Optical Phenomena Research Articles

Rossby waves with barotropic–baroclinic coherent structures and dynamics for the (2 + 1)-dimensional coupled cylindrical KP equations with variable coefficients

Starting from the classical quasi-geostrophic potential vorticity equation with equal depth two-layer fluid, the coupled cylindrical Kadomtsev–Petviashvili (KP) equations with variable coefficients for Rossby waves are studied. To be more general, the phase velocity is considered an indefinite integral about time and improves the analysis procedure. So the variable coefficients are obtained and some previous studies are reasonably explained. The cylindrical wave theory is therewith utilized to reduce the coupled cylindrical KP equations with variable coefficients, and based on the modified Hirota bilinear method, the lump solutions and interaction solutions are found. Through numerical simulations, the Rossby lump waves on both sides of the y axis move closer to the center, and their amplitude gradually decreases and tends to flatten with the generalized Rossby parameter growth. In the Rossby waves flow field, the dipole structures propagate to the east and lead to the appearance of the compress phenomenon during barotropic–baroclinic interaction. It is possibly useful for further theoretical research on atmospheric phenomena.

Effects of the El Niño-Southern Oscillation and seasonal weather conditions on Aedes aegypti infestation in the State of São Paulo (Brazil): A Bayesian spatio-temporal study.

Seasonal fluctuations in weather are recognized as factors that affect both Aedes (Ae.) aegypti mosquitoes and the diseases they carry, such as dengue fever. The El Niño-Southern Oscillation (ENSO) is widely regarded as one of the most impactful atmospheric phenomena on Earth, characterized by the interplay of shifting ocean temperatures, trade wind intensity, and atmospheric pressure, resulting in extensive alterations in climate conditions. In this study, we investigate the influence of ENSO and local weather conditions on the spatio-temporal variability of Ae. aegypti infestation index. We collected seasonal entomological survey data of immature forms of Ae. aegypti mosquitoes (Breteau index), as well as data on temperature, rainfall and the Oceanic Niño Index (ONI) for the period 2008-2018 over the 645 municipalities of the subtropical State of São Paulo (Brazil). We grounded our analytical approach on a Bayesian framework and we used a hierarchical spatio-temporal model to study the relationship between ENSO tracked by ONI, seasonal weather fluctuations and the larval index, while adjusting for population density and wealth inequalities. Our results showed a relevant positive effect for El Niño on the Ae. aegypti larval index. In particular, we found that the number of positive containers would be expected to increase by 1.30-unit (95% Credible Intervals (CI): 1.23 to 1.37) with El Niño events (i.e., ≥ 1°C, moderate to strong) respect to neutral (and weak) events. We also found that seasonal rainfall exceeding 153.12 mm appears to have a notable impact on vector index, leading potentially to the accumulation of ample water in outdoor discarded receptacles, supporting the aquatic phase of mosquito development. Additionally, seasonal temperature above 23.30°C was found positively associated to the larval index. Although the State of São Paulo as a whole has characteristics favourable to proliferation of the vector, there were specific areas with a greater tendency for mosquito infestation, since the most vulnerable areas are predominantly situated in the central and northern regions of the state, with hot spots of abundance in the south, especially during El Niño events. Our findings also indicate that social disparities present in the municipalities contributes to Ae. aegypti proliferation. Considering the anticipated rise in both the frequency and intensity of El Niño events in the forthcoming decades as a consequence of climate change, the urgency to enhance our ability to track and diminish arbovirus outbreaks is crucial.

A tutorial on the physics of light and image shading.

This paper provides an overview of the many different ways that light interacts with surfaces in the natural environment to provide useful information for visual perception. It begins with a discussion of how the concept of light has evolved over the course of human history. It then considers a wide variety of optical phenomena including Lambert's laws of illumination, the effects of microscopic surface structure on patterns of reflection, the bidirectional reflectance distribution function, the refraction of transmitted light, chromatic dispersion, thin film interference, sub-surface scattering, the Fresnel effects, indirect illumination from multiple reflections, caustics, and the structure of the light field. The primary goal of this discussion is to provide the necessary background information to help students and young researchers more easily understand the scientific literature on the perception of 3D shape and material properties from patterns of image shading.

Rationalizing the Influence of Small-Molecule Dopants on Guanine Crystal Morphology.

