Refractive Index Distribution Research Articles

All-optical complex field imaging using diffractive processors.

Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However, conventional image sensors are intensity-based and inherently lack the capability to directly measure the phase distribution of a field. This limitation can be overcome using interferometric or holographic methods, often supplemented by iterative phase retrieval algorithms, leading to a considerable increase in hardware complexity and computational demand. Here, we present a complex field imager design that enables snapshot imaging of both the amplitude and quantitative phase information of input fields using an intensity-based sensor array without any digital processing. Our design utilizes successive deep learning-optimized diffractive surfaces that are structured to collectively modulate the input complex field, forming two independent imaging channels that perform amplitude-to-amplitude and phase-to-intensity transformations between the input and output planes within a compact optical design, axially spanning ~100 wavelengths. The intensity distributions of the output fields at these two channels on the sensor plane directly correspond to the amplitude and quantitative phase profiles of the input complex field, eliminating the need for any digital image reconstruction algorithms. We experimentally validated the efficacy of our complex field diffractive imager designs through 3D-printed prototypes operating at the terahertz spectrum, with the output amplitude and phase channel images closely aligning with our numerical simulations. We envision that this complex field imager will have various applications in security, biomedical imaging, sensing and material science, among others.

Modeling Absorption Dynamics of Differently Shaped Gold Glioblastoma and Colon Cells Based on Refractive Index Distribution in Holotomographic Imaging.

Herein, it is demonstrated that the toxic effect of gold nanoparticles (Au NPs) on three different cancer cell lines (U-118 and LN-299 glioblastoma and HCT-116 colon) depends on their absorption dynamics by cells, related to the shapes of the NPs. This hypothesis is confirmed by showing that i) based on refractive index (RI) values, typical for cell components and gold nanoparticles, it is possible to show the absorption dynamics and accumulation locations of the latter ones inside and outside of the cells. Moreover, ii) the saturation of the accumulated Au NPs volume in the cells depends on the nanoparticle shape and is reached in the shortest time for star-shaped Au NPs (AuS NPs) and in the longest time for spherical Au NPs (AuSph NPs) and on the cancer cells, where the longest and the shortest saturation are noticed for HCT-116 and LN-229 cells, respectively. A physical model of Au NPs absorption dynamics is proposed, where the diameter and shape of the Au NPs are used as parameters. The obtained theoretical data are consistent with experimental data in 85-98%.

3D Laser Writing of Low-Loss Cross-Section-Variable Type-I Optical Waveguide Passive/Active Integrated Devices in Single Crystals.

Optical waveguides fabricated in single crystals offer crucial passive/active optical components for photonic integrated circuits. Single crystals possess inherent advantages over their amorphous counterpart, such as lower optical losses in visible-to-mid-infrared band, larger peak emission cross-section, higher doping concentration. However, the writing of Type-I positive refractive index modified waveguides in single crystals using femtosecond laser technology presents significant challenges. Herein, we introduce a novel femtosecond laser direct writing technique that combines slit-shaping with an immersion oil objective to fabricate low-loss Type-I waveguides in single crystals. This approach allows for precise control of waveguide shape, size, mode-field and refractive index distribution, with a spatial resolution as high as 700nm and a high positive refractive index variation on the order of 10-2, introducing new degrees of freedom to design and fabricate passive/active optical waveguide devices. As a proof-of-concept, we successfully produced a 7mm-long circular-shaped gain waveguide (∼10µm in diameter) in an Er3+-doped YAG single crystal, exhibiting a propagation loss as low as 0.23dB/cm, a net gain of ∼3dB and a polarization-insensitive character. The newly-developed technique is theoretically applicable to arbitrary single crystals, holding promising potential for various applications in integrated optics, optical communication, and photonic quantum circuits. This article is protected by copyright. All rights reserved.

