The ability to interpret information through automatic sensors is one of the most important pillars of modern technology. In particular, the potential of biosensors has been used to evaluate biological information of living organisms, and to detect danger or predict urgent situations in a battlefield, as in the invasion of SARS-CoV-2 in this era. This work is devoted to describing a panoramic overview of optical biosensors that can be improved by the assistance of nonlinear optics and machine learning methods. Optical biosensors have demonstrated their effectiveness in detecting a diverse range of viruses. Specifically, the SARS-CoV-2 virus has generated disturbance all over the world, and biosensors have emerged as a key for providing an analysis based on physical and chemical phenomena. In this perspective, we highlight how multiphoton interactions can be responsible for an enhancement in sensibility exhibited by biosensors. The nonlinear optical effects open up a series of options to expand the applications of optical biosensors. Nonlinearities together with computer tools are suitable for the identification of complex low-dimensional agents. Machine learning methods can approximate functions to reveal patterns in the detection of dynamic objects in the human body and determine viruses, harmful entities, or strange kinetics in cells.

This study analyzes the nonlinear optical properties exhibited by graphene, focusing on the nonlinear absorption coefficient and the nonlinear refractive index. The evaluation was conducted using the Z-scan technique with a 532 nm wavelength laser at various intensities. The nonlinear optical absorption and the nonlinear optical refractive index were measured. Four machine learning models, including linear regression, decision trees, random forests, and gradient boosting regression, were trained to analyze how the nonlinear optical absorption coefficient varies with variables such as spot radius, maximum energy, and normalized minimum transmission. The models were trained with synthetic data and subsequently validated with experimental data. Decision tree-based models, such as random forests and gradient boosting regression, demonstrated superior performance compared to linear regression, especially in terms of mean squared error. This work provides a detailed assessment of the nonlinear optical properties of graphene and highlights the effectiveness of machine learning methods in this context.

Fractional electrodamage in A549 human lung cancer cells was analyzed by introducing a non-integer order parameter to model the influence of electrical stimulation on cellular behavior. Numerical simulations were conducted to evaluate the conversion of electrical energy to heat within A549 cancer cells, emphasizing the electrocapacitive effects and electrical conductivity in modulating dielectric properties. Using the Riemann–Liouville fractional calculus framework, experimental results were accurately fitted, demonstrating the non-integer nature of electrodamage processes. The study identified a strong dependency of electrical behavior on frequency, revealing a critical role of fractional dynamics in the dielectric breakdown and susceptibility of A549 cells to voltage changes. These findings advance our understanding of cellular responses to electrical fields and provide insights into applications in cancer diagnostics, monitoring, and potential therapeutic treatments.

Methylene blue (MB) concentrations in residual water were detected using fractional calculus, the Rössler chaotic attractor and laser systems. A Nd:YVO4 nanosecond pulsed laser at 532 nm, with pulse energies ranging from 2 µJ to 7 µJ, was applied to irradiate different water samples containing MB concentrations from 20 µl to 100 µl. Fractional calculus was employed with the purpose of modeling the temperature distribution in the samples, with the Caputo fractional derivative describing photothermal effects induced by laser irradiation. Different MB concentrations were detected by using the Rössler chaotic attractor, it monitored variation on concentrations, associating attractor shapes with MB concentrations. Lower concentrations showed a weaker attractor response, whereas higher concentrations manifest stronger attractor shapes in magnitude. Raman spectroscopy confirmed the detection of MB in residual water from the Requena dam, located in Tepeji del Río de Ocampo, Hidalgo, Mexico. The application of fractional calculus improved the prediction of heat distribution in the samples, by incorporating numerical simulation. The results suggest that this approach is suitable for real-time monitoring, as it associates MB concentrations with distinct chaotic attractor shapes. This technique shows promise for the detection of other contaminants as well. Future research should focus on refining this method and expanding its application to develop innovative monitoring solutions.

A fractional description for the optically induced mechanisms responsible for conductivity and multiphotonic effects in ZnO nanomaterials is studied here. Photoconductive, electrical, and nonlinear optical phenomena exhibited by pure micro and nanostructured ZnO samples were analyzed. A hydrothermal approach was used to synthetize ZnO micro-sized crystals, while a spray pyrolysis technique was employed to prepare ZnO nanostructures. A contrast in the fractional electrical behavior and photoconductivity was identified for the samples studied. A positive nonlinear refractive index was measured on the nanoscale sample using the z-scan technique, which endows it with a dominant real part for the third-order optical nonlinearity. The absence of nonlinear optical absorption, along with a strong optical Kerr effect in the ZnO nanostructures, shows favorable perspectives for their potential use in the development of all-optical switching devices. Fractional models for predicting electronic and nonlinear interactions in nanosystems could pave the way for the development of optoelectronic circuits and ultrafast functions controlled by ZnO photo technology.

This work reports the modification in the homogeneity of ablation effects with the assistance of nonlinear optical phenomena exhibited by C. albicans ATCC 10231, forming a biofilm. Equivalent optical energies with different levels of intensity were irradiated in comparative samples, and significant changes were observed. Nanosecond pulses provided by an Nd:YAG laser system at a 532 nm wavelength in a single-beam experiment were employed to explore the photodamage and the nonlinear optical transmittance. A nonlinear optical absorption coefficient −2 × 10⁻⁶ cm/W was measured in the samples studied. It is reported that multiphotonic interactions can promote more symmetric optical damage derived by faster changes in the evolution of fractional photoenergy transference. The electrochemical response of the sample was studied to further investigate the electronic dynamics dependent on electrical frequency, and an electro-capacitive behavior in the sample was identified. Fractional differential calculations were proposed to describe the thermal transport induced by nanosecond pulses in the fungi media. These results highlight the nonlinear optical effects to be considered as a base for developing photothermally activated phototechnology and high-precision photodamage in biological systems.