Inhomogeneous Refractive Index Research Articles

Orbital angular momentum sidebands in second harmonic generation of a vortex beam by a nonlinear crystal with inhomogeneous refractive index

The manipulation of the orbital angular momentum (OAM) spectrum in new wavelengths generated by frequency conversion has a wide range of applications in quantum information technology and modern communications. Here, the second harmonic generation of a vortex beam in a nonlinear crystal with an inhomogeneous refractive index is considered. It is shown that by using a segmented oven and generating a controllable temperature gradient along the thickness of the nonlinear crystal, a transverse phase mismatch can be induced in the vortex beam. Accordingly, the OAM spectrum of the vortex beam can be changed by generating new OAM components in the spectrum. Compared with the nonlinear Bragg diffraction method, the presented method has the advantage of longer interaction length and higher efficiency.

Measurement error of tracer-based velocimetry in single-phase turbulent flows with inhomogeneous refractive indices

Inhomogeneous refractive index fields lead to errors in optical flow velocity measurements. Former respective studies are mostly in quasi two-dimensional flows, and attribute the measurement errors to spatial gradients in the refractive index field, while less attention has been paid to flows with three-dimensional refractive index fields which usually change in space and in time. In this study, ray tracing simulations were carried out in a three-dimensional flow, which is from a direct numerical simulation of single-phase turbulent mixing of two fluids. Given the data of the numerical simulation as reference, the ray tracing simulation is used to quantify the measurement errors of the flow velocity and flow acceleration for tracer-based velocimetry, i.e. particle tracking velocimetry in this study. The errors of both flow velocity and flow acceleration are attributed to the spatial and the spatio-temporal gradients of the refractive indices, respectively, which are closely inherited from flow characteristics. While the dominant type of error depends on the studied flow, the main measurement error for the considered turbulent mixing flow is caused by the random error. When the maximum spatial difference of the refractive indices is about 10−6, the relative random measurement error is about 1 % in velocity and about 200 % in acceleration, respectively. When the maximum index difference is about 10−2 (water), the relative random measurement errors of velocity and acceleration are 2000 % and 105 %, respectively, for the flow considered in this study.

Lambertian illumination of dielectric scattering media with monochromatic light

We study the Lambertian illumination of dielectric media with monochromatic light by numerically solving Maxwell's equations in three dimensions. We compute the average energy density inside spherical and cubic objects with a uniform refractive index. The Lambertian illumination of objects with uniform refractive index reproduces the known enhancement of the average energy density equal to the third power of the refractive index if the surface is sufficiently textured. Furthermore, inhomogeneous refractive index distributions with scattering areas much smaller than the wavelength, of the order of the wavelength, and larger than the wavelength are studied. The average energy density inside these media is compared to effective medium theories. Our investigation shows that the average energy density enhancement inside scattering media with scatterers much smaller than the wavelength can be modeled accurately with effective medium approximations.

Latent image volumetric additive manufacturing.

Volumetric additive manufacturing (VAM) enables rapid printing into a wide range of materials, offering significant advantages over other printing technologies, with a lack of inherent layering of particular note. However, VAM suffers from striations, similar in appearance to layers, and similarly limiting applications due to mechanical and refractive index inhomogeneity, surface roughness, etc. We hypothesize that these striations are caused by a self-written waveguide effect, driven by the gelation material nonlinearity upon which VAM relies, and that they are not a direct recording of non-uniform patterning beams. We demonstrate a simple and effective method of mitigating striations via a uniform optical exposure added to the end of any VAM printing process. We show this step to additionally shorten the period from initial gelation to print completion, mitigating the problem of partially gelled parts sinking before print completion, and expanding the range of resins printable in any VAM printer.

