Nonlinear Shaping Research Articles

Second-harmonic generation and manipulation in lithium niobate slab waveguides by grating metasurfaces

Nonlinear optical processes in waveguides play important roles in compact integrated photonics, while efficient coupling and manipulations inside the waveguides still remain challenging. In this work, we propose a new scheme for second-harmonic generation as well as beam shaping in lithium niobate slab waveguides with the assistance of well-designed grating metasurfaces at λ = 1064 nm . By encoding the amplitude and phase into the holographic gratings, we further demonstrate strong functionalities of nonlinear beam shaping by the metasurface design, including dual focusing and Airy beam generation. Our approach would inspire new designs in the miniaturization and integration of compact multifunctional nonlinear light sources on chip.

Artificial neural networks for nonlinear pulse shaping in optical fibers

We use a supervised machine-learning model based on a neural network to predict the temporal and spectral intensity profiles of the pulses that form upon nonlinear propagation in optical fibers with both normal and anomalous second-order dispersion. We also show that the model is able to retrieve the parameters of the nonlinear propagation from the pulses observed at the output of the fiber. Various initial pulse shapes as well as initially chirped pulses are investigated.

Periodically poled LiNbO3 crystals from 1D and 2D to 3D

A periodically-poled LiNbO3 (PPLN) crystal features space-dependent second-order nonlinear coefficients, which is one of the most important materials to effectively control nonlinear optical interactions through quasi-phase matching (QPM). By using electric-field poling method, 1D and 2D PPLN crystals have been successfully fabricated for laser frequency conversion, quantum light sources, nonlinear beam shaping and nonlinear optical imaging. Recently, femtosecond laser engineering technique is utilized to prepare 3D domain structures inside LiNbO3 crystal, which provides a promising platform to control nonlinear interacting waves in 3D configuration. After 40 years of developments, PPLN crystals still have exciting prospects in fundamental researches and practical applications for integrated photonic chip, quantum information processing, and so on.

Nonlinear patterns shaping the domain on which they live

Nonlinear stripe patterns in two spatial dimensions break the rotational symmetry and generically show a preferred orientation near domain boundaries, as described by the famous Newell–Whitehead–Segel (NWS) equation. We first demonstrate that, as a consequence, stripes favour rectangular over quadratic domains. We then investigate the effects of patterns ‘living’ in deformable domains by introducing a model coupling a generalized Swift–Hohenberg model to a generic phase field model describing the domain boundaries. If either the control parameter inside the domain (and therefore the pattern amplitude) or the coupling strength (‘anchoring energy’ at the boundary) are increased, the stripe pattern self-organizes the domain on which it ‘lives’ into anisotropic shapes. For smooth phase field variations at the domain boundaries, we simultaneously find a selection of the domain shape and the wave number of the stripe pattern. This selection shows further interesting dynamical behavior for rather steep variations of the phase field across the domain boundaries. The here-discovered feedback between the anisotropy of a pattern and its orientation at boundaries is relevant e.g. for shaken drops or biological pattern formation during development.

Nonlinear Beam Shaping in Domain Engineered Ferroelectric Crystals.

Domain engineered ferroelectric crystals are a type of microstructure functional material that is used widely in the area of nonlinear optics. Herein, research processes in the area of nonlinear beam shaping using domain engineered crystals in the past decade are reviewed. The newly developed design methods, such as the nonlinear Huygens-Fresnel principle, nonlinear volume holography, and caustic design, which have analogs in linear optics, are introduced. Using the proposed methods for nonlinear beam shaping, multiple function integration, generation of Airy beams, and arbitrary curved trajectories are realized. As an extra degree of freedom, orbital angular momentum of light beams is generated and manipulated through domain engineering. Discussions and future directions in this field are presented.

Efficient nonlinear beam shaping in three-dimensional lithium niobate nonlinear photonic crystals

Nonlinear beam shaping refers to spatial reconfiguration of a light beam at a new frequency, which can be achieved by using nonlinear photonic crystals (NPCs). Direct nonlinear beam shaping has been achieved to convert second-harmonic waves into focusing spots, vortex beams, and diffraction-free beams. However, previous nonlinear beam shaping configurations in one-dimensional and two-dimensional (2D) NPCs generally suffer from low efficiency because of unfulfilled phase-matching condition. Here, we present efficient generations of second-harmonic vortex and Hermite-Gaussian beams in the recently-developed three-dimensional (3D) lithium niobate NPCs fabricated by using a femtosecond-laser-engineering technique. Since 3D χ(2) modulations can be designed to simultaneously fulfill the requirements of nonlinear wave-front shaping and quasi-phase-matching, the conversion efficiency is enhanced up to two orders of magnitude in a tens-of-microns-long 3D NPC in comparison to the 2D case. Efficient nonlinear beam shaping paves a way for its applications in optical communication, super-resolution imaging, high-dimensional entangled source, etc.