Insights on the effect of process conditions on the optical properties of silver ion exchanged soda-lime silicate glass

The effects of ion exchange time and temperature on the optical properties and plasmonic response of silver ion exchanged soda-lime silicate glass were investigated using scanning electron microscopy (SEM) in energy dispersive spectrometry (EDS) configuration, m-lines spectroscopy, photoluminescence (PL) spectroscopy, and UV–visible absorption spectroscopy. SEM analyses in EDS mode provided profiles of silver oxide molar concentration. These profiles were directly correlated to the silver diffusion coefficient using an adjustment procedure. The effective indices of ion exchanged glasses measured by the standard prism coupling technique (m-lines) allowed access to refractive index distributions in ion exchange regions. These ion-exchanged glasses underwent evaluation to determine their potential suitability for use in multimode planar systems. The PL results acquired after ion exchange demonstrated that the creation of Ag0 atoms from Ag+ ions was responsible for the decline and quenching of PL intensity at ion exchange times and temperatures increase. Silver nanoparticles were generated in the samples subjected to ion exchange at 480 °C without the need for post-exchange treatments. The emergence of the surface plasmon resonance band around 427 nm in the optical absorption spectra confirmed the formation of Ag nanoparticles in annealed glasses. Estimates of the UV–visible absorption spectra indicated an average size of silver nanoparticles ranging from 1.8 to 2.4 nm.

Deep-learning based 3D birefringence image generation using 2D multi-view holographic images

Refractive index stands as an inherent characteristic of a material, allowing non-invasive exploration of the three-dimensional (3D) interior of the material. Certain materials with different refractive indices produce a birefringence phenomenon in which incident light is split into two polarization components when it passes through the materials. Representative birefringent materials appear in calcite crystals, liquid crystals (LCs), biological tissues, silk fibers, polymer films, etc. If the internal 3D shape of these materials can be visually expressed through a non-invasive method, it can greatly contribute to the semiconductor, display industry, optical components and devices, and biomedical diagnosis. This paper introduces a novel approach employing deep learning to generate 3D birefringence images using multi-viewed holographic interference images. First, we acquired a set of multi-viewed holographic interference pattern images and a 3D volume image of birefringence directly from a polarizing DTT (dielectric tensor tomography)-based microscope system about each LC droplet sample. The proposed model was trained to generate the 3D volume images of birefringence using the two-dimensional (2D) interference pattern image set. Performance evaluations were conducted against the ground truth images obtained directly from the DTT microscopy. Visualization techniques were applied to describe the refractive index distribution in the generated 3D images of birefringence. The results show the proposed method’s efficiency in generating the 3D refractive index distribution from multi-viewed holographic interference images, presenting a novel data-driven alternative to traditional methods from the DTT devices.

Modeling and correction of image drift in dynamic shadowgraphy experiments

The study of phoretic transport phenomena under non-stationary conditions presents several challenges, mostly related to the stability of the experimental apparatus. This is particularly true when investigating with optical means the subtle temperature and concentration fluctuations that arise during diffusion processes, superimposed to the macroscopic state of the system. Under these conditions, the tenuous signal from fluctuations is easily altered by the presence of artifacts. Here, we address an experimental issue frequently reported in the investigation by means of dynamic shadowgraphy of the non-equilibrium fluctuations arising in liquid mixtures under non-stationary conditions, such as those arising after the imposition or removal of a thermal stress, where experiments show systematically the presence of a spurious contribution in the reconstructed structure function of the fluctuations, which depends quadratically from the time delay. We clarify the mechanisms responsible for this artifact, showing that it is caused by the imperfect alignment of the sample cell with respect to gravity, which couples the temporal evolution of the concentration profile within the sample with the optical signal collected by the shadowgraph diagnostics. We propose a data analysis protocol that enables disentangling the spurious contributions and the genuine dynamics of the fluctuations, which can be thus reliably reconstructed.Graphic The imposition of a thermal gradient across a liquid mixture results in a time-dependent refractive index distribution. In the presence of a misalignment of the confining cell with respect to gravity, this leads to a deflection of the optical probe beam used to monitor concentration fluctuations within the sample in quantitative shadowgraphy experiments. If not properly accounted for, this effect can introduce a significant bias in the optical signal.

