Inhomogeneous Refractive Index Research Articles

Investigation of microwave power transfer near sea surface with 2D parabolic equation method

AbstractDue to the existence of the evaporation duct near‐sea‐surface described as an inhomogeneous refractive index of atmosphere, microwaves can be trapped in the duct and propagate along it. To investigate wireless power transfer (WPT) over the sea surface, we utilize the two‐dimensional parabolic equation to calculate the electric field distribution and to obtain the transferred power. By analysing the propagation results with specific evaluation functions, we obtained the proper conditions for long‐distance WPT over the sea surface. When the initial field distributes uniformly on the one‐meter aperture, the frequency is 12 GHz, and the centre position is 4 m, a unique focusing spot can be obtained in the duct and nearly 5%, 8%, and 12% of the initial power remains at a distance of 10 km with a receiving aperture of 1, 2, and 3 m, respectively. The presented WPT scheme near the sea surface has potential applications in the power supply or charging for ships or small islands.

Simulation of Inhomogeneous Refractive Index Fields Induced by Hot Tailored Forming Components

For effective quality control in hot forming applications, it is imperative that optical geometry reconstruction is conducted while the workpiece remains in its hot state to ensure the early detection of material distortion effects. This requirement is especially vital in the fabrication of hybrid bulk metal components with locally adapted properties, which are essential to address current challenges and demands on components, as well as to conserve resources. The utilization of hybrid materials results in differing thermal expansion coefficients, which significantly impact the shrinkage behavior of the component. Furthermore, the formation of these components involves exposure to high‐temperature gradients up to 1100 °C, causing the surrounding air to heat up and result in density variations. These variations generate an inhomogeneous refractive index field (IRIF), which substantially affects the surface reconstruction capabilities of optical measurement systems. Understanding the formation and dynamics of these refractive index fields is crucial to minimize uncertainties in optical measurements. This study aims to provide a comprehensive simulation model for the IRIF generated by hot‐forged tailored forming components. Utilizing this model, a priori information on the propagation characteristics of the IRIF can be obtained, thereby facilitating optimized positioning of the measurement system and minimizing reconstruction errors.

Turbulence-enhanced THz generation by multiple chaotically-distributed femtosecond filaments in air

Remote generation of electromagnetic waves in the terahertz (THz) by the volume of air medium gains increasing scientific interest due to the demand for this spectral range in solving various practical problems including those belonging to the nonlinear atmospheric optics. During self-focusing and filamentation of high-power femtosecond laser pulses in air, the source of THz radiation is the plasma of laser filaments. One of the main challenges of THz generation by a laser filament is increasing the value of optical energy conversion to the long-wavelength band. In this paper, we present the results of our studies on DC-biased THz generation during single-color filamentation in air of focused femtosecond Ti:Sapphire-laser pulses (800 nm, pulse energy up to 40 mJ). The distinctive feature of our study is that a femtosecond optical pulse propagates through a spatially-localized heated air layer containing randomly inhomogeneous refractive index perturbations, which mimics strong air turbulence. For the first time to our knowledge, we show, that the turbulent air layer formed at the beginning of the optical path allows increasing the yield of THz radiation up to 1.5 times due to the formation of multiple chaotically-arranged filaments resulting from random perturbations of the optical beam energy profile that reduces the subsequent THz (re)absorption in the filament plasma.

A combined uncertainty and sensitivity analysis of melting in a cubical cavity, Part A: Model validation