Nonlinear wavefront shaping with optically\xa0induced three-dimensional nonlinear photonic crystals

Generation of coherent light with desirable amplitude and phase profiles throughout the optical spectrum is a key issue in optical technologies. Nonlinear wavefront shaping offers an exceptional way to achieve this goal by converting an incident light beam into the beam (or beams) of different frequency with spatially modulated amplitude and phase. The realization of such frequency conversion and shaping processes critically depends on the matching of phase velocities of interacting waves, for which nonlinear photonic crystals (NPCs) with spatially modulated quadratic nonlinearity have shown great potential. Here, we present the first experimental demonstration of nonlinear wavefront shaping with three-dimensional (3D) NPCs formed by ultrafast-light-induced ferroelectric domain inversion approach. Compared with those previously used low-dimensional structures, 3D NPCs provide all spatial degrees of freedom for the compensation of phase mismatch in nonlinear interactions and thereby constitute an unprecedented system for the generation and control of coherent light at new frequencies.

Frequency Comb Generation at 800 nm in Waveguide Array Quantum Well Diode Lasers

A traveling wave model for a semiconductor diode laser based on quantum wells is presented as well as a comprehensive theoretical model of the lasing dynamics produced by the intensity discrimination of the nonlinear mode-coupling in a waveguide array. By leveraging a recently developed model for the detailed semiconductor gain dynamics, the temporal shaping effects of the nonlinear mode-coupling induced by the waveguide arrays can be characterized. Specifically, the enhanced nonlinear pulse shaping provided by the waveguides are capable of generating stable frequency combs wavelength of 800 nm in a GaAs device, a parameter regime not feasible for stable combline generation using a single waveguide. Extensive numerical simulations showed that stable waveform generation could be achieved and optimized by an appropriate choice of the linear waveguide coupling coefficient, quantum well depth, and the input currents to the first and second waveguides. The model provides a first demonstration that a compact, efficient and robust on-chip comb source can be produced in GaAs.

Compliant Parametric Dynamic Movement Primitives

SummaryIn this paper, we propose and implement an advanced manipulation framework that enables parametric learning of complex action trajectories along with their haptic feedback profiles. Our framework extends Dynamic Movement Primitives (DMPs) method with a new parametric nonlinear shaping function and a novel force-feedback coupling term. The nonlinear trajectories of the action control variables and the haptic feedback trajectories measured during execution are encoded with parametric temporal probabilistic models, namely parametric hidden Markov models (PHMMs). PHMMs enable autonomous segmentation of a taught skill based on the statistical information extracted from multiple demonstrations, and learning the relations between the model parameters and the properties extracted from the environment. Hidden states with high-variances in observation probabilities are interpreted as parts of the skill that could not be reliably learned and autonomously executed due to possibly uncertain or missing information about the environment. In those parts, our proposed force-feedback coupling term, which computes the deviation of the actual force feedback from the one predicted by the force-feedback PHMM, acts as a compliance term, enabling a human to scaffold the ongoing movement trajectory to accomplish the task. Our method is verified in a number of tasks including a real pick and place task that involves obstacles of different heights. Our robot, Baxter, successfully learned to generate the trajectory taking into the heights of the obstacles, move its end effector stiffly (and accurately) along the generated trajectory while passing through apertures, and allow human–robot collaboration in the autonomously detected segments of the motion, for example, when the gripper picks up the object whose position is not provided to the robot.

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator.

