Refractive Index Distribution Research Articles

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.

Quantitative real-time phase microscopy for extended depth-of-field imaging based on the 3D single-shot differential phase contrast (ssDPC) imaging method.

Optical diffraction tomography (ODT) is a promising label-free imaging method capable of quantitatively measuring the three-dimensional (3D) refractive index distribution of transparent samples. In recent years, partially coherent ODT (PC-ODT) has attracted increasing attention due to its system simplicity and absence of laser speckle noise. Quantitative phase imaging (QPI) technologies represented by Fourier ptychographic microscopy (FPM), differential phase contrast (DPC) imaging and intensity diffraction tomography (IDT) need to collect several or hundreds of intensity images, which usually introduce motion artifacts when shooting fast-moving targets, leading to a decrease in image quality. Hence, a quantitative real-time phase microscopy (qRPM) for extended depth of field (DOF) imaging based on 3D single-shot differential phase contrast (ssDPC) imaging method is proposed in this research study. qRPM incorporates a microlens array (MLA) to simultaneously collect spatial information and angular information. In subsequent optical information processing, a deconvolution method is used to obtain intensity stacks under different illumination angles in a raw light field image. Importing the obtained intensity stack into the 3D DPC imaging model is able to finally obtain the 3D refractive index distribution. The captured four-dimensional light field information enables the reconstruction of 3D information in a single snapshot and extending the DOF of qRPM. The imaging capability of the proposed qRPM system is experimental verified on different samples, achieve single-exposure 3D label-free imaging with an extended DOF for 160 µm which is nearly 30 times higher than the traditional microscope system.

Structurally embedded gradient index lens for guided wave amplification in polymers

Guided wave inspection is a commonly used technique in structural health monitoring, yet there are challenges associated with ultrasonic inspection of polymeric structures due to high material damping resulting in wave attenuation. In this work, we present a structurally embedded gradient-index phononic crystal (GRIN-PC) lens for elastic wave amplification in polyvinyl chloride (PVC) structures to overcome the attenuation problem in long-range guided wave inspection. The GRIN-PC lens is made up of cylindrical brass stubs of varying heights or diameters embedded in the PVC base structure, providing a hyperbolic secant profile of refractive index distribution transverse to the wave propagation direction. We first demonstrate flexural wave focusing in a PVC plate by implementing the embedded lens design via numerical simulations and experiments. Then, the embedded GRIN-PC lens concept is implemented to PVC pipe for multi-mode wave focusing using a single lens design which is studied through numerical simulations. The proposed GRIN-PC lens design reduces the amplitude decay due to material damping by amplifying the wave energy at the focal regions of the lens. The embedded lens concept developed for polymers can also benefit other applications requiring the transmission of wave energy in structures with high material damping.

Experimental investigation on the internal stress of bismuth-doped fiber and its effect on the noise figure of Bismuth-doped fiber amplifier.

The noise figure (NF) of a fiber amplifier is one of the key measures of amplification performance, which characterizes the quality of the amplified signal. Residual stresses are inevitably generated during the manufacturing process of optical fibers, and this can lead to changes in the refractive index (RI) distribution of the fiber. Further, the change in RI distribution causes the mode-field characteristics of the fiber to change as well, and this ultimately has an impact on the NF performance of the amplifier. However, until now, there have been fewer studies on the effect of residual stress on the NF of the fiber amplifiers. In this work, we took a commercial single-mode bismuth-doped fiber (BDF) as an example and used a self-developed stress test device to measure its residual stress and refractive index distribution and compare it with that of a passive fiber. We also comprehensively compared the distribution of residual stress and refractive index of the fiber at different pump powers and pump wavelengths. Finally, we performed numerical simulations of the bismuth-doped fiber amplifier (BDFA) based on the BDF under the theoretical mode field area and BDF after the expansion of the mode field area due to stresses to compare the NF performance. The results demonstrate that: the entire cross-section (core and cladding) of the BDF exhibits tensile stress (>0 MPa), where the residual stress at the core of the BDF is nearly 9.8 MPa higher than that of the passive fiber; The residual stress makes the mode-field area of the BDF expand by 26.7% compared with the theoretical values, which ultimately makes the NF of the BDFA rise from 4.6 dB to 4.7 dB; The stress at the BDF core is exacerbated by pump excitation, where it is elevated by about 26% and 5% compared to vacancy at 1240 nm and 1310 nm pumps, which is most likely attributed to thermal effects. Therefore, it is necessary to consider the effect of residual stresses in the fabrication of optical fibers to better achieve the radius of the expected indicators. This work contributes to the better development of O-band BDFAs, especially for pre-simulation of the actual performance of BDFAs with a practical reference.