3D Measurements and Characterizations of Refractive Index Distributions of Volume Holographic Gratings Using Low‐Coherence Holotomography

AbstractHolographic Optical Elements (HOEs) employ refractive index (RI) modulation to manipulate light, establishing their widespread application in augmented and virtual reality technologies. Despite significant strides in HOEs' fabrication, a comprehensive 3D examination and measurement of these elements remain largely unexplored. This study targets this void by conducting an in‐depth exploration of the 3D RI distributions of volume holographic gratings (VHGs), a quintessential representative of HOEs. Direct tomographic measurements of the 3D RI distributions within millimeter‐scale VHGs are performed at a spatial resolution of 156 nm × 156 nm × 1.2 µm and an RI precision of 2×10−4. This level of precision facilitates a systematic high‐resolution characterization of VHGs. The findings present a substantial evolution from traditional measurement techniques and promise to considerably advance the evaluation of intricate HOE structures and refine the corresponding fabrication processes.

Abstract 7401: High-level multiplexed virtual immunofluorescence staining using holotomography and deep learning

Abstract Multiplexed immunofluorescence (IF) staining plays a crucial role in cancer research, allowing simultaneous visualization of multiple biomarkers to elucidate complex cellular interactions within the tumor microenvironment. However, the conventional multiplexed IF approach has inherent limitations, characterized by labor-intensiveness and a constrained capacity for high-level multiplexing. These challenges hinder its scalability and comprehensive analysis of intricate molecular landscapes.To overcome the limitations of conventional multiplexed IF, we propose a novel approach that integrates holotomography (HT) and deep learning. HT is a label-free imaging technique that quantitatively measures the refractive index distribution of the specimen without any staining. To provide subcellular specificity to the label-free HT images, HT is integrated with virtual staining. Virtual staining is a deep learning-based framework that converts label-free images to the desired stained images, in this case, from HT images to multiplexed IF images. This synergistic combination of HT and deep learning may address the current limitations of multiplexed IF protocols.Our proposed methodology aims at high-level multiplexed virtual IF staining from label-free cancer tissue slides using HT and deep learning. This approach not only eliminates the need for chemical staining but also enhances the level of multiplexing through computational staining. Specifically, we acquire HT and fluorescence images of stained tissue slides for training. Utilizing this paired dataset, we then employ supervised learning to create a neural network that can map between label-free HT images and corresponding fluorescence images. Subsequently, the trained neural network is applied to label-free tissue slides, inferring fluorescence images without the need for chemical staining.We believe the proposed virtual staining framework will contribute to a more efficient and scalable paradigm for cancer research, facilitating a deeper understanding of tumor biology, and advancing the field of precision medicine. Citation Format: Juyeon Park, Su-Jin Shin, Geon Kim, Kwang Suk Lee, Ji Eun Heo, YongKeun Park. High-level multiplexed virtual immunofluorescence staining using holotomography and deep learning [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 7401.

Refractive index measurement deflectometry for measuring gradient refractive index lens.

A method based on deflectometry to measure the refractive index distribution of radial gradient refractive index (GRIN) lens is proposed in this paper. The method establishes the relationship between the refractive index distribution and the direction of light ray by deriving the propagation equation of light in a non-uniform medium. By measuring the deflection angle using the principle of deflectometry and the assumption of central refraction, the refractive index distribution of the radial GRIN lens is determined. The specific principle of refractive index measurement deflectometry (RIMD) is described in detail, and the correctness and accuracy of the method are verified through numerical simulations. Furthermore, the effects of calibration error, lens surface shape on the accuracy of the measurement results are analyzed. In the experimental section, the proposed method is applied to measure a radial GRIN lens, and the results are compared with the nominal parameters in terms of shape distribution and numerical values, demonstrating good consistency. The measurement error is controlled within the order of 10-3. This method enables rapid and convenient acquisition of full-field information of GRIN lens and holds promising potential for playing an important role in lens manufacturing and production.

Alternating projection combined with fast gradient projection (FGP-AP) method for intensity-only measurement optical diffraction tomography in LED array microscopy.