The aim of this article is to visually demonstrate the utilization of an interferometric method for encoding complex fields associated with coherent laser radiation. The method is based on the coherent sum of two uniform waves, previously encoded into a phase-only spatial light modulator (SLM) by spatial multiplexing of their phases. Here, the interference process is carried out by spatial filtering of light frequencies at the Fourier plane of certain imaging system. The correct implementation of this method allows arbitrary phase and amplitude information to be retrieved at the output of the optical system. It is an on-axis, rather than off-axis encoding technique, with a direct processing algorithm (not an iterative loop), and free from coherent noise (speckle). The complex field can be exactly retrieved at the output of the optical system, except for some loss of resolution due to the frequency filtering process. The main limitation of the method might come from the inability to operate at frequency rates higher than the refresh rate of the SLM. Applications include, but are not limited to, linear and non-linear microscopy, beam shaping, or laser micro-processing of material surfaces.

High-energy femtosecond pulse shaping, compression, and contrast enhancement using multicore fiber

Nonlinear spatiotemporal dynamics of femtosecond pulses in a hexagonal seven-core silica fiber pumped by a sub-μJ 370fs Er:fiber chirped pulse amplification (CPA) system were studied. Nonlinear pulse shaping and compression in the central core and pedestal coupling to the outer cores were directly measured by frequency-resolved optical gating. Further compression of the pulses spectrally broadened in the multicore fiber down to 53fs was demonstrated. Two orders of magnitude contrast enhancement of the pulses after compression was observed.

Thermally-induced nonlinear spatial shaping of infrared femtosecond pulses in nematic liquid crystals

An optically-induced thermal non-linear effect in a nematic liquid-crystal (E7) cell is evidenced through weak light-absorption by the ITO coating of an infrared pulsed femtosecond laser (m). Strong spatial self-phase modulation is generated, thus a multiple-ring pattern is observed in the far-field. The sign of the nonlinearity is changed depending on the laser polarization. The refractive index and thermal gradients are measured as a function of the laser intensity and we observe that the temperature can increase close to the nematic phase transition. The fidelity and stability of the process open new prospects for spatial shaping devices and delimits the operating wavelength range for ultrafast liquid-crystal based electro-optic application.

Nonlinear sculpturing of optical pulses with normally dispersive fiber-based devices

We present a general method to determine the parameters of nonlinear pulse shaping systems based on pulse propagation in a normally dispersive fiber that are required to achieve the generation of pulses with various specified temporal properties. The nonlinear shaping process is reduced to a numerical optimization problem over a three-dimensional space, where the intersections of different surfaces provide the means to quickly identify the sets of parameters of interest. We also show that the implementation of a machine-learning strategy can efficiently address the multi-parameter optimization problem being studied.

Dynamic computer-generated nonlinear optical holograms in a non-collinear second-harmonic generation process.

The nonlinear holography technique is a powerful tool for all-optical switching and manipulation of an arbitrary harmonic wave. The common method of realizing such nonlinear holography is by configuring the structure of nonlinear photonic crystals. However, it is a challenge to dynamically tune the harmonic wave pattern. To overcome the long-term existing non-dynamic property of such nonlinear holographs, we realize dynamic computer-generated nonlinear optical holograms in the non-collinear second-harmonic (SH) generation process in which only one infrared beam is modulated. Arbitrary patterns in both fundamental-frequency and second-harmonic wavebands can be generated at the same time. This Letter offers a flexible and dynamic method for arbitrary nonlinear wavefront shaping technology.

Application of nonlinear pulse shaping of femtosecond pulse generation in a fiber amplifier at 500 MHz repetition rate

We numerically and experimentally demonstrate that a nonlinear pulse shaping technique based on pre-chirping management in a short gain fiber can be exploited to improve the quality of a compressed pulse. With prior tuning of the pulse chirp, the amplified pulse express different nonlinear propagating processes. A spectrum with s flat top and more smooth wings, showing a similariton feature, generates with the optimal initial pulse chirp, and the shortest pulses with minimal pulse pedestals are obtained. Experimental results show the ability of nonlinear pulse shaping to enhance the quality of compressed pulses, as theoretically expected.

Inertial Properties in Haptic Devices: Non-Linear Inertia Shaping vs. Force Feedforward

Abstract The inertia of haptic devices limits the user’s manipulation and dynamically couples the Cartesian motion, which influences the transparency and fidelity in haptic feedback. By employing force-torque sensing, we investigate two approaches to reduce the apparent inertial effect of haptic devices and to overcome dynamic coupling. First, in order to shape the apparent inertia felt by the user, non-linear inertia shaping (NIS) is presented and introduced to the field of haptics. NIS is based on non-linear dynamic decoupling (NLD). Second, as a standard approach, force feedforward control (FF) is presented that uniformly scales down the apparent inertia. We demonstrate that FF is a special case of NIS, under the assumption that gravitational, centripetal and Coriolis terms are neglected. Simulations and experiments were conducted on DLR’s bi-manual haptic device HUG. It is shown that NIS is suited to compensate for the coupling effects, while FF can reduce the apparent inertia more effectively.