Latent heat thermal energy storage systems exploit the solid–liquid phase transition of a material to store thermal energy almost isothermally with high energy density. Numerical methods are increasingly being used for the targeted design of these storage systems. The problem, however, is that the results obtained with these methods – despite a frequently shown near-perfect agreement between validation experiments and simulation results – are subject to large uncertainty. To illustrate the extent of this problem and to show approaches to solving it, a combined uncertainty and sensitivity analysis of the melting process of a paraffin (octadecane) in a cuboid heated from one side is carried out in this two-paper series. In part A, we present the model and validate it; in part B we use it to carry out the combined uncertainty and sensitivity analysis. The validation of the model is performed with the help of experimental results. For this purpose, we measure the liquid phase fraction, the position of the phase boundary, the velocity field in the liquid and the temperature inside the test capsule. We make sure that the experimental results are reproducible. Systematic deviations are discussed and, if possible, the results are corrected for their value. When measuring the velocity field using particle image velocimetry (PIV), the greatest systematic deviation is due to the inhomogeneous refractive index field in the liquid phase. Finally, it is shown that, in the present case, the influence is very low if constant material properties evaluated at the mean temperature are taken for each phase compared to a temperature-dependent implementation. An exception is the density. If the density change during melting is not taken into account the deviation of the melt fraction lies between 6 and 8%. In summary, the validation of the numerical model is very satisfactory and demonstrates the suitability of the model for performing the investigations of the part B paper.

Deepened Photodynamic Therapy through Skin Optical Clearing Technology in the Visible Light Window.

The trade-off that shorter wavelength light facilitates the efficient generation of reactive oxygen species (ROS) from photosensitizer (PS) while facing the drawback of limited penetration depth through skin tissue restricts the further development of photodynamic therapy (PDT). Here, we address this contradiction and achieve visible-light-tailored deep PDT combined with the skin optical clearing technology. With the help of the prepared skin optical clearing gel, the refractive index inhomogeneity between skin tissue components is greatly attenuated, and the light scattering effect within the skin tissue is remarkably reduced. As a consequence, the transmittance of visible light at 600 nm through in vitro porcine skin and in vivo mouse skin after treatment increases from approximately 10 and 40 to 70 and 70%, respectively. Furthermore, in the tumor cell eradication experiment, the local ROS generation efficiency in the experimental group is several times higher than that in the control group owing to improved visible transmittance, which is thus responsible for the complete eradication of tumor cells, even when shaded by skin tissue. The results suggest that this strategy may serve as a valuable supplement to the current deep PDT strategies.

Study of short-wavelength pass dichroic laser mirror coatings with hafnia–silica mixture layers

Hafnia/silica (HfO2/SiO2) short-wavelength pass dichroic laser mirror (DLM) coatings are widely utilized in high-power laser systems. However, the half-wave hole effect resulting from the refractive index inhomogeneity of HfO2 severely restricts the spectra and potential applications of these coatings. To address this issue, an investigation was conducted on HfO2–SiO2 mixture coatings with different proportions, which were produced by electron beam co-evaporation. Compared to the inhomogeneous growth characteristics observed in pure HfO2 coatings, the introduction of 10 % or higher SiO2 admixing in HfO2–SiO2 mixture coatings results in an amorphous structure characterized by excellent refractive index homogeneity and improved surface smoothness. Leveraging this, different DLM coatings with the objective of achieving high transmittance across the 400 to 900 nm range were designed and prepared, while ensuring high reflectance at 1064 nm. The incorporation of HfO2–SiO2 mixture layers instead of pure HfO2 layers in the mirror coatings led to a fundamental inhibition of the half-wave hole effect throughout the entire broad transmission band, resulting in a substantial improvement in the optical performance of the coatings. Moreover, by incorporating several types of HfO2–SiO2 mixture layers with different proportions in the coating stacks, the transmittance of DLM coatings in the pass band can be further increased, and the transmission fluctuations at different wavelengths can be further compressed. Additionally, compared to traditional DLM coatings with HfO2 layers, DLM coatings incorporating HfO2–SiO2 mixture layers exhibit lower roughness, higher laser-induced damage threshold (LIDT) at 532 nm, and similar LIDT at 1064 nm. These results indicate a promising strategy for fabricating DLM coatings tailored for high-power laser systems.