Design of three-level Nd-doped laser fiber based on anti-resonant structure

900-nm Nd-doped fiber laser can find widespread applications including biomedical diagnosis, laser detection, and spectral analysis. The four-level gain competition of Nd<sup>3+</sup> around 1060 nm severely constrains the laser power scaling of the 900-nm three-level Nd-doped fiber laser. In this work, we propose a large-mode-area Nd-doped double-layer solid-core anti-resonant fiber with a core diameter of 27 μm for generating a high-power 900-nm laser based on the resonant and anti-resonant conditions of anti-resonant fiber. The transmission properties and mode profiles of the designed fiber are analyzed theoretically by using the full-vector finite-element method combined with an optimized mesh size. By introducing the double-layer anti-resonant elements into the active fiber and optimizing the fiber structure parameters and refractive index distribution, the high-order modes are well coupled with cladding modes. Finally, the designed fiber exhibits a confinement loss below 0.1 dB/m for fundamental mode and the confinement losses of all high-order modes are greater than 10 dB/m in 880–913 nm band. More importantly, around 1060 nm, the confinement losses of all modes can reach up to 100 dB/m, which enables the designed Nd-doped fiber to effectively suppress parasitic lasing and even amplified spontaneous emission. The Nd-doped solid-core anti-resonant fiber proposed in this study shows broad application prospects in the fields of 900-nm high-power fiber laser and amplifier. The developed chemical vapor deposition process combined with stack-and-draw technology can be adopted for the fabrication of the designed fiber. In order to ensure the optical performance of the anti-resonant fiber, it is necessary to accurately control the thickness of all anti-resonant tubes, the glass composition of the active core and background area in actual fabrication.

Non-invasive Visualization and Characterization of Bile Canaliculus Formation Using Refractive Index Tomography.

The vital role of bile canaliculus (BC) in liver function is closely related to its morphology. Electron microscopy has contributed to understanding BC morphology; however, its invasiveness limits its use in living specimens. Here, we report non-invasive characterization of BC formation using refractive index (RI) tomography. First, we investigated and characterized the RI distribution of BCs in two-dimensional (2D) cultured HepG2 cells. BCs were identified based on their distinct morphology and functionality, as confirmed using a fluorescence-labeled bile acid analog. The RI distribution of BCs exhibited three common features: (1) luminal spaces with a low RI between adjacent hepatocytes; (2) luminal spaces surrounded by a membranous structure with a high RI; and (3) multiple microvillus structures with a high RI within the lumen. Second, we demonstrated the characterization of BC structures in a three-dimensional (3D) culture model, which is more relevant to the in vivo environment but more difficult to evaluate than 2D cultures. Various BC structures were identified inside HepG2 spheroids with the three features of RI distribution. Third, we conducted comparative analyses and found that the BC lumina of spheroids had higher circularity and lower RI standard deviation than 2D cultures. We also addressed comparison of BC and intracellular lumen-like structures within a HepG2 spheroid, and found that the BC lumina had higher RI and longer perimeter than intracellular lumen-like structures. Our demonstration of the non-destructive, label-free visualization and quantitative characterization of living BC structures will be a basis for various hepatological and pharmaceutical applications.

The influence of refractive index profile on supercontinuum beams self-cleaning in graded index multimode fiber

We propose a theoretical scheme to improve the fundamental mode energy proportion of the supercontinuum (SC) generation in graded-index multimode fiber (GRIN-MMF). With this scheme, we conduct numerical investigations into the influence of various core refractive index profile parameters on beam-self cleaning of fundamental mode, establishing an optimal parameter range (α=2.0∼2.06). Within this range, the energy proportion of the fundamental mode gradually increases from 32% to 65% as the propagation distance. Additionally, our simulation provides the initial demonstration that the supercontinuum (SC) broadening is correlated with the distribution of core refractive indices within the graded-index multimode fiber.