Many spectacular optical phenomena in animals are produced by reflective assemblies of guanine crystals. The crystals comprise planar H-bonded layers of π-stacked molecules with a high in-plane refractive index. By preferentially expressing the highly reflective π-stacked (100) crystal face and controlling its cross-sectional shape, organisms generate a diverse array of photonic superstructures. How is this precise control over crystal morphology achieved? Recently, it was found that biogenic guanine crystals are composites, containing high quantities of hypoxanthine and xanthine in a molecular alloy. Here, we crystallized guanine in the presence of these dopants and used computations to rationalize their influence on the crystal morphology and energy. Exceptional quantities of hypoxanthine are incorporated into kinetically favored solid solutions, indicating that fast crystallization kinetics underlies the heterogeneous compositions of biogenic guanine crystals. We find that weakening of H-bonding interactions by additive incorporation elongates guanine crystals along the stacking direction-the opposite morphology of biogenic crystals. However, by modulation of the strength of competing in-plane H-bonding interactions, additive incorporation strongly influences the cross-sectional shape of the crystals. Our results suggest that small-molecule H-bond disrupting additives may be simultaneously employed with π-stack blocking additives to generate reflective platelet crystal morphologies exhibited by organisms.

Optically Ambidextrous Reflection Circularly Polarized Luminescence Film with High Dissymmetry Factor and On‐Demand Handedness

AbstractThe self‐assembled cellulose nanocrystal (CNC) film has a left‐handed layered structure, which makes the reflection of right‐handed circularly polarized (CP) light a challenge. Herein, a nematic phase layer is designed and inserted into the chiral organization, to work as a half‐wave retarder and make the ambidextrous CP light reflection. The maximum reflectivity exceeds 80%, which breaks the 50% limitations of single‐direction light reflection and is the current maximum in all the reported CNC‐based films. This “sandwich‐like” structure displays different optical properties on both sides, displayed as the chromatism and the inversion of the circular dichroism signals. The dual CP light reflection and direction‐dependent optical phenomena are reserved in the synthesized circularly polarized luminescence (CPL) film, with the dissymmetry factor (glum) of −0.4245. However, this luminescent intensity and single‐direction emission are not enough in advanced optical systems. This work designs a triple CPL amplification path and develops the handedness inversion strategy, with the glum of −1.0551 and 0.4082. Then, the dual‐directional CPL emission films are designed, where the chiral optics can be switched on‐demand. Finally, the photonic crystal films are applied in the anti‐counterfeit and chiral superstructure induction.

Pressure scaling of femtosecond laser filamentation in air: Prospects for long-range atmospheric propagation

The principal trend of the last decades is the use of laser systems generating ultrashort (femtosecond) laser pulses of gigawatt and terawatt power in various spheres of human activity, in particular, in atmospheric researches. One of the important challenges within this problem is the use of the unique nonlinear optical phenomena manifesting in the atmosphere as pulse self-focusing, light-induced ionization of the medium, plasma generation and laser filamentation for remote laser diagnostics of the aerosol-gas constituents and efficient delivery of concentrated optical energy over long distances in the atmosphere. This brings to the forefront the problem of increasing the actual length of the nonlinear interaction of an ultrashort laser pulse with medium to kilometer distances whereas real physical length of most existing optical paths is usually limited by several hundred meters. We propose and theoretically substantiate an effective way to solve the problem of long-range atmospheric filamentation by transforming the propagation medium itself using short laboratory traces and optical cuvettes with gases of increased (over-atmospheric) pressure. Following the scaling laws of the optical characteristics of pressurized medium, the coefficients describing the interaction between optical wave and medium increase along with the increase in gas pressure. By the numerical simulations in the framework of the nonlinear Schrodinger equation, we show that this makes it possible to emulate kilometers-long atmospheric traces for laser beams of centimeter diameter and terawatt pulse power on the laboratory scale (tens of meters).