Formation of multiple complex light structures simultaneously in 3D volume using a single binary phase mask

Complex structure formation inside or through turbid media is a challenging task due to refractive index inhomogeneity, random light scattering, and speckle noise formation. In this article, we have coupled the data regression model in the R-squared metric and used its advantages as a fitness function in the genetic algorithm to advance the resolution and structural uniformity. As a compatible system with the binary genetic algorithm, we have presented a cost-effective iterative wavefront shaping system-design with binary phase modulation using an affordable ferroelectric liquid crystal (FLC) based binary-phase spatial light modulator (SLM). R-squared metric in the genetic algorithm is analyzed to optimize the binary phase mask, and the prototype system based on iterative binary phase modulation has been validated with a 120-grit ground glass diffuser and fresh chicken tissues of thickness 307 {upmu }text {m} and 812 {upmu }text {m}. The detailed results show that the proposed cost-effective wavefront shaping system with data regression model assisted R-squared fitness function can construct high-resolution multiple complex hetero-structures simultaneously in 3D volume using an optimized single phase-mask.

Nonlinear multispectral tomographic absorption deflection spectroscopy based on Bayesian estimation for spatially resolved multiparameter measurement in methane flame exhaust

In aerospace propulsion systems with high temperature, pressure, and distortion, inhomogeneous thermophysical gradients can cause line-of-sight deflection and spectral integral deviation. This introduces nonlinearity and measurement error into spectral models, impacting multiparameter field measurements. To address this, we developed a nonlinear multispectral tomographic absorption deflection spectroscopy (MTADS) technique, based on Bayesian inference, for temperature and gas concentration prediction. Our forward model considers inhomogeneous refractive index gradient and laser deflection, synthesising multispectral laser absorption signal through a gas mixing equation and multipoint ray tracing. Simulation results reveal inhomogeneous parameter distribution can cause non-Gaussian and non-zero mean deviations of the spectral absorption signal. The inverse model increases spectral lines to expand measurement signals under sparse optical arrangements. Combining the measured laser absorption signal with Bayesian statistical information of the estimated parameter field improves measurement robustness and accuracy. The maximum a posteriori (MAP) estimation introduces priors such as experiment samples, computational fluid dynamics data, and diffusive transport-induced spatial smoothing. A proof-of-concept based on methane diffusion flame data demonstrates the effectiveness of MTADS, enabling quantitative flame topology and parameter distribution, more accurate 2D temperature, and concentration imaging. These measurements are crucial for revealing chemical reaction dynamics and monitoring combustion systems.

Solutions Mixing Visualization in Continuous-Flow Microreactors via Interferometric Technique

The paper demonstrates the potential of interferometry as a visualization technique for studying the mixing processes of liquid reagents in continuous-flow microreactors. We visualized two types of instabilities: double-diffusion convection and Marangoni soluto-capillary convection. We employed two optical schemes, depending on how large values of refractive index inhomogeneities resulting from instabilities needed to be visualized, including the shear interferometer and the Fizeau interferometer. The interferometry enabled a qualitative investigation of the structure and dynamics of the generated convection. In addition, by implementing the phase shift method by the IntelliWave program, we quantified the efficiency of the mixing process between pumped liquids. These quantitative findings complemented our qualitative visualization, providing further evidence of the effectiveness of interferometry in studying mixing processes. Our results confirm that the interferometry technique is an effective tool for the visualization and analysis of convective flows in continuous-flow microreactors. Moreover, the insights gained from this research contribute to the broader understanding and optimization of mixing processes in microreactor systems.