Phase variation of Laguerre-Gaussian vortex beams in a homogeneous atmospheric medium under finite amplitude acoustic wave perturbation

In this article, we have derived the acoustic pressure and medium refractive index expressions in a homogeneous atmospheric medium perturbed by a planar finite amplitude acoustic wave. In a planar finite amplitude acoustic wave perturbation, we developed a Laguerre–Gaussian vortex beam transmission model in a homogeneous atmospheric medium. We investigated the effects of different acoustic source parameters on the phase of the Laguerre–Gaussian vortex beam transmission, considering the atmospheric medium’s viscous effect. The results show that acoustic waves of finite amplitude distort the refractive index distribution of a homogeneous atmospheric medium. At a given distance, the amplitude of the refractive index gradually increases with increasing acoustic wave transmission distance. At the same time, the phase of the Laguerre–Gaussian vortex beam is rotated by the perturbation of the finite-amplitude acoustic wave, and the phase always returns to its initial position. Unlike linear acoustic waves, changes in the homogeneous atmospheric refractive index distribution and the homogeneous phase of the Laguerre–Gaussian vortex light no longer satisfy the periodic variation when perturbed by finite-amplitude acoustic waves. Under the same conditions, the effect of finite-amplitude acoustic waves on the phase of the Laguerre–Gaussian vortex light is stronger than that of linear acoustic waves. Finally, the effects of different acoustic pressure and frequency of the source on the phase of the Laguerre–Gaussian vortex beam transmission are calculated. The results show that different acoustic parameters at the source can be used to achieve phase modulation at different distances and intensities.

Multi-harmonic structured illumination-based optical diffraction tomography

Imaging speed and spatial resolution are key factors in optical diffraction tomography (ODT), while they are mutually exclusive in 3D refractive index imaging. This paper presents a multi-harmonic structured illumination-based optical diffraction tomography (MHSI-ODT) to acquire 3D refractive index (RI) maps of transparent samples. MHSI-ODT utilizes a digital micromirror device (DMD) to generate structured illumination containing multiple harmonics. For each structured illumination orientation, four spherical spectral crowns are solved from five phase-shifted holograms, meaning that the acquisition of each spectral crown costs 1.25 raw images. Compared to conventional SI-ODT, which retrieves two spectral crowns from three phase-shifted raw images, MHSI-ODT enhances the imaging speed by 16.7% in 3D RI imaging. Meanwhile, MHSI-ODT exploits both the 1st-order and the 2nd-order harmonics; therefore, it has a better intensity utilization of structured illumination. We demonstrated the performance of MHSI-ODT by rendering the 3D RI distributions of 5 µm polystyrene (PS) microspheres and biological samples.

Environmental Knowledge-Driven Over-the-Horizon Propagation Loss Prediction Based on Short- and Long-Term Parallel Double-Flow TrellisNets

Accurate perceptual knowledge of atmospheric characteristics in the propagation path is of great significance for the design of communication systems. However, the atmosphere above the ocean is inhomogeneous, which brings challenges to accurate prediction of propagation loss. Moreover, the atmospheric refractive index distribution model calculated from atmospheric data requires at least two stations with near-sea meteorological data. In real maritime over-the-horizon communication or detection, only one station transmits and receives meteorological data, and the received meteorological data and propagation loss have large temporal noise. To address these issues, first, a denoising model based on the one-dimensional convolution autoencoder (1DCAE) is constructed to filter out the temporal noise of input environmental meteorological data and propagation loss. Second, to accurately predict the influence of environmental factors on the prediction of propagation loss, a deep-learning framework called short- and long- term parallel double-flow TrellisNets (SL-TrellisNets) is proposed to predict the loss. Finally, the extensive experiments demonstrated that the root mean square and mean absolute errors of the proposed 1DCAE are dramatically reduced. Our proposed SL-TrellisNets outperforms the other state-of-the-art techniques in terms of propagation loss prediction. In addition, we analyzed the impact of the environmental factors on the accuracy of over-the-horizon propagation loss prediction.