Unlocking multi-photon excited luminescence in pyrazolate trinuclear gold clusters for dynamic cell imaging

The family of coinage-metal-based cyclic trinuclear complexes exhibits abundant photophysical properties, promising for diverse applications. However, their utility in biochemistry is often hindered by large particle size and strong hydrophobicity. Meanwhile, the investigation into multi-photon excited luminescence within this family remained undocumented, limiting their potential in bio-imaging. Herein, we unveil the multi-photon excited luminescent properties of pyrazolate-based trinuclear gold(I) clusters, facilitated by excimeric gold(I)···gold(I) interactions, revealing a nonlinear optical phenomenon within this family. Furthermore, to address issues of poor biocompatibility, we employ electrospinning coupled with hydroxypropyl-beta-cyclodextrin as the matrix to fabricate a flexible, durable, transparent, and red emissive film with a photoluminescence quantum yield as high as 88.3%. This strategy not only produces the film with sufficient hydrophilicity and stability, but also achieves the downsizing of trinuclear gold(I) clusters from microscale to nanoscale. Following the instantaneous dissolution of the film in the media, the released trinuclear gold(I) nanoparticles have illuminated cells and bacteria through a real-time, non-toxic, multi-photon bio-imaging approach. This achievement offers a fresh approach for utilizing coinage-metal-based cyclic trinuclear complexes in biochemical fields.

Surpassing the Diffraction Limit in Label-Free Optical Microscopy.

Super-resolution optical microscopy has enhanced our ability to visualize biological structures on the nanoscale. Fluorescence-based techniques are today irreplaceable in exploring the structure and dynamics of biological matter with high specificity and resolution. However, the fluorescence labeling concept narrows the range of observed interactions and fundamentally limits the spatiotemporal resolution. In contrast, emerging label-free imaging methods are not inherently limited by speed and have the potential to capture the entirety of complex biological processes and dynamics. While pushing a complex unlabeled microscopy image beyond the diffraction limit to single-molecule resolution and capturing dynamic processes at biomolecular time scales is widely regarded as unachievable, recent experimental strides suggest that elements of this vision might be already in place. These techniques derive signals directly from the sample using inherent optical phenomena, such as elastic and inelastic scattering, thereby enabling the measurement of additional properties, such as molecular mass, orientation, or chemical composition. This perspective aims to identify the cornerstones of future label-free super-resolution imaging techniques, discuss their practical applications and theoretical challenges, and explore directions that promise to enhance our understanding of complex biological systems through innovative optical advancements. Drawing on both traditional and emerging techniques, label-free super-resolution microscopy is evolving to offer detailed and dynamic imaging of living cells, surpassing the capabilities of conventional methods for visualizing biological complexities without the use of labels.

First-principle calculations of the electronic structure and optical properties of β-Ga2O3 with various vacancy defects

In this work, the effects of five types of vacancy defects on the electronic, optical and thermodynamic properties of β-Ga2O3 were investigated using first-principle calculations. The findings revealed that oxygen vacancies were more prevalent than gallium vacancies, with tetrahedral gallium vacancies being easier to form than octahedral ones. Vacancy defects induced a shift in the energy bands towards the lower energy end, with gallium vacancies reducing the bandgap from 4.9 eV to 3.1 eV, while the effect of oxygen vacancies on the bandgap was negligible. Oxygen vacancies introduced deep impurity levels near the Fermi level, while gallium vacancies introduced shallow impurity levels, primarily due to contributions from O-2p, Ga-4s, and Ga-4p orbital electrons. The differential charge density diagrams illustrated that gallium vacancies had a more pronounced impact on electronic distribution compared to oxygen vacancies, with VO3 exhibiting the least influence. As the temperature increases, the β-Ga2O3 with VO1 and VO2 exhibit higher thermodynamic stability compared to the intrinsic β-Ga2O3 and the one with VO3, while the intrinsic β-Ga2O3 has a superior heat capacity value compared to the β-Ga2O3 containing the five vacancy defects. The defect energy levels resulting from vacancies enhanced light absorption and conductivity, particularly oxygen vacancies, which improved the absorption capacity of β-Ga2O3 in the visible light range. These findings provide valuable insights for elucidating optical absorption experimental phenomena and photoluminescence.

Experimental Observation of Raman Assisted and Kerr Optical Frequency Comb in a 4H-Silicon-Carbide on Insulator Microresonator

Kerr nonlinear microcavities have garnered significant interest owing to their rich dynamics of nonlinear optical phenomena and compatibility with on-chip photonic integration. Recently, silicon carbide has emerged as a compelling platform due to its unique optical properties. In this study, we demonstrate Raman-assisted and Kerr optical frequency generation in a 4H-silicon carbide-on-insulator microresonator. By pumping the transverse electric (TE00) mode within the device, we observe a stimulated Raman scattering (SRS) Stokes with the Raman shift at approximately 775 cm-1, achieved with an on-chip power of 350 mW. Furthermore, by red-tuning the TE00 pump wavelength, we have achieved the coexistence of Raman and Kerr frequency combs. Using another device on the same chip with light variation of the taper we can observe the Raman and Kerr frequency combs within a spectral bandwidth ranging from ∼ 1440 to 1960 nm. The inclusion of the Raman-assisted comb extends the comb’s coverage into longer wavelength regimes, making it highly desirable for spectroscopy applications.

