Nonlinear Wavefront Research Articles

Nonlinear geometric phase coded ferroelectric nematic fluids for nonlinear soft-matter photonics

Simultaneous manipulation of multiple degrees of freedom of light lies at the heart of photonics. Nonlinear wavefront shaping offers an exceptional way to achieve this goal by converting incident light into beams of new frequencies with spatially varied phase, amplitude, and angular momenta. Nevertheless, the reconfigurable control over structured light fields for advanced multimode nonlinear photonics remains a grand challenge. Here, we propose the concept of nonlinear geometric phase in an emerging ferroelectric nematic fluid, of which the second-order nonlinear susceptibility carries spin-dependent nonlinearity phase. A case study with photopatterned q-plates demonstrates the generation of second-harmonic optical vortices with spin-locked topological charges by using cascaded linear and nonlinear optical spin-orbit interactions. Furthermore, we present the dynamic tunability of second-harmonic structured light through temperature, electric field, and twisted elastic force. The proposed strategy opens new avenues for reconfigurable nonlinear photonics, with potential applications in optical communications, quantum computing, high-resolution imaging, etc.

Helically twisted nonlinear photonic crystals.

Nonlinear photonic crystals with a helical structure in the second-order nonlinear coefficient (χ(2)) are fabricated using infrared femtosecond laser poling in ferroelectric Sr0.61Ba0.39Nb2O6 crystals. The quasi-orbital angular momentum of the helical χ(2) structure can be imprinted on the interacting photons during nonlinear optical processes, allowing the topological charge of the generated photons at new frequencies to be controlled. Here we study the case of a double-helix nonlinear photonic structure for the generation of a second-harmonic vortex beam from a Gaussian pump beam without phase singularity. The conservation law for orbital angular momentum in the second-harmonic process is also verified, with the topological charge of the pump photons being fully compensated by the double-helix structure. The flexible control of light carrying orbital angular momentum (OAM) at new frequencies will find important applications in both classical and quantum photonics, such as nonlinear wavefront shaping and multidimensional entanglement of photons.

Intrinsic nonlinear geometric phase in SHG from zincblende crystal symmetry media

Abstract We demonstrate that AlGaAs thin films and metasurfaces generate a distinct intrinsic nonlinear geometric phase in their second harmonic signals, differing significantly from previous studies on nonlinear dielectric, plasmonic, or hybrid metasurfaces. Unlike conventional observations, our study reveals that the second harmonic phase remains unaffected by the linear optical response at both pump and harmonic wavelengths, introducing a novel realm of achievable phase functions yet to be explored. Furthermore, we explore the interplay between this intrinsic nonlinear geometric phase and the geometric phase induced by rotations of nanoresonators within metasurface arrangements. Our findings extend the capabilities of nonlinear wavefront shaping metasurfaces, exploiting phase manipulation to uncover unique phenomena exclusive to the nonlinear regime.

Nonlinear wave propagation in a bistable optical chain with nonreciprocal coupling

The propagation of nonlinear waves, such as fires, weather fronts, and disease spread, has drawn attention since the dawn of time. A well-known example of nonlinear wave–fronts–in our daily lives is the domino waves, which propagate equally toward the left or right flank due to their reciprocal coupling. However, there are other situations where front propagation is not fully understood, such as bistable fronts with nonreciprocal coupling. These couplings are characterised by the fact that the energy emitter and receiver are not interchangeable. Here, we study the propagation of nonlinear waves in a bistable optical chain forced by nonreciprocal optical feedback. The spatiotemporal evolution and the front speeds are characterised as a function of the nonreciprocal coupling. We derive an equation to describe the interacting optical elements in a liquid crystal light valve with nonreciprocal optical feedback and compare the experimental results with numerical simulations of the coupled bistable systems.

Third Harmonic Generation Enhancement and Wavefront Control Using a Local High-Q Metasurface.

