveguide arrays

The special symmetry properties of the discrete nonlinear Schrödinger equation allow a complete revival of the initial wave function employed in the context of stationary propagation of light in a waveguide array. As an inverting system, we propose a short array of almost isolated waveguides, which cause a relative π phase shift in the neighboring waveguides. By means of numerical simulations of the model equations, we demonstrate what we believe is a novel mechanism for the negative refraction of spatial solitons.

Pinned modes in lossy lattices with local gain and nonlinearity

We introduce a discrete linear lossy system with an embedded "hot spot" (HS), i.e., a site carrying linear gain and complex cubic nonlinearity. The system can be used to model an array of optical or plasmonic waveguides, where selective excitation of particular cores is possible. Localized modes pinned to the HS are constructed in an implicit analytical form, and their stability is investigated numerically. Stability regions for the modes are obtained in the parameter space of the linear gain and cubic gain or loss. An essential result is that the interaction of the unsaturated cubic gain and self-defocusing nonlinearity can produce stable modes, although they may be destabilized by finite-amplitude perturbations. On the other hand, the interplay of the cubic loss and self-defocusing gives rise to a bistability.

Generalized Exact Dynamic Localization in Curved Coupled Optical Waveguide Arrays

We observed exact dynamic localization in its general case in strongly coupled curved waveguide arrays with periodic, nonsquare-wave curvatures. We achieved a six times change in the dynamic localization bandwidth by changing a design parameter in our deviated-square-wave curvature. By analyzing the relation between the bandwidth and curvature profile, we offer a general method to control the localization bandwidth.

Phase-Only Beam Optimization for GaAs Optical Waveguide Phase Array

Optical waveguide phased arrays have highlighted advantages than other electro-optical material optical arrays in scanning angle, response speed etc. For diffraction fields of uniform waveguide have strong side-lobes, which have influence on scanning performance of phased arrays. So side-lobes compression is one of the main issues for optical waveguide phased array device development. Based on photoelectric effect, the relations of voltage and phase are analysised. Phase-only array beam control using a Genetic Algorithm, an efficiency-optimized scheme, for uniform optical waveguide array with process errors is proposed. Phase distributions are arranged as randomly increasing distributions and random distributions. The results show phase-only optical waveguide arrays control, without the reconstruction of devices, has fine side-lobes compression effects with -9.89[dB] side-lobes intensity ratio. So the performance of scanning beams gets well improved.

Symmetric and asymmetric localized modes in linear lattices with an embedded pair ofχ(2)-nonlinear sites

We construct families of symmetric, antisymmetric, and asymmetric solitary modes in one-dimensional bichromatic lattices with the second-harmonic-generating ($\chi ^{(2)}$) nonlinearity concentrated at a pair of sites placed at distance $l$. The lattice can be built as an array of optical waveguides. Solutions are obtained in an implicit analytical form, which is made explicit in the case of adjacent nonlinear sites, $l=1$. The stability is analyzed through the computation of eigenvalues for small perturbations, and verified by direct simulations. In the cascading limit, which corresponds to large mismatch $q$, the system becomes tantamount to the recently studied single-component lattice with two embedded sites carrying the cubic nonlinearity. The modes undergo qualitative changes with the variation of $q$. In particular, at $l\geq 2$, the symmetry-breaking bifurcation (SBB), which creates asymmetric states from symmetric ones, is supercritical and subcritical for small and large values of $q$, respectively, while the bifurcation is always supercritical at $l=1$. In the experiment, the corresponding change of the phase transition between the second and first kinds may be implemented by varying the mismatch, via the wavelength of the input beam. The existence threshold (minimum total power) for the symmetric modes vanishes exactly at $q=0$, which suggests a possibility to create the solitary mode using low-power beams. The stability of solution families also changes with $q$.