Phase regulation of lightwave transmission in inhomogeneous atmospheric medium using plane acoustic field

Based on the acousto-optic effect and the Gladstone–Dale relationship, the relationship about variations of the refractive index of the isotropic homogeneous atmospheric medium and the inhomogeneous atmospheric medium with the sound pressure under the disturbance of the plane sound field is derived. Models for the transmission of plane light waves and Laguerre-Gaussian beams through homogeneous atmospheric medium and inhomogeneous atmospheric medium disturbed by plane acoustic waves are established. The results show that the refractive index distribution of the homogeneous atmospheric medium exhibits a homogeneous periodic distribution after being disturbed by the plane sound field. For large-scale angles of longitudinal variation of atmospheric pressure, the plane sound field has little effect on the distribution of the refractive index of the inhomogeneous atmosphere. For small-scale angles, the inhomogeneous atmospheric refractive index gradually decreases with height and fluctuates with the influence of sound pressure. When the plane acoustic wave disturbs the homogeneous atmospheric medium, the isophase plane of the plane light wave will fluctuate significantly due to the influence of the acoustic wave. The phase of the LG beam rotates and always returns to the original phase. When the plane acoustic wave disturbs the inhomogeneous atmospheric medium, the phase change of the plane light wave will change periodically with the change law of the sound wave. The overall optical path is an inclined plane, but due to the disturbance of the sound wave, the optical path will fluctuate. The phase of the LG beam still rotates, but unlike the homogeneous medium, its phase does not return to its original phase due to the change of its refractive index with height.

Multiplexing temperature-compensated open-cavity Fabry-Perot sensors at a fiber tip.

We investigate multiplexing of four highly sensitive Fabry-Perot (FP) microresonators at the tip of a single-mode optical fiber for refractive index (RI) measurements with simultaneous temperature compensation. The individual sensing elements for RI or temperature consist of either open-cavity FP resonators or solid fiber core regions fabricated by diamond-blade dicing of single-mode optical fibers, respectively. The reflectivity of the open resonators is further enhanced by matched dielectric coatings. At the same time, the solid core resonators formed by the fiber pieces between the open cavities are used as thermometers. This allows immediate compensation for temperature cross-sensitivity during RI measurements. The general performance of the sensor is demonstrated by measuring the RI of sucrose solutions, where we use phase tracking of the characteristic Fourier transform components of the backreflected optical spectrum for evaluation. The temperature sensitivity is on average 20±/∘C with an accuracy of 0.01°C, fully sufficient for biomedical applications. Meanwhile, the four RI sensing (open) cavities show high sensitivity of approximately 1160 nm/RIU. Due to the compact size of the sensor, small spatial inhomogeneities of RI can be accurately detected. If the cavities are additionally filled with molecularly imprinted polymers or coated with thin functional layers, they could also be used for the detection of trace substances in biomedical laboratory-on-a-fiber applications.

Stereoscopic particle image velocimetry in inhomogeneous refractive index fields of combustion flows.

Particle image velocimetry (PIV) measurements in reactive flows are disturbed by inhomogeneous refractive index fields, which cause measurement deviations in particle positions due to light refraction. The resulting measurement errors are known for standard PIV, but the measurement errors for stereoscopic PIV are still unknown. Therefore, for comparison, the velocity errors for standard and stereoscopic PIV are analyzed in premixed propane flames with different Reynolds numbers. For this purpose, ray-tracing simulations based on the time-averaged inhomogeneous refractive index fields of the studied non-swirled flame flows measured by the background-oriented Schlieren technique are performed to quantify the resulting position errors of the particles. In addition, the performance of the volumetric self-calibration relevant to tomographic PIV is analyzed with respect to the remaining position errors of the particles within the flames. The position errors cause significant standard PIV errors of 2% for the velocity component radial to the burner symmetry axis. Stereoscopic PIV measurements result in measurement errors of up to 3% radial to the burner axis and 13% for the velocity component perpendicular to the measurement plane. Due to the lower refractive index gradients in the axial direction, no significant velocity errors are observed for the axial velocity component. For the investigated flame configurations, the position errors and velocity errors increase with the Reynolds numbers. However, this dependence needs to be verified for other flame configurations such as swirled flame flows.

About copying a free-space electromagnetic field by an invisible object

The structure of a monochromatic electromagnetic field inside a spherical object that does not distort the wave field of external sources outside its surface has been studied using transformation optics methods. It is assumed that the object is made of isotropic materials with equal values of permittivity and permeability and consists of a spherical volume of material with a positive spatially uniform refractive index and an adjacent spherical layer of material with a negative inhomogeneous refractive index (i.e., it is a spherical superlens made of isotropic materials). It is shown that the field inside a sphere with a positive refractive index is the reduced-size copy of the field in which the object was located. This copy contains information about the radiation field of external sources in a spherical free-space volume whose radius depends on the object parameters and can be significantly larger than the radius of the object. It is shown that the copying properties of the object with given dimensions can be fully preserved if its outer layer is made of anisotropic materials.