High quality factor optical nanostructures provide a great opportunity to enhance nonlinear optical processes such as third harmonic generation. However, the field enhancement in these high quality factor structures is typically accompanied by optical mode nonlocality. As a result, the enhancement of nonlinear processes comes at the cost of their local control as needed for nonlinear wavefront shaping, imaging, and holography. Here we show simultaneous strong enhancement and spatial control over third harmonic generation with a local high-Q metasurface relying on higher-order Mie resonant modes. Our results demonstrate third harmonic generation at an efficiency of up to 3.25 × 10-5, high quality wavefront shaping as illustrated by a third harmonic metalens, and a flatband, angle independent, third harmonic response up to ±11° incident angle. The demonstrated high level of local control and efficient frequency conversion offer promising prospects for realizing novel nonlinear optical devices.

Wavelength-dependent nonlinear wavefront shaping in 3D nonlinear photonic crystal

Wavelength-dependent nonlinear wavefront shaping in 3D nonlinear photonic crystal

Bayesian eikonal tomography using Gaussian processes


 Eikonal tomography has become a popular methodology for deriving phase velocity maps from surface wave phase delay measurements. Its high efficiency makes it popular for handling datasets deriving from large-N arrays, in particular in the ambient-noise tomography setting. However, the results of eikonal tomography are crucially dependent on the way in which phase delay measurements are predicted from data, a point which has not been thoroughly investigated. In this work, I provide a rigorous formulation for eikonal tomography using Gaussian processes (GPs) to smooth observed phase delay measurements, including uncertainties. GPs allow the posterior phase delay gradient to be analytically derived. From the phase delay gradient, an excellent approximate solution for phase velocities can be obtained using the saddlepoint method. The result is a fully Bayesian result for phase velocities of surface waves, incorporating the nonlinear wavefront bending inherent in eikonal tomography, with no sampling required. The results of this analysis imply that the uncertainties reported for eikonal tomography are often underestimated.

Assessing phase reconstruction accuracy for different nonlinear curvature wavefront sensor configurations

Assessing phase reconstruction accuracy for different nonlinear curvature wavefront sensor configurations

Nonlinear generation of an optical bottle beam in domain-engineered ferroelectric crystals.

Nonlinear wavefront shaping in periodically poled ferroelectric crystals has received great attention because it offers a convenient way to generate a structured light beam at new frequencies. In contrast to structurally uniform beams like Laguerre-Gaussian or Hermite-Gaussian modes, here we demonstrate the possibility to generate a spatially varied optical bottle beam via a frequency doubling process in a domain-engineered Sr0.61Ba0.39Nb2O6 (SBN) crystal. The nonlinear holography method was employed to design the modulation pattern of the second-order nonlinear coefficient χ(2), and the femtosecond laser poling was used to imprint the χ(2) pattern into the SBN crystal via ferroelectric domain inversion. The second harmonic bottle beam with zero intensity in its center that is surrounded in all three dimensions by light was observed with the incidence of a fundamental Gaussian beam. These results are useful for nonlinear generation and control of structured light at new frequencies, which has important applications in nonlinear photonics and quantum optics.

Numerical investigation on nonlinear ship waves by LCM and WSAM

This paper investigates the nonlinear ship waves by implementing the longitudinal cut method (LCM) and wake survey analysis method (WSAM) in the computational fluid dynamics (CFD) simulation. LCM is first implemented and validated for a Series 60, Cb = 0.6 ship model to guarantee accurate prediction of the wave pattern resistance (Rwp). To illustrate the reliability, WSAM is performed for a wall-sided model, incorporating the local adaptive mesh refinement (LAMR) and surface tension models to capture nonlinear bow waves. Far and near-field wave patterns and momentum loss resistance (RML) are compared with the experiment.With the well-predicted nonlinear bow waves, the velocity discontinuity property across the nonlinear wavefront and the vortex motion beneath the nonlinear waves are clearly observed by velocity vector and Q-criteria iso-surface visualization. By LCM and WSAM analysis, the discrepancy between wave resistance (Rw) and Rwp is attributed to the nonlinearity in ship waves, and expression to evaluate this part of resistance (Rnw) is discussed and summarized. Finally, the influence of velocity and draft on Rnw and bow wave angle (β) is systematically analyzed and discussed. This study hopes to provide insights to evaluate the nonlinearity in ship waves and further understand its underlying mechanism.

