Nonlinear Shaping Research Articles

2-dB SNR Gain from Nonlinear Radio Signal Shaping in a Digital-Analog Hybrid RoF System

2-dB SNR Gain from Nonlinear Radio Signal Shaping in a Digital-Analog Hybrid RoF System

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.

Ultrafast reverse saturable absorption and all-optical computing with boron dipyrromethene (BODIPY) chromophore derivatives

Ultrafast reverse saturable absorption (RSA) in chromophore-based borondipyrro-methenes (BODIPYs) derivatives, 1,7-Diphenyl-3,5-bis(9,9-dimethyl-9H-fluoren-2-yl)-boron-diuoride-azadipyrromethene (ZL-61) and 1,7-Diphenyl-3,5-bis(4-(1,2,2-triphenyl-vinyl)phenyl)-boron-diuoride azadipyrromethene (ZL-22), has been theoretically analyzed with femtosecond (fs) laser pulses at 800 nm and 850 nm. The results are in good agreement with the reported experimental results. The effect of input pulse intensity, pulse width, nonlinear absorption (NLA) coefficients, sample thickness and laser pulse shaping on transmittance has been studied and optimized for high contrast and low-power operation. All-optical fs NOT and the universal NOR and NAND Boolean logic gates have been designed with ZL-61 and ZL-22. The logic gates with top-hat input pulse profile have a sharp switch ON/OFF time compared to the Gaussian input laser profile. Ultrafast operation at relatively low pump intensities opens up exciting prospects for the applicability of BODIPY derivatives for ultrafast low-power all-optical computing and information processing.

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.

The statistical characteristics of the atmospheric anisotropic inhomogeneities and their effect on the intensity fluctuations of infrasound field

The influence of anisotropic wind velocity and temperature inhomogeneities on the attenuation of infrasound field intensity with increasing distance from a point source and on its altitude distribution is studied. The field is calculated as a function of receiver height and horizontal distance from the source using method of the pseudo-differential parabolic equation for the atmosphere with model realizations of anisotropic effective sound speed fluctuations. These realizations are obtained from the nonlinear shaping model for the gravity wave perturbations which produces the fluctuations with both the vertical and horizontal spectra consistent with the observed spectra. When propagating in the stratospheric and thermospheric wave guides the multiple scattering of infrasound field from the anisotropic fluctuations results in certain vertical wave number spectra and probability density functions of infrasound intensity fluctuations in the stratospheric (altitudes 30–40 km) and mesospheric layers (50–70 km). The statistical characteristics of the intensity fluctuations as a function of distance from the source (up to 2200 km) were studied. The same characteristics were obtained for the infrasound field scattered from the inhomogeneities whose vertical profile was retrieved from the infrasound signals from surface explosions detected in the shadow zone.

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.

Robust Q-compensated multidimensional impedance inversion using seislet-domain shaping regularization

Acoustic impedance (AI) inversion plays a vital role in seismic interpretation because AI contains valuable information on lithology and contributes to reservoir characterization. However, the effect of anelastic attenuation dissipates the energy and distorts the phase of seismic waves during their propagation in the earth. Such attenuation-induced effects will degrade the quality of AI inversion unless some preprocessing routines are performed in advance (e.g., inverse Q filtering). In order to invert for AI from nonstationary seismic data directly and enhance the lateral continuity, we have developed a robust Q-compensated multidimensional AI inversion method. The proposed method incorporates the Q-filtering operator into the conventional convolution model and provides an improved iteration scheme, which can avoid some of the errors introduced by those compensation-related processing routines. Furthermore, with the help of seislet nonlinear shaping regularization, the proposed method can accelerate the convergence rate during inversion and further improve the lateral continuity and accuracy of the final inverted results in the presence of noise. Synthetic and field data have been used to validate the effectiveness and robustness of the proposed method. The results demonstrate that compared with the conventional method, the proposed method can retrieve AI from nonstationary seismic data directly with improved efficiency and remove those possible artifacts caused by ambient noise.