Band-specific phase engineering for curving and focusing light in waveguide arrays

Band-specific design of curved light caustics and focusing in optical waveguide arrays is introduced. Going beyond the discrete, tight-binding model, which we examined recently, we show how the exact band structure and the associated diffraction relations of a periodic waveguide lattice can be exploited to phase-engineer caustics with predetermined convex trajectories or to achieve optimum aberration-free focal spots. We numerically demonstrate the formation of convex caustics involving the excitation of Floquet-Bloch modes within the first or the second band and even multiband caustics created by the simultaneous excitation of more than one band. Interference of caustics in abruptly autofocusing or collision scenarios are also examined. The experimental implementation of these ideas should be straightforward since the required input conditions involve phase-only modulation of otherwise simple optical wavefronts. By direct extension to more complex periodic lattices, possibilities open up for band-specific curving and focusing of light inside two-dimensional or even three-dimensional photonic crystals.

Anyons in one-dimensional lattices: a photonic realization

Anyons are nonlocal quasi-particles carrying fractional statistics that interpolate between bosons and fermions. Here we propose a photonic realization of anyons moving on a one-dimensional lattice, which is based on light transport in an engineered square array of optical waveguides with a helically bent axis. Our photonic simulator enables visualization of the nonlocal nature of anyons in Fock space and the persistence of correlated tunneling even in the absence of particle interaction.

Anderson cross-localization

We report Anderson localization in two-dimensional optical waveguide arrays with disorder in waveguide separation introduced along one axis of the array, in an uncorrelated fashion for each waveguide row. We show that the anisotropic nature of such disorder induces a strong localization along both array axes. The degree of localization in the cross-axis remains weaker than that in the direction in which disorder is introduced. This effect is illustrated both theoretically and experimentally.

Integration of Optical Waveguide Array and Multilayer Substrate Integrated Waveguide for Electrooptical Modulator

Integration of an optical waveguide array using four waveguides in a Mach-Zehnder (MZ) structure and a two-layer low-loss substrate integrated waveguide (SIW) structure is presented to propose a new class of electrooptical phase modulators. In the proposed SIW modulator, synthesized rectangular waveguide in planar form is used as “electrodes” to guide millimeter-wave signals instead of conventional coplanar waveguide (CPW) for an electrooptical modulator, thus providing low-loss non-TEM mode propagation. In this study, two layers of a lithium niobate (LiNbO3) substrate for creating a high field interaction between the millimeter-wave and optical signals are considered and studied. Fabrication of the proposed structure by titanium diffusion in an LiNbO3 substrate as the optical waveguides and laser micromachining of the SIW via-holes has been done. The validation of our simulated results is also performed by the measurement of CPW-to-SIW transitions in the LiNbO3 substrate. Optical loss of 0.8 dB/cm at the wavelength of 1550 nm is obtained for an MZ structure using an optical waveguide array consisting of four waveguiding channels. In addition, it is shown that 5-GHz bandwidth over a 60-GHz operating frequency range can easily be obtained for the proposed modulator.

Reduced loss and improved mode discrimination in resonant optical waveguide arrays

Coherent laser arrays designed using resonant optical waveguides (ROWs) have proven to offer one of the most promising methods of monolithic beam combining in diode lasers. However, the high lateral transmission that provides strong optical coupling also leads to increased loss – a detriment to laser efficiency and performance. Presented is a derivation of additional design rules to eliminate lateral radiation loss from ROW arrays while still maintaining all the strong coupling properties. Additionally, it is speculated that improved mode discrimination and enhanced field uniformity should result from the proposed design modifications.

Defect Analysis on Optical Waveguide Arrays by Synchrotron Radiation Microtomography

In recent years, great attention has been devoted to the study and realization of polymeric optical waveguides embedded in printed circuit boards due to the increasing need of transferring large amounts of data at high speed within computer and telecommunication devices. Nonuniform microstructural defects that can be induced during the manufacturing process can dramatically influence the waveguide performance. The synchrotron radiation computed microtomography technique was used to obtain 3-D microstructural information, specifically to observe small defects, such as porosities, in a nondestructive way. Porosity level and pore size range were evaluated.