Nanostructure silver absorbance with polarized light spectroscopy (PLS) and mobile imaging

This study presents a novel interdisciplinary approach for characterizing the optical properties of nanostructured silver films, combining methodologies from polarized light spectroscopy (PLS) and mobile app-based spectroscopic image detection. Silver nanofilms were deposited using electron beam evaporation (EBE) and subsequently analyzed for their absorbance across the visible light spectrum through PLS spectroscopy. The innovative aspect of this study lies in the validation of PLS spectral data using a mobile application developed with MIT App Inventor, which analyzes the intensity of light beams captured in images taken by a smartphone. The findings indicate that the silver nanofilm exhibits peak absorbance at approximately 400 nm within the violet region, corroborated by the mobile app’s data, which shows the lowest light intensity. However, discrepancies were observed from 500 to 600 nm, likely due to ambient light interferences and inherent optical phenomena such as diffraction, reflection, and refraction. Despite these deviations, the app’s readings closely align with the PLS data, supporting the film’s selective absorption properties. This study demonstrates the potential of this multidisciplinary technique in nanomaterial research, highlighting the application of nanotechnology in material science and the transformative potential of integrating software engineering for in-depth material characterization. These findings open avenues for advancements in both academic and practical applications.

Optical soliton solutions of the nonlinear complex Ginzburg-Landau equation with the generalized quadratic-cubic law nonlinearity having the chromatic dispersion

In this study, we consider the complex Ginzburg-Landau equation with the generalized quadratic-cubic law of self-phase modulation. This model finds applications in various fields, such as the study of superconductivity, nonlinear optical phenomena, pattern formation, and designing photonic devices and systems. This manuscript successfully employs the new Kudryashov method to derive analytical solutions for complex Ginzburg-Landau equations with the generalized quadratic-cubic law of self-phase modulation. The 3D, contour, and 2D graphical representations of the acquired solutions are represented. Therefore, W-shaped, bright, and dark soliton structures are derived. Through rigorous analysis and interpretation, valuable insights into the influence of the parameters of the presented model on the soliton behavior are achieved.

Ensuring Operational Performance and Environmental Sustainability of Marine Diesel Engines through the Use of Biodiesel Fuel

This article considers the issues of ensuring operational performance and environmental sustainability of marine diesel engines by using biodiesel fuel. This research was conducted on 5S60ME-C8 MAN-B&W Diesel Group and 6DL-16 Daihatsu Diesel marine diesel engines, which are operated using RMG380 petroleum fuel and B10 and B30 biodiesel fuels. The efficiency of biofuel usage was assessed based on environmental (reduced nitrogen oxide concentration in exhaust gases) and economic (increased specific effective fuel consumption) criteria. It was found that the use of B10 and B30 biofuels provides a reduction in nitrogen oxide concentration in exhaust gases by 14.71–25.13% but at the same time increases specific effective fuel consumption by 1.55–6.01%. Optimum fuel injection advance angles were determined that ensure the best thermal energy, economic and environmental performance of diesel engines. The optimum angle of biofuel supply advance is determined experimentally and should correspond to the limits recommended by the diesel engine operating instructions. It has been proven experimentally that the use of biofuel increases the environmental sustainability of marine diesel engines by 13.75–29.42%. It increases the diesel engines environmental safety in case of emergency situations as well as accidental and short-term emissions of exhaust gases with an increased content of nitrogen oxides into the atmosphere phenomena that are possible in starting modes of diesel engine operation as well as in modes of sudden load changes. It is the increase in the environmental friendliness of marine diesel engines in the case of using biofuel that is the most positive criterion and contributes to the intensity of biofuel use in power plants of sea vessels.