Light Confinement by Local Index Tailoring in Inhomogeneous Dielectrics

AbstractThe engineering of light confinement is a topic with a long history in optics and with significant implications for the control of light‐matter interaction. In inhomogeneous and disordered media, however, multiple scattering prevents the application of conventional approaches for the design of light fields with desired properties. This is because any local change to such a medium typically affects these fields in a non‐local and complicated fashion. Here, we present a theoretical methodology for tailoring an inhomogeneous 1D Hermitian dielectric index distribution that allows us to control the intensity profile of an incoming light field purely locally, that is, with little or no influence on the field profile outside of a designated region of interest. Strongly increasing or decreasing the light's intensity at arbitrary positions inside the medium thereby becomes possible without, in fact, changing the external reflectance or transmittance. These local modifications of the medium can thus be made undetectable to far field measurements. We apply this approach to locally control the confinement of light inside 1D materials with inhomogeneous continuous refractive index profiles and extend it to multilayer films as well as to chains of coupled micro‐resonators.

The Speed of Light Is Slowed Down as It Travels Near the Surface of an Obstacle

The speed of propagation of light that passes through a medium at a slower speed determines the refractive index with respect to the wavelength. Subsequently, the refractive index of vacuum (free space) that light travels at speed c is 1 by definition.
 This study proposes that the speed of light is slowed down in an inhomogeneous space close to the surface of the obstacles, including the edges of the apertures. Furthermore, the inhomogeneous refractive index near these surfaces will increase as the distance from the object is reduced. Therefore, light propagates through apertures as it encounters a medium with a variable refractive index.

Light scattering in TIRF microscopy: A theoretical study of the limits to surface selectivity

In TIRF microscopy, the sample resides near a surface in an evanescent optical field that, ideally, decreases in intensity with distance from the surface in a pure exponential fashion. In practice, multiple surfaces and imperfections in the optical system and refractive index (RI) inhomogeneities in the sample (often living cells) produce propagating scattered light that degrades the exponential purity. RI inhomogeneities cannot easily be avoided. How severe is the consequent optical degradation? Starting from Maxwell’s equations, we derive a first-order perturbative approximation of the electric field strength of light scattered by sample RI inhomogeneities of several types under coherent evanescent field illumination. The approximation provides an expression for the scattering field of any arbitrary RI inhomogeneity pattern. The scattering is not all propagating; some is evanescent and remains near the scattering centers. The results presented here are only a first-order approximation, and they ignore multiple scattering and reflections off the total internal reflection (TIR) surface. For simplicity, we assume that the RI variations in the z direction are insignificant within the depth of the evanescent field and consider only scattering of excitation light, not fluorescence emission light. The general conclusion of most significance from this study is that TIR scattering from a sample with RI variations typical of those on a cell culture alters the effective thickness of the illumination to only ∼50% greater than it would be without scattering. The qualitative surface selectivity of TIR fluorescence is largely retained even in the presence of scattering. Quantitatively, however, scattering will cause a deviation from the incident exponential decay at shorter distances, adding a slower decaying background. Calculations that assume a pure exponential decay will be approximations, and scattering should be taken into account. TIR scattering is only slightly dependent on polarization but is strongly reduced for the highest accessible incidence angles.

Reconfigurable large-scale bulk metamaterials for broadband ultrasonics

Recent research has focused on developing smart metamaterials with programmable acoustic properties, but past designs have only demonstrated the ability to tune small samples composed of at most few dozen cells. Their reconfiguration mechanisms are not scalable to larger structures and yield lossy designs unsuitable for ultrasound applications of interest today such as ultrasound imaging. This work introduces a method to create ultrasonic metamaterials programmable on very large macroscopic scales. Remarkably, the method can impose desired, inhomogeneous acoustic properties to bulk metamaterials composed of arbitrarily large collections of unit cells using only one controller. The concept is experimentally demonstrated by designing a low loss ultrasonic beam forming and steering device that has very high directivity, is programmable, and has the bandwidth requirement necessary for ubiquitous ultrasound applications. The device consists of two patterned plates composed of thousands of unit cells tuned to form the prescribed inhomogeneous refractive index profiles needed for beamforming and dynamic steering. The geometry of the cells is collectively modified by rotating one of the plates about one of its ends. The technique to reconfigure broadband bulk metamaterials at ultrasound frequencies will enable unprecedented wave control on a large scale and with very low power consumption.