Hamiltonian methods of modeling and control of AC microgrids with spinning machines and inverters

This paper presents a novel approach to the modeling and control of AC microgrids that contain spinning machines, power electronic inverters and energy storage devices. The inverters in the system can adjust their frequencies and power angles very quickly, so the modeling focuses on establishing a common reference frequency and angle in the microgrid based on the spinning machines. From this dynamic model, nonlinear Hamiltonian surface shaping and power flow control method is applied and shown to stabilize. From this approach the energy flow in the system is used to show the energy storage device requirements and limitations for the system. This paper first describes the model for a single bus AC microgrid with a Hamiltonian control, then extends this model and control to a more general class of multiple bus AC microgrids. Simulation results demonstrate the efficacy of the approach in stabilizing and optimization of the microgrid.

Nonlinear Shaping Architecture Designed with Using Evolutionary Structural Optimization Tools

The paper explores the possibilities of using Structural Optimization Tools (ESO) digital tools in an integrated structural and architectural design in response to the current needs geared towards sustainability, combining ecological and economic efficiency. The first part of the paper defines the Evolutionary Structural Optimization tools, which were developed specifically for engineering purposes using finite element analysis as a framework. The development of ESO has led to several incarnations, which are all briefly discussed (Additive ESO, Bi-directional ESO, Extended ESO). The second part presents result of using these tools in structural and architectural design. Actual building projects which involve optimization as a part of the original design process will be presented (Crematorium in Kakamigahara Gifu, Japan, 2006 SANAA“s Learning Centre, EPFL in Lausanne, Switzerland 2008 among others). The conclusion emphasizes that the structural engineering and architectural design mean directing attention to the solutions which are used by Nature, designing works optimally shaped and forming their own environments. Architectural forms never constitute the optimum shape derived through a form-finding process driven only by structural optimization, but rather embody and integrate a multitude of parameters. It might be assumed that there is a similarity between these processes in nature and the presented design methods. Contemporary digital methods make the simulation of such processes possible, and thus enable us to refer back to the empirical methods of previous generations.

Full-waveform inversion using seislet regularization

Because of inaccurate, incomplete, and inconsistent waveform records, full-waveform inversion (FWI) in the framework of a local optimization approach may not have a unique solution, and thus it remains an ill-posed inverse problem. To improve the robustness of FWI, we have developed a new model regularization approach that enforced the sparsity of solutions in the seislet domain. The construction of seislet basis functions requires structural information that can be estimated iteratively from migration images. We implement FWI with seislet regularization using nonlinear shaping regularization and impose sparseness by applying soft thresholding on the updated model in the seislet domain at each iteration of the data-fitting process. The main extra computational cost of the method relative to standard FWI is the cost of applying forward and inverse seislet transforms at each iteration. This cost is almost negligible compared with the cost of solving wave equations. Numerical tests using the synthetic Marmousi model demonstrate that seislet regularization can greatly improve the robustness of FWI by recovering high-resolution velocity models, particularly in the presence of strong crosstalk artifacts from simultaneous sources or strong random noise in the data.

Second-harmonic focusing by a nonlinear turbid medium via feedback-based wavefront shaping.

Scattering has usually been considered detrimental for optical focusing or imaging. Recently, more and more research has shown that strongly scattering materials can be utilized to focus coherent light by controlling or shaping the incident light. Here, purposeful focusing of second-harmonic waves, which are generated and scattered from nonlinear turbid media via feedback-based wavefront shaping, is presented. This Letter shows a flexible manipulation of both disordered linear and nonlinear scattering signals, indicating more controllable degrees of freedom for the description of turbid media. This technique also provides a possible way to an efficient transmission of nonlinear signal at a desired location in the form of a focal point or other patterns. With the combination of random nonlinear optics and wavefront shaping methods, more interesting applications can be expected in the future, such as nonlinear transmission matrix, multi-frequency imaging, and phase-matching-free nonlinear optics.