Exploring the Nonlinear Interplay between Urban Morphology and Nighttime Thermal Environment

The nighttime thermal environment affects people's nighttime leisure activities and energy consumption. While increasing studies have examined the interplay between urban morphologies and daytime temperature, a gap exists in understanding the nonlinear relationship in the nighttime thermal environment. To address this, the study employs a data-driven ensemble model to downscale Moderate Resolution Imaging Spectroradiometer (MODIS) thermal environment data for four seasons, aligning it with the scale of urban morphology. Furthermore, an additive interpretation algorithm investigates the impact of nonlinear factors shaping the urban thermal environment during nighttime. The findings reveal that in contrast to daytime temperatures, built environment variables exert a more pronounced effect on nighttime surface temperatures than natural variables. Specifically, plot ratio and building height are the greatest contributors to the warming observed across all seasons. On the other hand, increasing the sky view factor of streets proves to be an effective strategy for mitigating nighttime temperatures. Overall, our study sheds new light on the complex interplay between urbanization and the nighttime thermal environment, assisting planners in understanding how the built environment affects the urban temperature and sustainable development path.

Design of nonlinear pulse shaper for flexible repetition rate ultrashort pulse generation

Nonlinear pulse shaping based on Mamyshev regenerator is a powerful approach for ultrashort pulse generation. The performance strongly depends on the initial seed parameters. We investigate and design a nonlinear pulse shaper seeded by a long pulsed gain-switched laser diode for generation of high quality ultrashort pulses with flexible repetition rate. The shaper architecture provides more flexibility on the input diode requirements and can yield shorter pulses with the improved laser relative intensity noise. The system optimization is based on numerical simulations mapping the favourable parameters at each stage of the system and enabling identification of limiting factors.

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

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

Non-linear virtual impedance shaping strategy for predominantly resistive islanded power networks

Non-linear virtual impedance shaping strategy for predominantly resistive islanded power networks

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.

Probabilistic Amplitude Shaping and Nonlinearity Tolerance: Analysis and Sequence Selection Method

Probabilistic amplitude shaping (PAS) is a practical means to achieve a shaping gain in optical fiber communication. However, PAS and shaping in general also affect the signal-dependent generation of nonlinear interference. This provides an opportunity for nonlinearity mitigation through PAS, which is also referred to as a nonlinear shaping gain. In this paper, we introduce a linear lowpass filter model that relates transmitted symbol-energy sequences and nonlinear distortion experienced in an optical fiber channel. Based on this model, we conduct a nonlinearity analysis of PAS with respect to shaping blocklength and mapping strategy. Our model explains results and relationships found in literature and can be used as a design tool for PAS with improved nonlinearity tolerance. We use the model to introduce a new metric for PAS with sequence selection. We perform simulations of selection-based PAS with various amplitude shapers and mapping strategies to demonstrate the effectiveness of the new metric in different optical fiber system scenarios.

Eco-Friendly Transitions in Top Ten CO2 Producing Countries: A Dynamic Panel Investigation of Green Finance, Technology Transfer and Financial Development for Reducing Environmental Degradation

This study delves into the imperative challenge of fostering eco-friendly transitions within the top 10 CO2 producing countries, employing a sophisticated dynamic panel investigation. Centered on the pivotal drivers of green finance, technology transfer, and financial development, the research seeks to comprehensively understand their synergistic role in mitigating environmental degradation. Utilizing advanced econometric techniques, notably the Nonlinear Autoregressive Distributed Lag (NARDL) model, the investigation unfolds the intricate dynamics and nonlinear relationships shaping the effectiveness of these transitions over time. The findings not only contribute empirical insights but also bear substantial policy implications. They underscore the necessity for robust regulatory frameworks and international cooperation to incentivize green investments, facilitate technology transfer, and promote financial development geared towards sustainability. In addressing the environmental challenges posed by these leading CO2 emitters, this research advocates for a holistic approach that integrates economic growth with environmental stewardship, thereby paving the way for transformative and resilient eco-friendly practices on a global scale.

