Discrete Optical Systems Research Articles

Investigating the effects of various input beam profiles on the propagations of light in two-dimensional interfaced binary

In this work, we numerically study how various input beam profiles influence the linear and nonlinear light propagation at the interface of two-dimensional (2D) binary waveguide arrays. It is revealed that, due to the presence of the central homogeneous interfaced waveguides, light beams are effectively steered into the preferred direction. Interestingly, the formation of discretely localized states in nonlinear modes can be intentionally utilized to optimize the stability and intensity of the signals at the central interfaced channels. This study thus opens alternative possibilities to achieve reliable distant beam propagation through discrete optical systems.

Modeling and Digital Correction of Optical Axis Pointing Error for Discrete Optical System

Modeling and Digital Correction of Optical Axis Pointing Error for Discrete Optical System

Thermal diffusion coupling mechanism and its application of discrete waveguide

For discrete optical systems integrated into optical fibers, the optical fields of the individual waveguides are coupled and correlated with each other. This paper studies how to adjust the refractive index of discrete waveguides by thermal diffusion, so as to enhance the coupling between discrete waveguides, and also constructs the discrete waveguide thermally diffused model and the thermally diffused coupling model of twin-core and three-core fibers. The multicore fiber is heated different times by a hydrogen-oxygen flame, and the outgoing light field at the end face of the optical fiber is monitored at the same time. Then, the three-dimensional refractive index measurement results of the thermally diffused multicore fiber verify the feasibility of thermal diffusion technology to change the refractive index of discrete waveguides for coupling. Thermal diffusion technology can be used to fabricate multicore fiber couplers. By combining multicore fiber and core-by-core inscribed fiber Bragg grating technology and by using thermal diffusion technology, the single-channel sensing measurement can be realized. The method of changing the refractive index of discrete waveguides through thermal diffusion has the advantages of high integration, high stability, and mass fabrication. The research on the thermal diffusion of discrete waveguides can improve the application potential of multicore fiber sensing systems, and promote the broad application of discrete waveguide structure optical fiber in the fields of optical communication, optical sensing, biomedicine, and artificial intelligence.

Fiber bundle optical system: imaging modeling and analysis

The fiber bundle (FB) optical system is widely used in many fields, such as medical imaging and military reconnaissance, owing to its advantages of high design freedom, small volume, and light weight. The traditional theory for the optical transfer function is not suitable for such a discrete sampling optical system. Researchers have developed numerical calculation methods to analyze the imaging quality of the discrete sampling optical system, in which the geometric model needs to be established and the coupling region needs to be determined. We have developed a simple and computationally efficient imaging theory that is suitable for various combinations of FB and CCD detectors. The coupling modulation transfer function (coupling-MTF) of discrete sampling optical systems of square-arrangement fiber bundles (SFBs) and hexagonal-arrangement fiber bundles (HFBs) are analyzed. Simulation results demonstrate that although SFB has a higher coupling-MTF than HFB, the latter is more convenient in coupling alignment operation. Our results have proven the effectiveness and universality of the proposed theory, and it can be used to guide the system design.

Supercharge optical arrays.

We introduce the notion of a supercharge optical array synthesized according to supersymmetric charge operators. Starting from an arbitrary array, mathematical supersymmetry transformation can be used systematically to create a zero-energy physical state below the ground state of the super-partner array. This zero mode, which is pinned deep in the mid-gap of the corresponding supercharge array owing to the square-root spectral relationship between a supercharge and a super-Hamiltonian array, is shown to be protected because of the chiral symmetry inherent to a supercharge array. A supercharge array can be used in practical applications to design a discrete optical system of waveguides or coupled resonators where the mid-gap zero mode facilitates robust light dynamics in either spatial or time domain.

Frequency diffraction management through arbitrary engineering of photonic band structures

It is of fundamental interest to control light diffraction in discrete optical systems. However, photon hopping in discrete systems is dominated by the nearest-neighbor coupling, limiting the realization of nonlocal diffraction phenomena. Here, we generalize the discrete diffraction from spatial to the frequency domain using optical phase modulators. By inducing long-rang couplings in the frequency lattice through periodic modulation signals, we find the lattice band structure can be artificially engineered, giving rise to the realization of arbitrary frequency diffraction. Particularly, we create linear, bilinear and semicircular band structures using sawtooth, triangular and semicircular modulation waveforms and realize the directional, bidirectional, omnidirectional frequency diffraction as well as the spectral "superlens". We also revisit frequency discrete Talbot effect and generalize the allowed incident period to arbitrary integers through band structure engineering. Moreover, as the frequency transition also carries a wave vector mismatch, an effective electric field will emerge, through which we can realize frequency Bloch oscillations that manifest the effects of arbitrary spectral routing and self-imaging. The study paves a promising way towards versatile spectrum management for both optical communications and signal processing.