Tomographic reconstruction of refractive index fields based on laser beam deflection measurement

Refractive index as one of the most important optical properties of materials is the key to utilize refractive index elements. However, it is very difficult to measure or estimate refractive index of media, especially for multi-dimensional inhomogeneous refractive index distribution. Therefore, an inverse scheme is presented for reconstructing refractive index field in rectangular gradient index medium based on ray deflection measurement in this work. A collection of rays from given positions along given directions transit the semitransparent medium and all exit boundary positions are recorded to construct the objective function of inverse problem. Runge–Kutta ray tracing technique is employed to simulate the curved ray path determined by Fermat principle in gradient-index medium. Conjugate gradient method as an inverse algorithm is used to reconstruct refractive index field. A series of simulation experiments are done to show the performance of the inverse strategy we developed. The results indicate that this inverse strategy for reconstructing refractive index field is accurate and effective.

Adapted Fringe Projection Sequences for Changing Illumination Conditions on the Example of Measuring a Wrought-Hot Object Influenced by Forced Cooling

Optical 3D geometry reconstruction, or more specific, fringe projection profilometry, is a state-of-the-art technique for the measurement of the shape of objects in confined spaces or under rough environmental conditions, e.g., while inspecting a wrought-hot specimen after a forging operation. While the contact-less method enables the measurement of such an object, the results are influenced by the light deflection effect occurring due to the inhomogeneous refractive index field induced by the hot air around the measurand. However, the developed active compensation methods to fight this issue exhibits a major drawback, namely an additional cooling of the object and a subsequent transient illumination component. In this paper, we investigate the cooling and its effect on temporal phase reconstruction algorithms and take a theoretical approach to its compensation. The simulated compensation measures are transferred to a fringe projection profilometry setup and are evaluated using established and newly developed methods. The results show a significant improvement when measuring specimens under a transient illumination and are easily transferable to any kind of multi-frequency phase-shift measurement.Dataset License: CC-BY

Noncollinear degenerate phase modulation in samples with inhomogeneous optical nonlinear properties [Invited

Digital inline pump-probe holography can be applied to estimate parameters of samples' optical nonlinear properties. Here we propose a mathematical model to describe noncollinear degenerate phase modulation in samples with inhomogeneities of nonlinear refractive index over all three dimensions, namely, two-layered samples and samples with local impurities. The impact of sample parameters in the considered configurations is analyzed. We show that analysis of inline digital holograms obtained by time-resolved inline digital holography can be successfully used for rapid detection and characterization of various types of nonlinear refractive index inhomogeneities.

О возможности исследования доли неоднородностей оптических нелинейных сред с помощью осевой цифровой голографии с временным разрешением

An approach to determining the fraction of local inhomogeneities nonlinear refractive index n2 in a transparent medium is considered. Data recording was performed using inline digital holography with femtosecond time resolution, where a set of probe beam inline digital holograms in the Fresnel diffraction zone to be recorded at various time delays between the pump and probe pulses. Digital holograms contain diffraction patterns that have information about the induced degenerate non-collinear phase modulation formed in the presence of nonlinear refractive index inhomogeneities. The developed algorithm is based on the calculation of the diffraction patterns Fourier spectrum and analysis of the intensity at zero spatial frequency. The proposed method has been validated in numerical modeling. An approach to determining the fraction of local inhomogeneities nonlinear refractive-index coefficient n2 in a transparent medium is considered. Data recording was performed using time-resolved inline digital holography, where a set of inline digital holograms in the Fresnel diffraction zone to be recorded in a probe beam at various time delays between the pump and probe pulses. Digital holograms contain diffraction patterns that have information about the induced degenerate noncollinear phase modulation formed in the presence of nonlinear refractive index inhomogeneities. The developed algorithm is based on the calculation of the diffraction patterns Fourier spectrum and analysis of the intensity at zero spatial frequency. The proposed method has been validated in numerical simulation.