Nonlinear Optical Wavefront Engineering with Geometric Phase Controlled All‐Dielectric Metadevice

AbstractOptical wavefront engineering with artificial nanostructures has important applications in laser manufacturing, bioimaging, optical communications, etc. In the linear optical regime, metasurfaces are widely utilized to realize wavefront engineering functionalities, such as imaging with a flat lens and generation of vortex beams and holographic images. On the other hand, it is highly desirable to directly control the wavefront of light during nonlinear optical processes. Here, the nonlinear optical wavefront engineering with geometric phase controlled all‐dielectric metadevices is experimentally demonstrated. This is realized by integrating the multifunctional dielectric metasurface with the conventional nonlinear optical crystals. It is demonstrated that the nonlinear metadevice can be used to generate optical vortices and nonreciprocal holographic images at second harmonic frequencies. The proposed all‐dielectric metadevice represents an important strategy to develop compact and multifunctional nonlinear optical sources.

A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing

Advanced adaptive optics (AO) instruments have applications in ophthalmic imaging, free-space optical communications and the future generation of extremely large telescopes. These AO systems are designed to perform real-time corrections of dynamic wavefront aberrations. The corrections can be performed by converting wavefront measurements into deformable mirror (DM) actuator commands. The role of the DM is to mitigate aberrations by restoring a planar wavefront. Optimal DM actuator commands therefore require precise phase measurements across the entire wavefront. Reconstructing a wavefront from wavefront sensor (WFS) data is an inverse problem that depends on the type of WFS implemented. Nonlinear Fourier-type WFSs are included in the design of many current and upcoming AO systems. Conventionally, these sensors perform AO control based on simplifications and linearisations of the underlying models. However, in nonlinear regimes, approximation errors critically degrade image quality. This study looks at overcoming nonlinear wavefront sensing regimes by introducing a nonlinear, iterative algorithm for Fourier-type wavefront reconstruction. The algorithm used is well-known in the field of inverse problems. The underlying mathematical theory for modelling Fourier-type WFSs is provided, along with how these models can be used to perform nonlinear wavefront reconstruction. A significant advantage of the analysis presented is its generalised applicability to any Fourier-type sensor. The only input required is the mathematical expression for the optical element transfer function. The generalised and full mathematical model of Fourier-type WFSs is introduced in a Sobolev space setting. Necessary inputs are derived for the nonlinear iterative algorithms, such as Fréchet derivatives and adjoints. The generalised theory is then expanded to solve the inverse problem of wavefront reconstruction for all Fourier-type WFSs. Moreover, the study concentrates on the pyramid WFS (PWFS)—one of the most well-known Fourier-type WFSs—and shows a Hilbert transform representation of the amplitude of the incoming light on its detector. The developed theory is demonstrated using a simulated PWFS to measure an example wavefront.

Chiral Third-Harmonic Metasurface for Multiplexed Holograms.

Chiral nonlinear metasurfaces could natively synergize nonlinear wavefront manipulation and circular dichroism, offering enhanced capacity for multifunctional and multiplexed nonlinear metasurfaces. However, it is still quite challenging to simultaneously enable strong chiral response, precise wavefront control, high nonlinear conversion efficiency, and independent functions on spins and chirality. Here, we propose and experimentally demonstrate multiplexed third-harmonic (TH) holograms with four channels based on a chiral Au-ZnO hybrid metasurface. Specifically, the left- and right-handed circularly polarized (LCP and RCP) components of the TH holographic images can be designed independently under the excitation of an LCP (or RCP) fundamental beam. In addition, the TH conversion efficiency is measured to be as large as 10-5, which is 8.6 times stronger than that of a bare ZnO film with the same thickness. Thus, our work provides a promising platform for realizing efficient and multifunctional nonlinear nanodevices.