Quantitative evaluation of refractive index inhomogeneity and its effect on the imaging performance of high-precision injection molded optical lens

High-precision injection molded plastic lenses are gradually substituting the application of glass lenses in advanced imaging and illumination optical systems for their high efficiency and reproducibility. Despite the surface deviation of the plastic lenses having been reduced to micron dimension, the imaging performance of the systems could not be guaranteed. More and more investigations demonstrated that the inhomogeneity of refractive index (RI) variation of plastic lenses was much higher than that of glass lenses. However, the effect of refractive index inhomogeneity on imaging performance is still not well understood, and is not fully considered in the optical design and injection molding process. Thus, an integrated analytical approach was proposed to quantitatively evaluate the inhomogeneity of the refractive index and to reveal its effect on the imaging performance of the optical system. It was found that the inhomogeneity reached 3.44 × 10−3, which was three orders of magnitude higher than that of the glass blank (2.80 × 10−6). Both the magnitude and distribution of refractive index variation significantly degraded the quality and homogeneity of the modulation transfer function (MTF) and spot diagram, from calculated imaging performance considering the inhomogeneity. The maximum MTF was reduced by 60 % compared with the design value. Comparative investigation also demonstrated that refractive index inhomogeneity had an equivalent effect on the imaging performance in comparison with the micron order surface deviation. Reducing the degradation of refractive index inhomogeneity provides an efficient way to improve the imaging performance of advanced optical systems.

Nonlinear waves in a composite optical structure containing a dielectric layer between a photorefractive crystal and a medium with an exponential index profile

Three-layered asymmetric structure with different optical properties of the layers is considered. The structure consist of a photorefractive crystal with diffusion nonlinearity and very weak dark intensity, which is separated by optically linear dielectric layer from medium with spatially distributed refractive index according with an exponential profile. The paper objective is a theoretical analysis of wave disturbances arising from the introduction of a dielectric waveguide layer between photorefractive and graded-index media. Waves of new four kinds are described theoretically by exact solutions to the wave equation with spatial inhomogeneous and intensity-dependent refractive index. The waves differ from each other in the distribution profile and the range of existence. Waves with both oscillating and non-oscillating field profiles inside the dielectric layer are obtained. It is found that the dielectric layer significantly affects the main characteristics of the field distribution in the waveguide structure in the direction transverse to the layers. It is shown controlling the values of the characteristics of the layers allows selecting the required field profile, which can be used to suppress oscillations or increase the field intensity in certain regions of a layered structure.

Replica symmetry breaking in a Rayleigh backscattering-based random fiber laser

Replica symmetry breaking (RSB) phase transition is observed in disordered photonics systems. The key requirements to observe RSB are provided by random lasers, i.e., gain and disorder. However, in a random fiber laser (RFL) with scattering provided by Rayleigh scattering of light, the condition of quenched disorder is not established due to environment perturbations. Here, RSB is observed in a Rayleigh backscattering-based RFL, where light scattering is due to the inhomogeneity of the optical fiber refractive index. This is done by using short-cavity erbium-RFL with reduced interaction with the environment. Spectral characterization is made, and narrow mode linewidths are demonstrated. The intensity dynamics and laser mode behavior are analyzed showing the presence of gain competition. The results indicate a connection between the replica symmetry or RSB, Lévy-like behavior of intensities, and the presence or not of correlated laser intensity fluctuations.

Thermal Lens Measurements of Thermal Expansivity in Thermosensitive Polymer Solutions

The weak absorption of a laser beam generates in a fluid an inhomogeneous refractive index profile acting as a negative lens. This self-effect on beam propagation, known as Thermal Lensing (TL), is extensively exploited in sensitive spectroscopic techniques, and in several all-optical methods for the assessment of thermo-optical properties of simple and complex fluids. Using the Lorentz-Lorenz equation, we show that the TL signal is directly proportional to the sample thermal expansivity α, a feature allowing minute density changes to be detected with high sensitivity in a tiny sample volume, using a simple optical scheme. We took advantage of this key result to investigate the compaction of PniPAM microgels occurring around their volume phase transition temperature, and the temperature-driven formation of poloxamer micelles. For both these different kinds of structural transitions, we observed a significant peak in the solute contribution to α, indicating a decrease in the overall solution density-rather counterintuitive evidence that can nevertheless be attributed to the dehydration of the polymer chains. Finally, we compare the novel method we propose with other techniques currently used to obtain specific volume changes.