Universal correlations after thermalization in periodic nonlinear systems

The evolution of random fields with known statistical properties is relatively straightforward to analyze in the linear regime, but becomes considerably more involved when nonlinearity, or interactions, are dominant. Previous works have shown that statistical physics techniques can be applied to predict the evolution of such systems. Here we study the evolution of random fields in a one-dimensional lattice of optical waveguides in the presence of strong nonlinearities, using the discrete nonlinear Schrödinger equation. Extending the 2009 work by Silberberg et al (Phys. Rev. Lett. 102 233904), we assume input fields with random amplitudes and phases. We derive analytic expressions for the system’s statistical properties at thermodynamic equilibrium. Specifically, expressions for the probability density functions of field intensities, of fields’ phase differences, and an expression for the field correlations. We express these properties in terms of the moments of the assumed statistical excitations, and verify the results with simulations. Most interestingly, we find that at thermodynamic equilibrium, correlations are formed through the interaction between sites. These exponentially decaying fields’ correlations take a universal form that is essentially independent of excitation amplitudes but visibly shrink with increased spread of the exciting amplitudes. Our results are valid not only to nonlinear discrete optical systems, but extend also to the evolution of bosonic atoms in optical lattices in the high-occupancy limit that are governed by the equivalent Gross–Pitaevskii equation.

Design, transform and control of optical field in discrete optical system: an example

A discrete optical system can broaden the spatial distribution of the input light through optical coupling in array waveguides, just like diffraction in continuous media. Here, we theoretically demonstrate several kinds of control methods of optical field propagation in a discrete optical system, which is composed of an Airy fiber with two perpendicular arrayed cores. A brief transform mechanism between Gaussian and Airy beam propagation in such a fiber is presented. The wavefront of the output beam from the Airy fiber is actually dependent on the phased arrayed modulation of coupling array cores. Except the optical wavelength changing, we propose two new methods, including fiber length and bending-induced refractive-index changing, to accomplish that modulation. The calculation results show that these new methods are very effective for the Airy phase modulation. By combining these methods and controlling the corresponding parameters, the Gaussian beam, the one-dimension Airy beam, and the two-dimension Airy beam can be obtained by one same Airy fiber. These methods are also generally applicable to the other discrete optical system and can be extended to generate any other types of optical beams, such as Bessel beams and Mathieu beams.

Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems

We experimentally address the significance of fidelity as a figure of merit in quantum state reconstruction of discrete (DV) and continuous variable (CV) quantum optical systems. In particular, we analyze the use of fidelity in quantum homodyne tomography of CV states and maximum-likelihood polarization tomography of DV ones, focussing attention on nonclassicality, entanglement and quantum discord as a function of fidelity to a target state. Our findings show that high values of fidelity, despite well quantifying geometrical proximity in the Hilbert space, may be obtained for states displaying opposite physical properties, e.g. quantum or semiclassical features. In particular, we analyze in details the quantum-to-classical transition for squeezed thermal states of a single-mode optical system and for Werner states of a two-photon polarization qubit system.

Nonlinear coupling in discrete optical waveguide arrays with quadratic nonlinearity

We demonstrate nonlinear coupling in a discrete optical system. This is achieved in waveguide arrays with quadratic nonlinearity, where the symmetries of the nonlinearly interacting waveguide modes are used to suppress the usually dominating nonlinear effects within individual waveguides. We derive a mathematical model to describe the nonlinear coupling in such waveguide arrays and show experimentally the profound effects of this nonlinear coupling mechanism on second-harmonic generation.

