Grating Spectrum Research Articles

Multistructured Accretion Flow of Sgr A*. I. Examination of a Radiatively Inefficient Accretion Flow Model

The extreme low-luminosity supermassive black hole Sgr A* provides a unique laboratory in which to test models of radiatively inefficient accretion flows (RIAFs). Previous fits to the quiescent Chandra ACIS-S spectrum found that a RIAF model with an equal inflow–outflow balance works well. In this work, we apply the RIAF model to the Chandra HETG-S spectrum obtained through the Chandra X-ray Visionary Program, which displays features suggestive of temperature and velocity structures within the plasma. A comprehensive forward model analysis accounting for the accretion flow geometry and HETG-S instrumental effects is required for a full interpretation of the quiescent Chandra HETG-S spectrum. We present a RIAF model that takes these effects into account. Our fits to the high-resolution grating spectrum indicate an inflow balanced by an outflow (s ∼ 1) alongside a temperature profile that appears shallower than what would be expected from a gravitational potential following 1/r. The data require that the abundance of iron relative to solar is Z Fe < 0.32 Z ⊙ (90% credible interval), much lower than the 2 Z ⊙ metallicity measured in nearby late-type giants. While future missions like NewAthena will provide higher spectral resolution, source separation will continue to be a problem. Leveraging Chandra’s unparalleled spatial resolution, which is not expected to be surpassed for decades, remains essential for detailed investigations of the densely populated Galactic center in X-rays.

Spectrum design of multimode fiber Bragg gratings based on suppression of mode coupling

The direct femtosecond laser inscription method is very competitive in the fabrication of fiber Bragg gratings, but its refractive index modification region is very limited and leads to low reflectivity and wide spectra of multimode fiber gratings. In this work, the relationship between the refractive index modification region, the coupling coefficient, and the spectrum of the multimode fiber grating is investigated based on the intrinsic mechanism of mode coupling; thus the annular and eccentric elliptic refractive index modification regions are accordingly proposed to suppress mode couplings in the multimode fiber Bragg grating, so as to achieve a highly discrete spectrum and narrow spectrum of the multimode fiber Bragg grating, respectively. This work can provide a solid theoretical foundation for the spectrum design of the multimode fiber Bragg grating, which can be utilized to customize the spectrum according to application scenarios such as optical communication, fiber lasers, filtering, and sensing.

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).

Simulation of the spatial distribution of scattered light under illumination of a resonant diffraction grating with structured light

In this paper, a comparative theoretical analysis and numerical simulation of the operation of various types of diffraction gratings in the far field is carried out using a Fourier transform. In more detail is discussed the spatial spectrum of binary amplitude gratings, including the diffraction patterns in the far field and in the focal plane and while taking into account variations in the fill-factor. When analyzing characteristics of experimentally created halide perovskite resonant gratings, the influence of the illuminating beam type on the formation of the first three diffraction orders is considered.

Stellar-wind variability in Cygnus X-1 from high-resolution excess variance spectroscopy with Chandra

Context. Stellar winds of massive stars are known to be driven by line absorption of UV photons, a mechanism that is prone to instabilities, causing the wind to be clumpy. The clumpy structure hampers wind mass-loss estimates, limiting our understanding of massive star evolution. The wind structure also impacts accretion in high-mass X-ray binary (HMXB) systems. Aims. We aim to analyse the wavelength-dependent variability of X-ray absorption in the wind to study its structure. Such an approach is possible in HMXBs, where the compact object serves as an X-ray backlight. We probe different parts of the wind by analysing data taken at superior and inferior conjunctions. Methods. We applied excess variance spectroscopy to study the wavelength-dependent soft (2–14 Å) X-ray variability of the HMXB Cygnus X-1 in the hard spectral state. Excess variance spectroscopy quantifies the variability of an object above the statistical noise as a function of wavelength, which allows us to study the variability of individual spectral lines. This technique was applied to high-resolution gratings spectra provided by Chandra, accounting for various systematic effects. The frequency dependence is investigated by changing the time binning. Results. The strong orbital phase dependence we observe in the excess variance is consistent with column-density variations predicted by a simple model for a clumpy wind. We identify spikes of increased variability with spectral features found by previous spectroscopic analyses of the same data set, most notably from silicon in over-dense clumps in the wind. In the silicon line region, the variability power is redistributed towards lower frequencies, hinting at increased line variability in large clumps. In prospect of the microcalorimetry missions that are scheduled to launch within the next decade, excess variance spectra present a promising approach to constraining the wind structure, especially if accompanied by models that consider changing ionisation.