Exciton-Exciton Interactions in Van der Waals Heterobilayers

Exciton-exciton interactions are key to understanding nonlinear optical and transport phenomena in van der Waals heterobilayers, which emerged as versatile platforms to study correlated electronic states. We present a combined theory-experiment study of excitonic many-body effects based on first-principle band structures and Coulomb interaction matrix elements. Key to our approach is the explicit treatment of the fermionic substructure of excitons and dynamical screening effects for density-induced energy renormalization and dissipation. We demonstrate that dipolar blueshifts are almost perfectly compensated by many-body effects, mainly by screening-induced self-energy corrections. Moreover, we identify a crossover between attractive and repulsive behavior at elevated exciton densities. Theoretical findings are supported by experimental studies of spectrally narrow, mobile interlayer excitons in atomically reconstructed, h-BN-encapsulated MoSe2/WSe2 heterobilayers. Both theory and experiment show energy renormalization on a scale of a few meV even for high injection densities in the vicinity of the Mott transition. Our results revise the established picture of dipolar repulsion dominating exciton-exciton interactions in van der Waals heterostructures and open up opportunities for their external design. Published by the American Physical Society 2024

Structure factor design of a liquid crystal beam steering device for augmented reality applications

The applications of AR and VR devices have been increasingly important in our daily life. There are some disadvantages remaining to be improved for real time application. In this paper, we demonstrated the design of an experiment based on the Taguchi method targeting a beam steering liquid crystal device possessing a 6 degree steering angle with fast switching (>60Hz) ability for viewing angle expansion in AR/VR devices. The approach of the best structure design was suggested from the recall table that concluded the optical phenomenon was affected by the selected parameters from simulation. The resulting design rule was a tape-out design to prepare the pattern ITO glass. The beam steering device was assembled according to the suggested cell gap. The device evaluation showed a 6.1 degree steering angle as predicted. The response time was measured as 10.5 ms, which is able to be driven well above 60 Hz.

The Diverse Electrochemistry and Photophysics of Pyrrolopyrroles

Pyrrole is among the most popular molecular scaffolds for biology. Tetrapyrroles, such as porphyrins, corrins and their derivatives, are the quintessential redox centers and chromophores exhibiting a wide range of electrochemical and optical characteristics. Similarly, pyrrolopyrroles, built on condensed five-member rings with nitrogens as heteroatoms, offer scaffolds for organic chromophores with diversity of redox and photophysical properties. For example, pyrrolo[3,2-b]pyrroles are stable electron-rich UV absorbers with quadrupole symmetry (Acc. Chem. Res. 2017, 50, 2334-2345). They can act as immensely potent electron donors and attaching electron-accepting moieties to them leads to the emergence of a myriad of optical phenomena, such as excited-state symmetry breaking (Commun. Chem. 2020, 3, 190) and generating white fluorescence by tuning donor-acceptor electronic coupling (Chem. Sci. 2023). Attaching carbonyls to the pyrrolopyrrole rings drastically changes their electronic properties, making them pronouncedly electron deficient and shifting their absorption to the visible spectral region. For example, 2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-diones, or diketopyrrolopyrroles (DPPs) for short, are excellent electron acceptors and photooxidants (Adv. Opt. Matter. 2015, 3, 2018-320). Their reduction potentials are susceptible to localized electric fields, which has allowed demonstrating dipole-induced rectification of photoinduced hole transfer (Angew. Chem. Int. Ed. 2018, 57, 12365-12369). This field susceptibility extends to the optical properties of DPPs, providing an extra dimension in their utility for photonics and optoelectronics. DPPs, and pyrrolopyrroles in general, are built on small bicyclic scaffolds, i.e., considerably smaller than those of other multi-pyrrole chromophores. The small size enhances the susceptibility of their redox properties to solvation and makes them attractive photoprobes. Therefore, this class of compounds have become indispensable agents for electrochemical and photonic science and engineering.

(Invited) Resonant Exciton Transfer in Mixed-Dimensional Heterostructures for Overcoming Dimensional Restrictions in Optical Processes