Optical diffraction tomography (ODT) is a powerful label-free measurement tool that can quantitatively image the three-dimensional (3D) refractive index (RI) distribution of samples. However, the inherent "missing cone problem," limited illumination angles, and dependence on intensity-only measurements in a simplified imaging setup can all lead to insufficient information mapping in the Fourier domain, affecting 3D reconstruction results. In this paper, we propose the alternating projection combined with the fast gradient projection (FGP-AP) method to compensate for the above problem, which effectively reconstructs the 3D RI distribution of samples using intensity-only images captured from LED array microscopy. The FGP-AP method employs the alternating projection (AP) algorithm for gradient descent and the fast gradient projection (FGP) algorithm for regularization constraints. This approach is equivalent to incorporating prior knowledge of sample non-negativity and smoothness into the 3D reconstruction process. Simulations demonstrate that the FGP-AP method improves reconstruction quality compared to the original AP method, particularly in the presence of noise. Experimental results, obtained from mouse kidney cells and label-free blood cells, further affirm the superior 3D imaging efficacy of the FGP-AP method.

Imaging the intracellular refractive index distribution (IRID) for dynamic label-free living colon cancer cells via circularly depolarization decay model (CDDM).

Label-free detection of intracellular substances for living cancer cells remains a significant hurdle in cancer pathogenesis research. Although the sensitivity of light polarization to intracellular substances has been validated, current studies are predominantly focused on tissue lesions, thus label-free detection of substances within individual living cancer cells is still a challenge. The main difficulty is to find specific detection methods along with corresponding characteristic parameters. With refractive index as an endogenous marker of substances, this study proposes a detection method of intracellular refractive index distribution (IRID) for label-free living colon cancer (LoVo) cells. Utilizing the circular depolarization decay model (CDDM) to calculate the degree of circular polarization (DOCP) modulated by the cell allows for the derivation of the IRID on the focal plane. Experiments on LoVo cells demonstrated the refractive index of single cell can be accurately and precisely measured, with precision of 10-3 refractive index units (RIU). Additionally, chromatin content during the interphases (G1, S, G2) of cell cycle was recorded at 56.5%, 64.4%, and 71.5%, respectively. A significantly finer IRID can be obtained compared to the phase measurement method. This method is promising in providing a dynamic label-free intracellular substances detection method in cancer pathogenesis studies.

The effect of misalignment on the coupling optics involving laser diode and single-mode triangular index fiber with an upside down tapered hyperbolic microlens on its tip

Abstract This article contains theoretical investigation of the performance of the coupler comprising laser diode and mono-mode circular core triangular index fiber (TIF), which contains on its tip an upside down tapered hyperbolic microlens (UDTHM). Here, we take care of probable angular and transverse mismatches. In our derivation, we use the refractive index distribution in the tapering area, the ray equation, and the relation involving refraction by hyperbolic microlens. We report analytical formulation of coupling efficiencies in the presence of specified types of misalignments using a relevant ABCD refraction matrix for a UDTHM in the vertical plane. In the fields of lasers and fibers, we use Gaussian field distribution in our analysis. Our research is based on two widely employed wavelengths, 1.3 µm and 1.5 µm. In this study, we used three TIF with V numbers of 4.380, 3.511, and 1.924, respectively. Little computation is required to execute the prescribed formulations. This study surfaces the sensitivity of the coupler in presence of the aforementioned types of offsets. The found results will prove valuable to manufacturers working in the domain of UDTHM.

Visualizing 3D Anisotropic Molecular Orientation in Polarization Holographic Optical Elements via Dielectric Tensor Tomography

AbstractThe ability to unveil the spatial distribution of refractive index (RI) within volumetric holographic optical elements (HOEs) is critical for quantitating their diffractive behaviors. Angle‐resolved far‐field measurements of diffractive intensity have been prevalent toward this end. However, this century‐old approach is unable to directly visualize the spatial distribution of RI at mesoscopic scale. More significantly, visualization of molecular orientation within photoaddressable polymers (PAPs), which serve as standard recording media for polarization HOEs (pHOEs), remains uncharted territory. The recent advent of dielectric tensor tomography (DTT) has paved the way for full characterization of 3D anisotropic dielectric tensors, encompassing principal RIs and their optic axes. This study embarks on direct visualization of the 3D spatial distribution of anisotropic molecular orientations within holographically recorded PAPs. Illuminating these PAPs with polarized light at varying angles, the diffracted vector fields essential for reconstructing the dielectric tensor tomogram are captured. After diagonalizing the dielectric tensors, periodic rotations of the anisotropic molecule orientations can be visualized in the PAPs, which have never been achieved so far. The homogeneity of grating patterns produced under diverse manufacturing conditions is also examined and juxtaposed.