An intrinsic sensitivity calibration scheme for high temperature measurements using femtosecond point-by-point written fiber Bragg gratings

A calibration method is presented for temperature measurements using fiber Bragg grating transducers written with the point-by-point technique and femtosecond laser impulsions in silica optical fibers. This method is based on the determination of the wavelength-independent thermal sensitivity coefficients of the waveguide over the temperature range of interest. The calibration law is calculated using the wavelength comb-like spectrum of high order fiber Bragg gratings, allowing measurement accuracy comparable to type N thermocouples up to 900°C. The effects of thermal cycling and annealing on measurement errors are also discussed.

Optical Reflection Induced by Flexural Acoustic Wave on Fiber Bragg Grating

Flexural acoustic waves can induce optical reflection peaks on one side of the Bragg wavelength in the reflection spectrum of a fiber Bragg grating, thus laying a cornerstone of active acoustic-optic fiber devices. The acoustically-induced refractive index distribution of FBG is deduced. The mechanism of forming acoustically-induced reflection peaks is investigated using mode coupling theory in vector mode presentation. A precise picture is depicted with the selection rules for mode coupling and observation of phase matching, such that the two-step and the three-step processes for acoustically-induced reflection peaks are identified with experimental confirmation. While the three-step coupling theory is discovered, our theoretical framework also refines the former scalar-mode two-step coupling theory. Empowering the theoretical prediction to perfectly match experiment, this work will facilitate the design and application of novel active fiber-optic devices based on acoustic-optic interactions.

Fabrication and characterization of polymer optical waveguide Bragg grating for pulse signal sensing.

Polymer materials have the advantages of a low Young's modulus and low-cost preparation process. In this paper, a polymer-based optical waveguide pressure sensor based on a Bragg structure is proposed. The change in the Bragg wavelength in the output spectrum of the waveguide Bragg grating (WBG) is used to linearly characterize the change in pressure acting on the device. The polymer-based WBG was developed through a polymer film preparation process, and the experimental results show that the output signal of the device has a sensitivity of 1.275 nm/kPa with a measurement range of 0-12 kPa and an accuracy of 1 kPa. The experimental results indicate that the device already perfectly responds to a pulse signal. It has significant potential application value in medical diagnostics and health testing, such as blood pressure monitoring, sleep quality monitoring, and tactile sensing.

Demodulation of the overlapping reflection spectrum of serial FBGs based on a weighted differential evolution algorithm.

This study addresses the wavelength demodulation problem of the overlapping reflection spectrum of serial fiber Bragg gratings (FBGs) with nearly-identical wavelength. Specifically, a novel demodulation model for the overlapping reflection spectrum was presented based on spectrum similarity, and this model encodes FBGs through reflectivity. Subsequently, a weighted differential evolution algorithm was employed to calculate the FBG wavelengths. And the factors affecting the demodulation accuracy of the proposed method were simulated and analyzed. Finally, the proposed method was applied to demodulate the overlapping reflection spectra of serial FBGs. The experiment results indicate that the proposed method is suitable for completely overlapping, partially overlapping, and non-overlapping reflection spectra of serial FBGs. The wavelength demodulation accuracy demonstrated here in fully overlapping situations for two, three, and four FBGs was only 4.5, 14.9, and 24.6 pm, respectively.

Deterministic rendering of structural color induced by atypical nano-gratings in ultra-precision diamond cutting

Ultra-precision diamond cutting (UPC) has been recently proposed for fast generation of nano-gratings to render diffractive structural color on various metallic surfaces. However, the complex nanoscale generation mechanism and atypical grating topography provide the significant challenges for deterministic rendering of structural color with standard representations. In this paper, an innovative diffraction prediction model is firstly proposed to describe the diffractive spectrum of atypical gratings under the full considerations of cutting process parameters, double working facets, material optical properties and environmental conditions. The standard CIE 1931 chromaticity diagram for grating-induced structural color is released for color gamut determination and optimization, where the color gamut range is defined by a novel concept of average saturation. The experimental results demonstrate the deterministic generation of three groups of nano-gratings with desired 3D topography, of which the measured angle-dependent diffractive spectrum and rendering color attributes show good agreements with theoretical results. Moreover, the new topography-modulation based strategies for achieving maximal color gamut and manipulating the ternary color attributes are clarified. The outcome of this paper lays the scientific foundations for deterministic rendering and performance enhancement of structural color enabled by UPC processes.

Femtosecond-laser-inscribed Bragg grating in hollow-core fiber for highly sensitive optofluidic sensing.