Nanomaterials exhibit unique optical phenomena, in particular excitonic quantum processes occurring at room temperature. The low dimensionality, however, imposes strict requirements for conventional optical excitation, and an approach for bypassing such restrictions is desirable. Here we report on exciton transfer in carbon-nanotube/tungsten-diselenide heterostructures, where band alignment can be systematically varied. The mixed-dimensional heterostructures display a pronounced exciton reservoir effect where the longer-lifetime excitons within the two-dimensional semiconductor are funneled into carbon nanotubes through diffusion. This new excitation pathway presents several advantages, including larger absorption areas, broadband spectral response, and polarization-independent efficiency. When band alignment is resonant, we observe substantially more efficient excitation via tungsten diselenide compared to direct excitation of the nanotube. We further demonstrate simultaneous bright emission from an array of carbon nanotubes with varied chiralities and orientations. Our findings show the potential of mixed-dimensional heterostructures and band alignment engineering for energy harvesting and quantum applications through exciton manipulation.Parts of this study are supported by JSPS (KAKENHI JP22K14624, JP22K14625, JP21K14484, JP22F22350, JP22K14623, JP21H05233, JP23H00262, JP20H02558) and MEXT (ARIM JPMXP1222UT1135). Y.R.C. is supported by JSPS (International Research Fellow). N.F. and C.F.F. are supported by RIKEN Special Postdoctoral Researcher Program. We thank the Advanced Manufacturing Support Team at RIKEN for technical assistance.[1] N. Fang, D. Yamashita, S. Fujii, M. Maruyama, Y. Gao, Y. R. Chang, C. F. Fong, K. Otsuka, K. Nagashio, S. Okada, Y. K. Kato, "Resonant exciton transfer in mixed-dimensional heterostructures for overcoming dimensional restrictions in optical processes," Nature Commun., accepted (2023). Preprint at arXiv:2307.07124.

Satellite and in situ measurements of water vapour in the Brazil‐Malvinas Confluence region

AbstractThis decade‐long study from the INTERCONF programme addresses the data gap on ocean dynamics in the Southern Hemisphere. Focusing on the Brazil‐Malvinas Confluence (BMC), we investigated the effect of temperature differences between the warm Brazil Current (BC) and the cold Malvinas Current (MC) on water vapour in the marine atmospheric boundary layer (MABL). Our results show a clear distinction: warmer BMC waters have 32% more water vapour (2 kg·m−2 on average) compared to the MC. This highlights the direct link between ocean temperatures and atmospheric processes. Analysis of radiosonde data alongside satellite measurements showed better agreement over cooler waters with lower water vapour, leading to lower variability. This suggests less atmospheric turbulence and improved data compatibility, especially for satellite retrievals such as AIRS. Comparisons between reanalysis data (CFSR), satellite sounders (AIRS) and radiosondes (RS) showed consistent air temperature profiles, with average errors within the 10% threshold for satellite measurements. While capturing humidity variations remains a challenge, especially at high concentrations (indicated by higher mean squared error values), our study highlights the reliability of satellite data, particularly over the cold BMC region. This research highlights the importance of studying the interactions between ocean fronts and atmospheric phenomena for a complete picture of Southern Hemisphere ocean dynamics. It offers valuable insights for scientists across disciplines, providing a broad perspective on the results and their significance in different contexts.

Optical Disc Structures and Diffraction Patterns: Theoretical Foundations and Experimental Applications

Abstract This investigation advances the experimental exploration of optical discs' diffraction phenomena, meticulously constructing optical pathways to ascertain the track pitch within the disc employing both transmission and reflection grating paradigms. Furthermore, this study devises a novel apparatus and methodology for the precise measurement of optical wavelengths, aiming to elucidate the intricate diffraction patterns and the underlying mechanisms of optical discs' structure. This endeavor not only validates the methodological soundness and efficacy of the proposed approach but also pioneers new avenues for research into physics experiments leveraging optical discs. The application of optical discs in educational settings transcends traditional experimental pedagogy, fostering students' capabilities to independently conceptualize experiments and delve into scientific explorations.

"Nonperturbative Nonlinearities": Perhaps Less than Meets the Eye.

We address challenges in characterizing changes in permittivity and refractive index beyond standard perturbative methods with special attention given to transparent conductive oxides (TCOs). We unveil a realistic limit to permittivity changes under high optical power densities. Our study covers both slow and ultrafast nonlinearities, demonstrating that all nonlinearities induce refractive index changes accurately described by a simple curve with saturation electric field (or irradiance) and maximum change of permittivity at saturation. Our model, grounded in material properties, like oscillator strength and characteristic times, offers a robust framework for understanding and predicting nonlinear optical phenomena in TCOs and other materials. We differentiate between the significance of higher-order nonlinear susceptibilities in ultrafast and slow nonlinear scenarios. We aim to provide valuable insights for researchers exploring strong light-matter interaction.