A Manufacturability‐Driven Method for Designing Metamaterial Focusing Acoustical Lenses

Herein, a method for designing and fabricating acoustic metamaterial focusing lenses for imaging applications such as nondestructive testing is proposed. First, a refractive index distribution is designed using the time delay method for a target focal length. Second, unit cell structures that can achieve the required refractive indices are found using the effective property retrieval method. At this point, factors such as fabrication cost and manufacturing limitations are considered. Finally, the pressure field from the designed lens is calculated using finite element (FE) modelling and iterated until the required focusing performance is achieved. To increase manufacturability, the unit cells necessarily become larger than required for the homogeneous regime. As an example, a lens of focal length 200 ± 10 mm at a frequency of 40 kHz is designed using cross‐shaped unit cells and fabricated using three‐dimensional printing. The design methodology leads to 2.4 mm (wavelength/3.6) unit cells which operate near the cut‐off frequency of the first mode. The lens is experimentally tested, achieving a focal length of 208 mm and a focal width of 12 mm (1.4 × wavelength), and showing good agreement with an FE model. The focusing ability of the lens is demonstrated by measuring the size of various holes in thin plates.

Photonic Spin Hall Effect as a Highly Sensitive Refractive Index Sensing Platform for Glucose

AbstractThis study presents an innovative refractive index (RI) sensor that measures glucose concentration by utilizing the photonic spin Hall effect (SHE) in a resonant optical tunneling effect (ROTE) structure. The ROTE structure consists of three InP layers with the high RI and two analyte layers (with a high‐low‐high‐low‐high RI distribution), in which glucose solution samples with the low RI are injected. By subjecting the InP layers to external bias‐assisted light, the photonic SHE can be flexibly manipulated, enabling the modulation of the sensing performance accordingly. It is found that the transverse shift of photonic SHE presents a large variation in response to the tiny change in glucose concentrations. By optimizing the parameters (i.e., intensity or wavelength) of bias light, the sensitivity of this sensor can reach as high as 735.7 µm RIU−1. Compared to traditional glucose sensors, this original work implements the novel photonic SHE with the superior sensing performance. Therefore, the proposed design shows promising potential for biomedical applications, such as medical diagnoses and drug discovery.

Right partial rainbow refractometry for measuring droplet refractive index and size

Rainbow refractometry can be employed for measuring the parameters of droplets or sprays. Considering the diversity of different measurement environments and droplet components, there are instances in experiments where optics fail to record the complete rainbow signal. To enhance the experimental data utilization, this paper investigates rainbow refractometry using the incomplete rainbow signal on the right side, focusing on its feasibility and accuracy. The concept that defines the incompleteness of the right-sided rainbow signal is termed as the dimensionless right signal partial ratio (RSPR). The study conducts a comprehensive analysis of refractive index, droplet diameter, and size distributions retrieved from the partial rainbow signals simulated by the Lorenz-Mie theory with varying RSPR values. For both partial standard and global rainbows, the critical value of the retrieval error is found to be whether the primary peak of the rainbow is preserved or not, i.e., RSPR = 1. Laboratory experiments verify the feasibility and effectiveness of employing rainbow refractometry with right partial rainbow signals. The study addresses the challenge of incomplete recording of rainbow signals in experiments, and is expected to improve experimental efficiency and data utilization.

Continuous-wave terahertz in-line holographic diffraction tomography with the scattering fields reconstructed by a physics-enhanced deep neural network