A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation

Abstract The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variational form of mollification. This approach is proved to be consistent, and the proposed numerical simulations are quite promising.

Self-reference interferometric measurement of scattering medium transmission matrix based on digital micromirror device superpixel method

When light propagates through complex medium, such as biological tissue and multimode fiber, refractive index inhomogeneity causes multiple scattering and distortion. This phenomenon is usually seen as obstacles for biomedical imaging, telecommunications, photodynamic therapy and so on. Thus, manipulation of the incident wavefront to compensate for the wavefront distortion due to multiple scattering has been an interdisciplinary subject of interest. Fortunately, wavefront shaping technologies have emerged to provide versatile solutions to minimize the influence of light scattering. By modulating the incident light into a special wavefront with a spatial light modulator, focusing through scattering medium is obtained. To date, several wavefront shaping techniques have been proposed, mainly including transmission matrix inversion, feedback based iterative optimization, and digital optical phase conjugation. Unlike a planar wavefront, the modulated light with special wavefront is transformed into a bright optical focus spot or a desired focus pattern after the scattering medium. Among the proposed approaches, the transmission matrix is considered as a significant tool to characterize a multiple scattering medium with the purpose of manipulating light propagation through it, which contains all the information related to the input field and the scattered output field. In this work, we experimentally measure the transmission matrix of scattering media based on self-reference interference method with a digital micromirror device. Unlike the conventional setup, which divides the incident wavefront into a signal part and reference part, in the self-reference interference method, the reference light is superimposed directly on the signal light to form a new set of input light fields. This self-reference interference method effectively improves the degree of freedom of optical field modulation. Moreover, the intensity ratio between the signal light and the reference light can be adjusted conveniently. In our experiment, this superimposed field is generated by a digital micromirror device with superpixel method. We measure the Hadamard basis and the OAM-basis transmission matrices of scattering medium, respectively. With the measured transmission matrices, single-spot, multi-spot and vortex focusing are achieved after scattering medium, verifying the accuracy of the measured transmission matrices. The strong diagonal presented in the norm of focusing operator also proves the accuracy of the measured transmission matrices. The proposed method may have potential applications in optical imaging and optical communication under scattering environment.

Profile thickness synthesis of thin-film waveguide Luneburg lens

In the work the link between the focusing inhomogeneity of the effective refractive index of waveguide Luneburg lens and the irregularity of the waveguide layer thickness generating this inhomogeneity is demonstrated. For the dispersion relation of irregular thin-film waveguide in the model of adiabatic waveguide modes the problem of mathematical synthesis and computer-aided design of the waveguide layer thickness profile for the Luneburg thin-film generalized waveguide lens with a given focal length is being solved. The calculations are carried out in normalized (in a special way) coordinates to adapt the used relations to computer calculations. The obtained solution is compared with the same solution within the cross-section’s method. The performance of the algorithm implemented in Delphi, was demonstrated by plotting the dispersion curves and plotting a family of dispersion curves, demonstrating a critical convergence. As an additional result, the thickness profiles of additional (irregular in thickness) waveguide layer, forming a thin film generalized waveguide Luneburg lens were synthesized. This result generalizes Southwell’s results.

Linear and Nonlinear Optical Properties of Well‐Defined and Disordered Plasmonic Systems: A Review

AbstractDisordered metallic nanostructures have features that are not realized in well‐defined nanometallic counterparts, such as broadband light localization and inhomogeneous refraction index at the nanoscale. Disordered metal systems with a networked inner architecture have both particles and voids with subwavelength dimensions which are randomly 3D organized in space. These disordered structures are benefited from high surface area and damage stability, permit guest materials permeability, and can be achieved in large scales employing less costs and expertise. Their abundant nanosize gaps and sharp tips can interact with incident light over a broadband range to generate a rich pattern of hot‐spots and can therefore function as an artificial leaf, for example. Here, the linear and nonlinear optical properties of both well‐defined and disordered plasmonic structures are reviewed with a focus on largescale 3D metallic networks. An efficiency comparison of those structures as an optical source for second harmonic generation is presented as well.