Improving focusability of post-compressed PW laser pulses using a deformable mirror

The use of the post-compression technique ensures gain in laser pulse peak power but at the same time degrades beam focusability due to the nonlinear wavefront distortions caused by a spatially nonuniform beam profile. In this paper a substantial focusability improvement of a post-compressed laser pulse by means of adaptive optics was demonstrated experimentally. The Strehl ratio increase from 0.16 to 0.43 was measured. Simulations showed that the peak intensity in this case reaches 0.52 of the theoretical limit.

Anomalous wavefront control of third-harmonic generation via graphene-based nonlinear metasurfaces in the terahertz regime.

Freely controlling wavefronts with metasurfaces has been widely studied in linear optical systems. By constructing phase gradient meta-atoms with nonlinear responses, the wavefronts of high-harmonic fields in nonlinear metasurfaces can be arbitrarily steered by following nonlinear generalized Snell's law (NGSL). However, for incident angles above the critical angle, NGSL fails to predict the generated nonlinear waves. In this work, by involving the reciprocal lattice effect of the nonlinear metasurface, we show a modified diffraction law to completely describe the nonlinear diffraction phenomena. This law is numerically demonstrated and confirmed by designed graphene-based nonlinear metasurfaces in the terahertz regime. Moreover, based on the diffraction law, we designed a nonlinear retroreflector and realized tunable control over a nonlinear wavefront in a single nonlinear metasurface. Our work provides a way to manipulate nonlinear waves and provides a better design of functional nonlinear metadevices.

Adaptive Models for Multi-Covariate Imaging of Sub-Resolution Targets (MIST).

Multi-covariate imaging of sub-resolution targets (MIST) is a statistical, model-based image formation technique that smooths speckles and reduces clutter. MIST decomposes the measured covariance of the element signals into modeled contributions from mainlobe, sidelobes, and noise. MIST covariance models are derived from the well-known autocorrelation relationship between transmit apodization and backscatter covariance. During in vivo imaging, the effective transmit aperture often deviates from the applied apodization due to nonlinear propagation and wavefront aberration. Previously, the backscatter correlation length provided a first-order measure of these patient-specific effects. In this work, we generalize and extend this approach by developing data-adaptive covariance estimation, parameterization, and model-formation techniques. We performed MIST imaging using these adaptive models and evaluated the performance gains using 152 tissue-harmonic scans of fetal targets acquired from 15 healthy pregnant subjects. Compared to standard MIST imaging, the contrast-to-noise ratio (CNR) is improved by a median of 8.3%, and the speckle signal-to-noise ratio (SNR) is improved by a median of 9.7%. The median CNR and SNR gains over B-mode are improved from 29.4% to 40.4% and 24.7% to 38.3%, respectively. We present a versatile empirical function that can parameterize an arbitrary speckle covariance and estimate the effective coherent aperture size and higher order coherence loss. We studied the performance of the proposed methods as a function of input parameters. The implications of system-independent MIST implementation are discussed.

Forecasting wavefront corrections in an adaptive optics system

We used telemetry data from the Gemini North ALTAIR adaptive optics system to investigate how well the commands for wavefront correction (both tip/tilt and high-order turbulence) can be forecasted to reduce lag error (due to wavefront sensor averaging and computational delays) and improve delivered image quality. We showed that a high level of reduction (∼5 for tip-tilt and ∼2 for high-order modes) in the RMS wavefront error was achieved using a “forecasting filter” based on a linear autoregressive model with only a few coefficients (∼30 for tip-tilt and ∼5 for high-order modes) to complement the existing integral servo-controller. Updating this filter to adapt to evolving observing conditions is computationally inexpensive and requires <10 s of telemetry data. We also used several machine learning models (long-short term memory and dilated convolutional models) to evaluate whether further improvements could be achieved with a more sophisticated nonlinear model. Our attempts showed no perceptible improvements over linear autoregressive predictions, even for large lags in which residuals from the linear models are high, suggesting that nonlinear wavefront distortions for ALTAIR at the Gemini North telescope may not be forecasted with the current setup.