Nonlinear generation of hollow beams in tunable plasmonic nanosuspensions

We experimentally demonstrate that a probe beam at one wavelength, although exhibiting a weak nonlinear response on its own, can be modulated and controlled by a pump beam at another wavelength in plasmonic nanosuspensions, leading to ring-shaped pattern generation. In particular, we show that the probe and pump wavelengths can be interchanged, but the hollow beam patterns appear only in the probe beam, thanks to the gold nanosuspensions that exhibit a strong nonlinear response to pump beam illumination at the plasmonic resonant frequencies. Colloidal suspensions consisting of either gold nanospheres or gold nanorods are employed as nonlinear media, which give rise to refractive index changes and cross-phase modulation between the two beams. We perform a series of experiments to examine the dynamics of hollow beam generation at a fixed probe power as the pump power is varied and find that nonlinear beam shaping has a different power threshold in different nanosuspensions. Our results will enhance the understanding of nonlinear light–matter interactions in plasmonic nanosuspensions, which may be useful for applications in controlling light by light and in optical limiting.

Polarization-controlled nonlinear computer-generated holography

Dynamic phase-only beam shaping with a liquid crystal spatial light modulator is a powerful technique for tailoring the intensity profile or wave front of a beam. While shaping and controlling the light field is a highly researched topic, dynamic nonlinear beam shaping has hardly been explored so far. One potential reason is that generating the second harmonic is a degenerate process as it mixes two fields at the same frequency. To overcome this problem, we propose the use of type II phase matching as a control mechanism to distinguish between the two fields. Our experiments demonstrate that distributions of arbitrary intensity can be shaped in the frequency-converted field at the same quality as for linear beam shaping and with conversion efficiencies similar to without beam shaping. We envision this method as a milestone toward beam shaping beyond the physical limits of liquid crystal displays by facilitating dynamic phase-only beam shaping in the ultraviolet spectral range.

On the Nonlinear Shaping Gain With Probabilistic Shaping and Carrier Phase Recovery

The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1\times 180$</tex-math></inline-formula> km, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$15\times 80$</tex-math></inline-formula> km, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$27\times 80$</tex-math></inline-formula> km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm.

Multiplexing Linear and Nonlinear Bragg Diffractions through Volume Gratings Fabricated by Femtosecond Laser Writing in Lithium Niobate Crystal

The femtosecond-laser-writing technique provides a flexible method for fabrication of nonlinear photonic crystals in three dimensions, providing structures that enable efficient complex nonlinear wave interactions and modulation for applications including nonlinear holography, nonlinear beam shaping, and waveguide-integrated wavelength conversion. However, the tightly focused laser pulse inevitably causes structural modification and then changes the local refractive index, resulting in additional linear modulation of the interacting waves. Here, we use the same periodic distributions of the refractive index and the second-order nonlinear coefficient for grating arrays engineered in lithium niobate crystals by femtosecond laser writing to achieve polarization-dependent linear and nonlinear Bragg diffractions simultaneously. The experimental results show that the linear and nonlinear diffraction efficiencies range up to 31% and 2.9 × 10−5, respectively, for grating arrays with dimensions of 100 μm (x) × 100 μm (y) × 100 μm (z). This work paves the way toward the realization of the multiplexing of linear and nonlinear optical modulations in a single structure for potential applications that include multidimensional optical data storage and optical coding.

Heatwaves and Mortality in Spain and Greece: A Comparative Analysis

Background: Heatwaves have become a public health emergency raising great public health concerns. Correspondingly, due to climate change, the increase in extreme weather events, such as heatwaves, floods and hurricanes, is predicted through state-of-the-art models and robust statistical analyses. Since the Mediterranean basin is recognized as the most prominent global climate change hot spot, further scientific research on the future impacts of heatwaves on human mortality, as well as human health and well-being, in the Mediterranean region is critical. Methods: The aim of the present study is to compare the relationship between three different causes of mortality (i.e., cardiological, respiratory and cardiorespiratory) and temperature between two countries (Spain and Greece) and five cities (i.e., Madrid, Barcelona, Valencia, Attica and Thessaloniki). To compare the five cities under examination, a robust statistical methodological framework (i.e., Threshold Regression Analysis (TRA)) was applied so as to examine the critical value above which the mean temperature affects cardiological, respiratory and cardiorespiratory mortality. Results: Our results prove that the relationship between mortality and temperature is a nonlinear relationship shaping a U- or J-shaped curve, meaning that mortality is affected by temperature in a non-constant way, indicating that mortality increases during both low and high temperatures. Conclusions: By calculating different temperature thresholds for the five cities under examination, we show that different temperature thresholds are more accurate for different climatic conditions. Hence, climatic conditions should be taken into account when examining the impacts of temperature on human health.