An optofluidic sensor based on a Bragg grating in hollow-core fiber (HCF) is experimentally demonstrated. The grating is inscribed into the HCF by femtosecond laser illumination through a phase mask. Periodic index modulation is introduced into the silica material surrounding the hollow core, causing cladding mode resonance, and multiple reflection peaks are observed in the grating spectrum. These reflection peaks later shift to longer wavelengths when high-index liquid is infiltrated into the HCF. The new reflection peak results from the backward coupling of the liquid core mode of the waveguide, the mode field of which overlaps with the grating modulation surrounding the liquid core. The resonant wavelength of the liquid-core fiber grating increases with the index value of the infiltrating liquid, and optofluidic refractive index sensing is realized with the device. The highest refractive index sensitivity, 1117 nm/RIU, is obtained experimentally in the index range of 1.476-1.54. The infiltrated hollow-core fiber Bragg grating also exhibits high temperature sensitivity due to the high thermal-optic coefficient of the liquid, and a sensitivity of -301 pm/°C is achieved in the temperature range of 25°C to 60°C.

Enhanced microwave metrology using an optical grating in Rydberg atoms.

An enhanced measurement of the microwave (MW) electric (E) field is proposed using an optical grating in Rydberg atoms. Electromagnetically induced transparency (EIT) of Rydberg atoms appears driven by a probe field and a control field. The EIT transmission spectrum is modulated by an optical grating. When a MW field drives the Rydberg transition, the central principal maximum of the grating spectrum splits. It is interesting to find that the magnitude of the sharp grating spectrum changes linearly with the MW E-field strength, which can be used to measure the MW E-field. The simulation result shows that the minimum detectable E-field strength is nearly 1/8 of that without gratings, and its measurement accuracy could be enhanced by about 60 times. Other discussion of MW metrology based on a grating spectrum is also presented.

THEORETICAL RESEARCHES OF THE EMBEDDED FIBER-OPTIC SYSTEM OF TESTING DEFORMATION AND TEMPERATURE OF POLYMER COMPOSITES

This article describes the results of theoretical researches of the system of optical testing of polymer composites by the method of two optical fibers with different sensitivity to deformation and temperature, using integrated arrays of fiber Bragg gratings. The features of the primary data processing from the optical testing system embedded into the composite are considered by the methods of weighted arithmetic mean and approximation by the Gaussian function. The basic relations for calculating the error in determining the temperature and strain with the help of fiber-optic embedded testing systems are obtained. A numerical model of the interrogator has been constructed, which makes it possible to estimate the systematic error of deformation and temperature measurements, including taking into account the noise of a real interrogator. It is shown that, taking into account a number of assumptions for the problem of simultaneous embedded testing of composites with fiber Bragg gratings, it is advisable to apply he method of primary processing of testing data using the approximation of the real spectra of fiber Bragg gratings by the Gaussian function, while in order to increase the reliability of testing, it is necessary to take into account the temperature correction characteristic of a particular interrogating device.

Accuracy of scanning interrogation of FBG sensors

Abstract Progress in the fibre optic technology spurred the development of optical fibre-based sensors. A successful fibre optics-based element for sensorial systems is fibre Bragg grating. It allows to read the measured value by the spectral shift of light, which is the variable with a good potential for accurate measurement. Various types of the interrogation of the light spectrum reflected from the measuring grating are discussed in this article and the work concentrates on the spectrum scanning that gives the good chances to diminish measuring errors by a proper choice of parameters. The focal point is the accuracy of establishing the correct value of the maximum reflectance wavelength. The significance of the noise in the photoelectric scanning signal for the measuring accuracy is analysed and the crucial factor is found in the minimizing the reflectance spectral width of the measuring grating and using the spectrum of the scanning light with the same or smaller spectral width. An important aspect is the relation of the maximal reflectance and the wavelength width of the measuring grating reflectance spectrum. The article also shows the potentiality of the apodized gratings for improving the scanning interrogation. A specific index apodization profile was analysed and its advantages are discussed.

Spectrum characteristics and temperature measurement error of FBG sensor based on rotor temperature monitoring system

For real-time temperature monitoring of a generator or electric motor rotor, the effects of rotation on the reflection spectrum of a polyimide-coated Fibre Bragg Grating (FBG) were analyzed using formulas. The measurement error resulting from the low-speed operation was evaluated, combined with the finite element method. Secondly, the key design of the FBG sensors and the mating part of the fiber optic rotary joint (FORJ) were investigated. The temperature of a rotating shaft was monitored to test the reliability of the measurement system. With a resolution of 0.1℃, the system was able to achieve an error of 0.5℃ over a range of 30-180℃. Finally, the critical conditions for the application of polyimide-coated and metal-coated FBGs were discussed. The results show that the variation of the center wavelength is more sensitive to the radius of the small-sized rotor, and the rotation speed of the large-sized rotor. It is at higher speeds that the thickness of the coating has a more pronounced effect on error, demonstrating that the accuracy of FBGs used in high-speed rotors could be rapidly improved by reducing the thickness of the metal coating. The reported results provide a basis for the thermal monitoring performance of FBG sensors during rotation.