Efficient Frequency Conversion with Geometric Phase Control in Optical Metasurfaces.

Metasurfaces have appeared as a versatile platform for miniaturized functional nonlinear optics due to their design freedom in tailoring wavefronts. The key factor that limits its application in functional devices is the low conversion efficiency. Recently, dielectric metasurfaces governed by either high‐quality factor modes (quasi‐bound states in the continuum) or Mie modes, enabling strong light–matter interaction, have become a prolific route to achieve high nonlinear efficiency. Here, an effective way of spatial nonlinear phase control by using the Pancharatnam–Berry phase principle with a high third harmonic conversion efficiency of 10−4 W−2 is demonstrated both numerically and experimentally. It is found that the magnetic Mie resonance appears to be the main contributor to the third harmonic response, while the contribution from the quasi‐bound states in the continuum is negligible. This is confirmed by a phenomenological model based on coupled anharmonic oscillators. Besides, the metasurface provides experimentally a high diffraction efficiency (80%–90%) in both polarization channels. A functional application of this approach is shown by experimentally reconstructing an encoded polarization‐multiplexed vortex beam array with different topological charges at the third harmonic frequency with high fidelity. The approach has the potential viability for future on‐chip nonlinear signal processing and wavefront control.

Mathematical modelling of proton migration in Earth mantle

In the study, we address the mathematical problem of proton migration in the Earth’s mantle and suggest a prototype for exploring the Earth’s interior to map the effects of superionic proton conduction. The problem can be mathematically solved by deriving the self-consistent electromagnetic field potential U(x, t) and then reconstructing the distribution function f(x,v,t). Reducing the Vlasov-Maxwell system of equations to non-linear sh-Gordon hyperbolic and transport equations, the propagation of a non-linear wavefront within the domain and transport of the boundary conditions in the form of a non-linear wave are examined. By computing a 3D model and through Fourier-analysis, the spatial and electrical characteristics of potential U(x, t) are investigated. The numerical results are compared to the Fourier transformed quantities of the potential (V) obtained through field observations of the electric potential (Kuznetsov method). The non-stationary solutions for the forced oscillation of two-component system, and therefore, the oscillatory strengths of two types of charged particles can be usefully addressed by the proposed mathematical model. Moreover, the model, along with data analysis of the electric potential observations and probabilistic seismic hazard maps, can be used to develop an advanced seismic risk metric.

Nonlinear wavefront engineering with metasurface decorated quartz crystal

Abstract In linear optical processes, compact and effective wavefront shaping techniques have been developed with the artificially engineered materials and devices in the past decades. Recently, wavefront shaping of light at newly generated frequencies was also demonstrated using nonlinear photonic crystals and metasurfaces. However, the nonlinear wave-shaping devices with both high nonlinear optical efficiency and high wave shaping efficiency are difficult to realize. To circumvent this constraint, we propose the idea of metasurface decorated optical crystal to take the best aspects of both traditional nonlinear crystals and photonic metasurfaces. In the proof-of-concept experiment, we show that a silicon nitride metasurface decorated quartz crystal can be used for the wavefront shaping of the second harmonic waves generated in quartz. With this crystal-metasurface hybrid platform, the nonlinear vortex beam generation and nonlinear holography were successfully demonstrated. The proposed methodology may have important applications in nonlinear structured light generation, super-resolution imaging, and optical information processing, etc.