Spatial Fluctuations of Optical Turbulence Strength in a Laboratory Turbulence Simulator

Controlled turbulence simulators in the laboratory have been extensively employed to investigate turbulence effects on light propagation in the atmosphere, driven by some advanced optical engineering such as remote sensing, energy-delivery systems, and free-space optical communication systems. Many studies have achieved rich results on the optical turbulence intensity, scintillation index, and power spectral density characteristics of the light propagation path in the center of a turbulence simulator, but a comprehensive analysis of the optical turbulence characteristics for different spatial locations is still lacking. We simulate turbulence with air as the medium in a classical convective Rayleigh–Bénard turbulence simulator through high-resolution computational fluid dynamics methods, the three-dimensional refractive index distribution is obtained, and the optical properties are analyzed comprehensively. It is found that the hot and cold plumes and the large-scale circulation strongly influence the inhomogeneity of Cn2 in the turbulence tank, making it weak in the middle and strong near the boundary. The refractive index power spectral density at different heights is centrally symmetric, with the slope gradually deviating from the −5/3 scaling power with increasing distance from the central region. Under the log-log plot, the variation of the refractive index variance with height exhibits a three-segmented feature, showing in order: a stable region, a logarithmic profile, and a power-law profile, in the region close to the boundary. These results will contribute to the construction of a suitable turbulence simulator for optical engineering applications.

Quantifying the Dynamics of Bacterial Biofilm Formation on the Surface of Soft Contact Lens Materials Using Digital Holographic Tomography to Advance Biofilm Research.

The increase in bacterial resistance to antibiotics in recent years demands innovative strategies for the detection and combating of biofilms, which are notoriously resilient. Biofilms, particularly those on contact lenses, can lead to biofilm-related infections (e.g., conjunctivitis and keratitis), posing a significant risk to patients. Non-destructive and non-contact sensing techniques are essential in addressing this threat. Digital holographic tomography emerges as a promising solution. This allows for the 3D reconstruction of the refractive index distribution in biological samples, enabling label-free visualization and the quantitative analysis of biofilms. This tool provides insight into the dynamics of biofilm formation and maturation on the surface of transparent materials. Applying digital holographic tomography for biofilm examination has the potential to advance our ability to combat the antibiotic bacterial resistance crisis. A recent study focused on characterizing biofilm formation and maturation on six soft contact lens materials (three silicone hydrogels, three hydrogels), with a particular emphasis on Staphylococcus epidermis and Pseudomonas aeruginosa, both common culprits in ocular infections. The results revealed species- and time-dependent variations in the refractive indexes and volumes of biofilms, shedding light on cell dynamics, cell death, and contact lens material-related factors. The use of digital holographic tomography enables the quantitative analysis of biofilm dynamics, providing us with a better understanding and characterization of bacterial biofilms.

Improved light extraction efficiency of AlGaN DUV light emitting diodes using Al/MgF2-based highly reflective film

AlGaN DUV light emitting diodes (DUV-LEDs) (275 nm emission) are safe, eco-friendly and smart alternatives for inactivating viruses and bacteria. However, DUV-LEDs suffer from the main bottleneck of low external quantum efficiencies, which are strongly associated with the low light extraction efficiency caused by the strong optical polarisation of Al-rich AlGaN. Optical simulation results show that the luminous intensity of DUV-LEDs was increased by 10% owing to the synergistic effect of the sidewalls and substrates. The optical power of DUV-LEDs was increased to 16.8%, the far-field pattern was expanded to 130 degrees and the emission intensity was more focused on the central region, proving that the highly reflective sidewalls and substrates could re-direct the sideways-travelling photons for extraction. Moreover, we also investigated the reflective mechanism of Al/MgF2 layers. Optimizing the refractive index distribution of Al/MgF2 layers could change the electric field intensity and improve the reflectivity. At the same time, the temperature of the sample after coating was significantly reduced by 6.83%. Thermal radiation benefits and the high stability of bonding interfaces are the main reasons to reduce the temperature of DUV-LEDs after Al/MgF2 coating. The present strategy is proposed from the point of view of chip fabrication, which is cost-effective and able to be manufactured at a large scale.