Discrete optical soliton scattering by local inhomogeneities

The nonlinear wave scattering by local inhomogeneities in discrete optical systems is studied both analytically and numerically. The presented theory describes the reflection and transmission of discrete optical solitons at a point defect. In particular, the derived expressions determine the reflected and transmitted pulses from the incident one. In the range of validity, the analytical results are in excellent agreement with the numerical simulations. It is demonstrated that the point defects in structured optical materials represent effective tool for controlling and manipulation of the nonlinear light pulses.

Frequency control of surface plasmons with oscillating metal-insulator-metal waveguides

A single frequency of surface plasmon polaritons (SPPs) will be converted to many discrete frequencies as they are transmitted through a metal-insulator-metal waveguide with its core width undergoing a harmonic oscillation. The process of the frequency conversion shares many key properties with the light diffraction in discrete optical systems. By employing the conception of optical diffraction management, we can control the discrete frequencies of SPPs such as the intensity and spectrum width by changing the initial phase of the waveguide oscillation. The study bridges the spatial discrete diffraction and frequency transition of SPP modes. Theoretical analysis based on the effective index method and coupled mode theory is provided in detail.

Nonlinear discrete optics in femtosecond laser-written photonic lattices

In recent years, photonic lattices fabricated by the femtosecond laser direct writing technique in fused silica have emerged as the tool of choice for the experimental investigation of light propagation in discrete optical systems with Kerr nonlinearity. In this article, we review the recent results of our research conducted in this field and present our latest findings on the reflection of transversely propagating light at kinks in planar photonic lattices with detuned pivotal site.

Selected papers in nonlinear dynamics in dissipative and discrete optical systems

In recent years much attention has been devoted to the study of intrinsic localization of light, i.e. the formation of solitons, in realistic nonlinear systems. This concerns essentially settings where the energy exchange with the environment (dissipative systems) and the noninstantaneous nonlinear response of the respective nonlinear material are taken into account. Another interesting aspect in nonlinear physics is the role of discreteness. Energy exchange (or dissipation) and the noninstantaneous response affect to a large extent the action of the nonlinearity, whereas discreteness offers new opportunities to control the linear properties of the system. Consequently, all these effects and their interplay will evoke a plethora of new soliton solutions. This special issue of Applied Physics B contains selected results of the DFG Research Unit 512 ‘Nonlinear spatio-temporal dynamics in dissipative and discrete optical systems’ together with guest contributions of Stefano Longhi, Politecnico di Milano, and the group of Zhigang Chen, San Francisco State University. The subject looked at by the Research Unit was in its infancy when we started our project. Meanwhile, it has attracted a great deal of interest and lies well in the mainstream of contemporary research in optics. In order to identify the wealth of the underlying physics, we looked at various optical systems spanning from fairly simple ones such as passive and active optical fibers and media exhibiting a secondor third-order nonlinearity to more

Quantum bouncing ball on a lattice: An optical realization

An optical realization of a quantum bouncing ball on a truncated lattice is theoretically proposed for light waves propagating near the edge of a circularly curved waveguide array. As compared to the analogous problem of matter waves bouncing on a perfectly reflecting surface under the influence of gravity, where the wave packets basically behave as classical particles, it is shown that the genuine quantum regimes of wave packet collapse and revival are accessible for the discrete optical system.

Diffraction managed solitons: asymptotic validity and excitation thresholds

Solitons in discrete optical systems have been a topic of keen interest over the past decade. In a diffraction managed waveguide array, where the waveguide's diffraction profile is varied periodically in the direction of propagation, the slow evolution of the electric field envelope is modelled by a nonlocal discrete equation that exhibits soliton solutions numerically. In this paper, we verify the validity of the asymptotic approximation, demonstrating that solutions of the averaged equation are close in the l2 sense to those of the original model for long time scales. Moreover, we prove that the averaged equation has stable ground state solutions, complementing previous experimental and numerical observations. Finally, we show that for a generalization of the averaged equation, ground states of an associated Hamiltonian exist if and only if their l2 norm exceeds a certain excitation threshold, which depends on the system's dimension and degree of nonlinearity.

Anomalous refraction and diffraction in discrete optical systems.

We experimentally prove that light propagation in a discrete system, i.e., an array of coupled waveguides, exhibits striking anomalies. We show that refraction is restricted to a cone, irrespective of the initial tilt of the beam. Diffraction can be controlled in size and sign by the input conditions. Diffractive beam spreading can even be arrested and diverging light can be focused. The results can be thoroughly theoretically explained.