Thermally stable laser-driven phosphor converted white light source using multilayer structured diffuser system

We report the development of a thermally stable laser-driven phosphor-converted white light source using a multilayer structured diffuser system for general illumination. The developed extended diffuser system comprises an acrylic sheet, two glass plates, and a phosphor layer with the arrangement in a glass-acrylic-phosphor-glass combination. The high-power laser beam was gradually distributed inside the diffuser system for exciting the phosphor layer optimally without burning the resin and thermal quenching. The method is simple and efficient in which both the directionality and scattering properties of laser source are exploited using the transmission properties of diffusers. The high specular transmission of diffusers resulted in the optimum transfer of laser directional photons for exciting the middle section of phosphor layer, and the remaining laser photons were scattered from diffuser surfaces. The glass-acrylic combination results the refractive index inhomogeneity inside the system and helped to expand the scattered photons throughout the phosphor layer. The radiant power distribution of blue laser source inside the system resulted in synchronization between optimal absorption quantum efficiency and fluorescent conversion quantum efficiency of the phosphor layer. As a result, the thermal quenching effect on phosphor inside the white light system was minimized for efficient illumination. With this geometry, a bright and thermally stable white light source was realized due to the proper distribution of high-power laser throughout the system. The luminescence properties of the proposed laser-based white light system were examined and found thermally stable in terms of spectral changes, luminance, and correlated color temperature.

Deterministic and Controllable Photonic Scattering Media via Direct Laser Writing

AbstractPhotonic scattering materials, such as biological tissue and white paper, are made of randomly positioned nanoscale inhomogeneities in refractive index that lead to multiple scattering of light. Typically these materials, both naturally occurring or man‐made, are formed through self assembly of the scattering inhomogeneities, making it extremely challenging to know the exact positions of these inhomogeneities, let alone control those. Here, the nanofabrication of photonic multiple‐scattering media using direct laser writing with a deterministic design is reported on. These deterministic multiple‐scattering media consist of submicron‐thick polymer nanorods that are randomly oriented within a cubic volume. The total transmission of light is studied as a function of the number of rods and of the sample thickness to extract the scattering and transport mean free paths using radiative transfer theory. Such ability to fabricate photonic multiple‐scattering media with deterministic and controllable properties opens up a myriad of opportunities for fundamental studies of light scattering, in particular, in the multiple‐scattering regime and with strong anisotropy and for new applications in solid‐state lighting and photovoltaics.

Aberration correction for flow velocity measurements using deep convolutional neural networks

Optical imaging-based flow measurement techniques, like particle image velocimetry, are vulnerable to optical distortions caused by inhomogeneous refractive index or fluctuating phase boundaries. These distortions can lead to blurred particle images and uncertain tracer particle position assignment, resulting in a degradation of velocity measurement accuracy. In order to improve the measurement accuracy, adaptive optics system can be applied to correct distortions. For imaging metrology in fluid mechanics, the optical distortions have features of large frequency range, high spatial frequency and large dynamic range. Actuator-based approaches are limited by its performances. In our work, a novel intelligent adaptive optic system was applied to flow measurement, a learning-based aberration correction method without wavefront corrector was demonstrated, which was used to correct distortions in imaging-based flow measurement. A particle image velocimetry setup which can measure wavefront aberration was built to generate training and test dataset for deep neural network, and also the distortion caused PIV image degradation model. The correction performance of the trained neural network was quantitatively evaluated by corrected PIV image quality and flow measurement result.

The dynamics of spatially confined oscillations

The possible relation of the wave nature of particles to gravitation as an emergent phenomenon is addressed. Hypothetical particles are considered as spatially confined oscillations (SCOs) and are constructed through the superposition of plane waves. The effect of a continuously changing refractive index (speed of propagation field) on SCOs is calculated and the continuous Ibn–Sahl–Snell law of refraction is derived. Refracted plane wave constituents of SCOs in an inhomogeneous medium cause the oscillation as a whole to accelerate as an entity. This acceleration is described by a geodesic equation, in much the same way as in general relativity. The proper time of an SCO can be defined via its oscillation frequency. The proper time and its change along the trajectory are equivalent to a particle in general relativity as described by the 0th component of its geodesic equation. An SCO in an inhomogeneous refractive index field exhibits general relativistic properties based on basic wave mechanics. Properties derived from direct calculations are length contraction, gravitational red- and blueshift, and Thomas precession. The presented theory is an approximation for oscillations which are small compared to changes in the refractive index field. SCOs in an inhomogeneous medium may thus yield a naturally emerging particle-field interaction with general relativistic properties and may allow a useful vantage point on the nature of gravitation using classical wave experiments.