Predicting optical properties of different photonic crystal fibers from 2D structural images using convolutional neural network and transfer learning

An efficient and accurate joint neural network has been established to predict the optical properties of different photonic crystal fibers using two-dimensional structural images. The input variables of this network are structural images derived from the two-dimensional material refractive index distribution of the fiber cross-section. The structural images have greater flexibility and facilitate generalization research and transfer learning testing on various types of optical fibers. The generalization properties of this neural network for other photonic crystal fibers with different lattice arrangements have been investigated, and the corresponding transfer learning method is also proposed. With this transfer learning method, only a small amount of data is required to train and update the parameter weights of the last fully connected hidden layers. As a result, efficient and accurate prediction performance can be achieved for other photonic crystal fibers with different lattice arrangements. The proposed joint neural network and the transfer learning method are flexible and efficient, which provide new approaches for more flexible optimization and reverse design of optical fiber structures in the two-dimensional parameter space.

An efficient nonparaxial and bidirectional wave propagation method for optical fibers & fiber components

We present an efficient method for nonparaxial (i.e., wide angle) and bidirectional wave propagation in optical fibers and fiber components. The method is applicable to all structures such as tapers and fiber gratings which are azimuthally symmetric in respect of the refractive index distribution and the geometry. We use the collocation method to numerically solve the Helmholtz equation as this method allows to take advantage of the symmetry of the structure. This results in reduction of a 3-D propagation problem to a 2-D propagation problem giving a computational advantage by orders of magnitude. The method can also be used to obtain modes with similar computational advantage. The method works for fields of all azimuthal symmetries, i.e., one can treat all LPlm modes. In order to show the applicability of the method we have included examples on obtaining modes (LP and OAM) in step-index and ring core fibers (RCFs), propagation through a tapered RCF and computation of reflection spectra of few-mode fiber Bragg gratings (FM-FBGs).

Pressure estimation via measurement of reduced light scattering coefficient by oblique laser incident reflectometry

Continuous measurement of pressure is vital in many fields of industry, medicine, and science. Of particular interest is the ability to measure pressure in a noninvasive and contact-free manner. This work presents the potential of oblique incident reflectometry (OIR) to monitor variation in pressure via the reduced scattering parameter (μs′). Pressure deforms the geometry of the medium and causes distortion of its internal structure and the spatial distribution of optical properties. Light scattering is related to the morphology (size, density, distribution, etc.) and refractive index distributions of the medium, and applied pressure will influence directly these parameters. Therefore, we assume that pressure can be quantitatively assessed through monitoring the reduced scattering coefficient. For this purpose, the technique of OIR to evaluate the scattering parameter during pressure variations was utilized. OIR is a simple noninvasive and contact-free imaging technique able to quantify both absorption and scattering properties of a sample. In our setup, the medium is illuminated obliquely by a narrow laser beam, and the diffuse reflectance light is captured by a CCD camera. In offline processing, the shift (δ) of the diffuse light center from the incident point is mathematically analyzed and μs′ coefficient (μs′∼δ−1) is extracted. We present here confirmation of the validity of this assumption through results of a series of experiments performed on turbid liquid and artery occlusion of a human subject under different pressure levels. Thus, μs′ has the potential to serve as a good indicator for the monitoring of pressure.

A precise compensation algorithm for visual measurement in non-uniform refractive index environment based on Hamiltonian ray tracing method

In complex large-scale industrial environments, light rays no longer propagate in a straight line due to the influence of non-uniform refractive index, which will lead to large measurement errors in visual measurement. In order to accurately compensate the error, this paper firstly quantitatively analyzes the influence of non-uniform refractive index distribution on visual measurement. Then the symplectic matrix ray-tracing method of Hamiltonian optics is used to reconstruct spatial light in the reverse direction with known light propagation end point and spatial refractive index distribution. Thus the traditional model of light propagation along a straight line in visual measurement can be changed and the measurement error introduced by non-uniform refractive index field can be corrected. Finally, the proposed Hamiltonian ray tracing method was verified through the spatial non-uniform refractive index field reconstructed by Background Oriented Schlieren(BOS) method. The experimental results verified the effectiveness and feasibility of this method.