Measurements of concentration distribution of hydrogen jet using deflection of center of the laser spot

The main purpose of this work is to propose a new method to evaluate the concentration distribution of the hydrogen jet by using a He–Ne laser through the jet. This research attempts to apply the expression of concentration Gaussian distribution, the refraction formula of inhomogeneous refractive index medium, and the concentration inversion function to disclose the displacement of the center of the laser spot at different heights in the gas jet. The spot images of the laser beam passing through the gas jet at three vertical heights z = 10d, 20d, 30d, and different radial positions are obtained. The radial spatial asymmetry of the gas jet is also found in the experiment. Finally, the calculated concentration distribution curve and the fluent simulation curve, it is found that the two results are very similar. Our findings show that the error between the concentration distribution of this method and the simulated concentration distribution reaches 2.43%.

<i>In Situ</i> Wear Measurement of Hot Forging Dies Using Robot Aided Endoscopic Fringe Projection

According to the current state of the art, wear conditions of forging dies are assessed visually in the dismantled state, as there is no measuring procedure available for inline wear measurement of hot forging dies. This paper introduces a handling concept for automated loading and in-situ tool inspection for a hot forging process. Based on an industrial robot and quickchange systems, the process integration of hightemperature grippers and an endoscopic 3D-measurement sensor for the in-situ inspection of hot forging dies is carried out. By adapting the measuring method of fringe projection to an endoscopic design, the measuring system can be navigated into the difficult-to-access geometry of the die and take high-precision 3D-measurements inside. The ambient air heated by the forming process creates an inhomogeneous refractive index field around the measuring system and the hot die, so that the straight beam path required for optical measuring systems cannot be ensured. This can lead to strong deviations in the reconstructed point clouds and the functional geometries derived from them. By means of a compressed air actuator, the measuring system can be protected from the hot tool and dirt as well as the effect of inhomogeneous refractive index can be reduced. With this approach the in-situ wear measurement at highly stressed regions using the example of the mandrel radius and the flash radius will be demonstrated. These functional elements are of particular relevance, as the thermalstress is high and large material flow takes place. For the wear measurement, the functional elements of the tool are examined in detail by fitting geometrical features into the reconstructed point clouds and determining the deviations from a reference geometry. In addition, the measurement data is validated with the aid of a commercially available state-of-the-art measurement system.

Spin Hall effects and the localization of massless spinning particles

The spin Hall effects of light represent a diverse class of polarization-dependent physical phenomena involving the dynamics of electromagnetic wave packets. In a medium with an inhomogeneous refractive index, wave packets can be effectively described by massless spinning particles following polarization-dependent trajectories. Similarly, in curved spacetime the gravitational spin Hall effect of light is represented by polarization-dependent deviations from null geodesics. In this paper, we analyze the equations of motion describing the gravitational spin Hall effect of light. We show that these equations are a special case of the Mathisson-Papapetrou equations for spinning objects in general relativity. This allows us to use several known results for the Mathisson-Papapetrou equations, and apply them to the study of electromagnetic wave packets. We derive conservation laws, we discuss the limits of validity of the spin Hall equations, and we study how the energy centroids of wave packets, effectively described as massless spinning particles, depend on the external choice of a timelike vector field, representing a family of observers. In flat spacetime, the relativistic Hall effect and the Wigner(-Souriau) translations are recovered, while our equations also provide a generalization of these effects in arbitrary spacetimes. We construct a large class of wave packets that can be described by the spin Hall equations, but also find its limits by giving examples of wave packets which are more general and are not described by the spin Hall equations. Lastly, we examine the assumption that electromagnetic wave packets are massless. While this is approximately true in many contexts, it is not exact. We show that failing to carefully account for the limitations of the massless approximation results in the appearance of unphysical ``centroids'' which are nowhere near the wave packet itself.