Efficient reconstruction scheme with deep neural network for highly compressive sensing of fiber Bragg grating spectrum

In this work, we propose an efficient reconstruction scheme for compressive sensing (CS) of fiber Bragg grating (FBG) spectrum. Taking advantage of the sparse reflection spectrum of the FBG array network, we have demonstrated the use of CS for compressing the spectrum at an excessively high compression factor up to 64. In addition to that, the spectral difference (SD) of the spectra is used to further enhance their sparsity for the CS model. In this investigation, four different configurations have been devised and tested to compare their performance and effectiveness. Configuration IV that is based on SD and deep neural network offers the best recovery performance. The proposed method is a potential tool for efficient data storage and transmission for FBG sensor network.

An Investigation of All Fiber Free-Running Dual-Comb Spectroscopy.

A dual-comb spectroscopy (DCS) system uses two phase-locked optical frequency combs with a slight difference in the repetition frequency. The spectrum can be sampled in the optical frequency (OF) domain and reproduces the characteristics in the radio frequency (RF) domain through asynchronous optical sampling. Therefore, the DCS system shows great advantages in achieving precision spectral measurement. During application, the question of how to reserve the mutual coherence between the two combs is the key issue affecting the application of the DCS system. This paper focuses on a software algorithm used to realize the mutual coherence of the two combs. Therefore, a pair of free-running large anomalous dispersion fiber combs, with a center wavelength of approximately 1064 nm, was used. After the signal process, the absorption spectra of multiple species were simultaneously obtained (simulated using the reflective spectra of narrow-bandwidth fiber Bragg gratings, abbreviated as FBG). The signal-to-noise ratio (SNR) could reach 13.97 dB (25) during the 100 ms sampling time. In this study, the feasibility of the system was first verified through the simulation system; then, a principal demonstration experiment was successfully executed. The whole system was connected by the optical fiber without additional phase-locking equipment, showing promise as a potential solution for the low-cost and practical application of DCS systems.

Structure-embedding network for predicting the transmission spectrum of a multilayer deep etched grating.

This Letter presents a structure-embedding network (SEmNet) to predict the transmission spectrum of a multilayer deep etched grating (MDEG). Spectral prediction is an important procedure in the MDEG design process. Existing approaches based on deep neural networks have been applied to spectral prediction to improve the design efficiency of similar devices, such as nanoparticles and metasurfaces. Due to a dimensionality mismatch between a structure parameter vector and the transmission spectrum vector, however, the prediction accuracy decreases. The proposed SEmNet can overcome the dimensionality mismatch problem of deep neural networks to increase the accuracy of predicting the transmission spectrum of an MDEG. SEmNet consists of a structure-embedding module and a deep neural network. The structure-embedding module increases the dimensionality of the structure parameter vector with a learnable matrix. The augmented structure parameter vector then becomes the input to the deep neural network to predict the transmission spectrum of the MDEG. Experiment results demonstrate that the proposed SEmNet improves the prediction accuracy of the transmission spectrum in comparison with the state-of-the-art approaches.

The calculation of a two-cascade long-period fiber grating of the refractive index

A method is proposed for calculating the spectral characteristics of cascade long-period fiber gratings of the refractive index of the core based on the method of partial regions and decomposition. According to the method, the structure is represented as a cascade connection of basic inhomogeneities, each of which is a junction of several optical fibers with different dielectric and geometric parameters. Approbation of the method was carried out by reducing the structure to a single long-period fiber grating and comparing the results with the results obtained using other calculation methods. The results matched graphical accuracy. The advantage of the method is the possibility to theoretically study the effect of dielectric and geometric parameters on the spectral properties of the structure, as well as significantly save time resources. The transmission spectra of gratings with different parameters of period T, grating length L, and distance between gratings Lf are presented.

X-Ray Spectroscopy in the Microcalorimeter Era 4: Optical Depth Effects on the Soft X-Rays Studied with Cloudy

In this paper, we discuss atomic processes modifying the soft X-ray spectra from optical depth effects like photoelectric absorption and electron scattering suppressing the soft X-ray lines. We also show the enhancement in soft X-ray line intensities in a photoionized environment via continuum pumping. We quantify the suppression/enhancement by introducing a “line modification factor (f mod).” If 0 ≤ f mod ≤ 1, the line is suppressed, which could be the case in both collisionally ionized and photoionized systems. If f mod ≥ 1, the line is enhanced, which occurs in photoionized systems. Hybrid astrophysical sources are also very common, where the environment is partly photoionized and partly collisionally ionized. Such a system is V1223 Sgr, an Intermediate Polar binary. We show the application of our theory by fitting the first-order Chandra Medium Energy Grating (MEG) spectrum of V1223 Sgr with a combination of Cloudy-simulated additive cooling-flow and photoionized models. In particular, we account for the excess flux for O vii, O viii, Ne ix, Ne x, and Mg xi lines in the spectrum found in a recent study, which could not be explained with an absorbed cooling-flow model.