Diffraction tomography is a promising, quantitative, and nondestructive three-dimensional (3D) imaging method that enables us to obtain the complex refractive index distribution of a sample. The acquisition of the scattered fields under the different illumination angles is a key issue, where the complex scattered fields need to be retrieved. Presently, in order to develop terahertz (THz) diffraction tomography, the advanced acquisition of the scattered fields is desired. In this paper, a THz in-line digital holographic diffraction tomography (THz-IDHDT) is proposed with an extremely compact optical configuration and implemented for the first time, to the best of our knowledge. A learning-based phase retrieval algorithm by combining the physical model and the convolution neural networks, named the physics-enhanced deep neural network (PhysenNet), is applied to reconstruct the THz in-line digital hologram, and obtain the complex amplitude distribution of the sample with high fidelity. The advantages of the PhysenNet are that there is no need for pretraining by using a large set of labeled data, and it can also work for thick samples. Experimentally with a continuous-wave THz laser, the PhysenNet is first demonstrated by using the thin samples and exhibits superiority in terms of imaging quality. More importantly, with regard to the thick samples, PhysenNet still works well, and can offer 2D complex scattered fields for diffraction tomography. Furthermore, the 3D refractive index maps of two types of foam sphere samples are successfully reconstructed by the proposed method. For a single foam sphere, the relative error of the average refractive index value is only 0.17%, compared to the commercial THz time-domain spectroscopy system. This demonstrates the feasibility and high accuracy of the THz-IDHDT, and the idea can be applied to other wavebands as well.

Lattice Boltzmann simulations on transient radiative transfer problems in irregular geometries with constant or graded refractive index

This work is concerned with the transient radiative transport in inhomogeneous two- or three-dimensional semitransparent graded-index media with irregular geometry. The lattice Boltzmann method is applied to the graded-index media mapped with non-orthogonal grids to solve the radiative transfer while the finite volume method expresses the angular processing. The solution of the transient radiation from the methodology developed is firstly validated with good accuracy by considering benchmark solutions available in the literature for comparisons for various forms of geometry including a cube, elliptic cylinder as well as irregular shapes. Afterwards, the solver is used to analyze the radiative transfer in graded-index media including regular and irregular geometries, and various governing parameters such as laser and optical properties, scattering laws, incident angle of the incoming beam, refractive index, and temperature distributions. Suitable calculations of the transient radiometric heat flux and incident energy help to evaluate the time-resolved reflectance and transmittance. The results from this study indicate that the present methodology and boundary treatments are simple and suitable to deal with multidimensional radiative transfer in irregular domains.

Enhanced functionalities of immune cells separated by a microfluidic lattice: assessment based on holotomography.

The isolation of white blood cells (WBCs) from whole blood constitutes a pivotal process for immunological studies, diagnosis of hematologic disorders, and the facilitation of immunotherapy. Despite the ubiquity of density gradient centrifugation in WBC isolation, its influence on WBC functionality remains inadequately understood. This research employs holotomography to explore the effects of two distinct WBC separation techniques, namely conventional centrifugation and microfluidic separation, on the functionality of the isolated cells. We utilize three-dimensional refractive index distribution and time-lapse dynamics to analyze individual WBCs in-depth, focusing on their morphology, motility, and phagocytic capabilities. Our observations highlight that centrifugal processes negatively impact WBC motility and phagocytic capacity, whereas microfluidic separation yields a more favorable outcome in preserving WBC functionality. These findings emphasize the potential of microfluidic separation techniques as a viable alternative to traditional centrifugation for WBC isolation, potentially enabling more precise analyses in immunology research and improving the accuracy of hematologic disorder diagnoses.

High turbidity underwater single-pixel imaging based on Unet++ and attention mechanism at a low sampling

Underwater environments contain significant scattering media, characterized by complex distributions of refractive index and reflectance within. These properties cause light to deviate from its original propagation direction and decrease the signal-to-noise ratio during it passes through the scattering media. Consequently, traditional imaging techniques are difficult to achieve clear underwater imaging. Single-pixel imaging (SPI) offers higher sensitivity and the ability to be imaged in extremely low-light conditions compared to traditional imaging methods, and it provides significant advantages for underwater imaging. This paper proposes a SPI system based on Unet++ that can reconstruct high-quality images under the low sampling rate in highly turbid water environments. Numerical simulations and physical experiments demonstrate that our approach can still achieve clear image reconstruction at a sampling rate of 3.125 % under the turbidity level of 80 NTU compared with other methods. Additionally, the network exhibits strong generalization capabilities, and our approach holds the capability to reconstruct high-quality images under low sampling in high turbidity underwater conditions.