Apodization Function Research Articles

Nonparaxial diffraction of the Cartesian oval

We study the nonparaxial diffraction of the well-known Cartesian oval in finite and infinite conjugate configurations. We started by expressing the refraction of the Cartesian oval by analytical closed-form equations. These equations are convenient to obtain the pupil apodization function of the Cartesian oval, which is needed to compute the diffraction pattern using Richard–Wolf theory. A comparison of the diffraction patterns of the Cartesian oval with finite/infinite objects, the aplanatic lens, and the parabolic mirror for radially polarized illumination is presented. From this comparison, we conclude that a Cartesian oval for a far object is not a good candidate for tight focusing and super-resolution applications and the performance of a Cartesian oval in a finite conjugate configuration is similar to the performance of an aplanatic lens and in some scenarios, it can perform better than the aplanatic lens.

First order surface grating fiber coupler under the period chirp and apodization functions variations effects

<p>The paper has demonstrated the first order surface grating fiber coupler under the period chirp and apodization functions variations effects. The Fiber coupler transmittivity/reflectivity, the fiber coupler grating index change and the fiber coupler mesh transmission cross-section are clarified against the grating length with the quadratic/cubic root period chirp and Gaussian/uniform apodization functions. The fiber coupler delay and dispersion are simulated and demonstrated with grating wavelength with quadratic/cubic root period chirp and Gaussian/uniform apodization function. As well as the fiber coupler output pulse intensity is simulated against the time period with the quadratic/cubic root period chirp and Gaussian/uniform apodization function. The fiber coupler peak intensity variations against the transmission range variations is also demonstrated by OptiGrating simulation software.</p>

Apodization sensor performance for TOPAS fiber Bragg grating

Optical sensors have more capabilities than electronic sensors, and therefore provide extraordinary developments, including high sensitivity, non-susceptibility to electromagnetic wave disturbances, small size, and multiplexing. Furthermore, fiber Bragg grating (FBG) is an optical sensor with a periodically changing grating refractive index, susceptible to strain and temperature changes. As a sensor, FBG’s performance required to optimize and improve the numerical apodization function and affect the effective refractive index is considered. The grating fiber’s apodization function can narrow the full width half maximum (FWHM) and reduce the optical signal’s side lobes. In all the apodization functions operated by FBG, Blackman has the highest sensitivity of 15.37143 pm/°C, followed by Hamming and Gaussian, with 13.71429 pm/°C and 13.70857 pm/°C, respectively, and Uniform grating fiber with the lowest sensitivity of 12.40571 pm/°C. Hamming, Uniform, and Blackman discovered the sensitivity for a strain to be 1.17, 1.16, and 1.167 pm/microstrain, respectively. The results obtained indicated that apodization could increase FBG’s sensitivity to temperature and strain sensors. For instance, in terms of other parameters, FWHM width, Hamming had the narrowest value of 0.6 nm, followed by Blackman with 0.612 nm, while Uniform had the widest FWHM of 1.9546 nm.

Femtosecond laser line-by-line inscription of apodized fiber Bragg gratings.

The reflection spectra of conventional fiber Bragg gratings (FBGs) with uniform index modulation profiles typically have strong sidelobes, which hamper the performance of FBG-based optical filters, fiber lasers, and sensors. Here, we propose and demonstrate a femtosecond laser line-by-line (LbL) scanning technique for fabricating apodized FBGs with suppressed sidelobes. This approach can flexibly achieve various apodized modulation profiles via precise control over the length and/or transverse position of each laser-inscribed index modification track. We theoretically and experimentally studied the influences of the apodization function on the side-mode suppression ratio (SMSR) in the fabricated apodized FBG, and the results show that a maximum SMSR of 20.6 dB was achieved in a Gaussian-apodized FBG. Subsequently, we used this method to fabricate various apodized FBGs, and the SMSRs in these FBGs were reduced effectively. Specifically, a dense-wavelength-division-multiplexed Gaussian-apodized FBG array with a wavelength interval of 1.50 nm was successfully fabricated, and the SMSR in such an array is 14 dB. Moreover, a Gaussian-apodized phase-shifted FBG and chirped FBG were also demonstrated with a high SMSR of 14 and 16 dB, respectively. Therefore, such an apodization method based on a modified femtosecond laser LbL scanning technique is an effective and flexible way to fabricate various FBGs with high SMSRs, which is promising to improve the performance of optical filters, fiber lasers, and sensors.

Integration of chirping and apodization of Topas materials for improving the performance of fiber Bragg grating sensors

The discovery of the fiber Bragg grating (FBG) is an early milestone in developing optical fiber technology, such as optical communication to monitoring material health structures as sensors. For optical communication, the FBG components are capable of filtering functions. As a sensor, it has a high sensitivity immune to electromagnetic wave interference, is small in size, and is resistant to extreme environmental conditions. The sensitivity of the FBG sensor is obtained from the shift in the peak wavelength of each of the temperature and strain quantities. However, the performance of the FBG sensor can be improved by engineering the distribution of the refractive index on the grid with the apodization and chirp functions. Apodization is a technique to improve the performance of the FBG to eliminate noise, narrow the full width half maximum, lower the side lobes of the main lobe, and improve the spectrum ripple factor. Apart from apodization, the chirp function also affects the sensor sensitivity and the refractive index distribution on the grid. Numerical experiments were carried out in designing the FBG component as a sensor using Gaussian apodization and Topas (cyclic olefin copolymer) for several chirp functions. The results show that the Gaussian apodization Topas for all chirp functions as a strain sensor has the same sensitivity, namely 0.84 pm/μstrain while for temperature sensors with the highest sensitivity is obtained at cubic root chirp of 13.82857 pm/°C followed by square root chirp of 13.74286 pm/°C, quadratic chirp 13.71429 pm/°C, and linear chirp 13.4 pm/°C. The Bragg wavelength shift was greater for 1 °C than for the 1 μstrain.

Coupled Apodization Functions Applied to Enhance Image Quality in Ultrasound Imaging using Phased Arrays

Coupled Apodization Functions Applied to Enhance Image Quality in Ultrasound Imaging using Phased Arrays

Influence of Two-Frequency Radiation Intensity Fluctuations on the Output Signal of a Vortex Optical Fiber Forming OAM Address in Polyharmonic Sensor Technology

A schematic diagram of a RoF radio-optic system with vortex signals is presented, in which the radio frequency is determined by the difference between the wavelengths of two lasers. It is assumed that the generation of a vortex signal can be performed through a vortex fiber-optic periodic structure, which can be obtained using a technology similar to the manufacture of long-period fiber Bragg gratings. The parameters of the grating are modeled assuming that the fundamental light-guide mode (LP01) is applied to the specified vortex element, and the higher-order mode (LP11) is reflected. It was found that the distortion of the vortex signal can be reduced by introducing apodization and chirping of this periodic structure. The following optimal parameters have been estimated: the apodization and chirp multiplier functions, at which the distortions of the amplitude and phase of the vortex signal, as well as the appearance of an unwanted angle distortion, will be minimal. It is shown that such gratings can be exploited in addressed sensors systems using the orbital angular momentum (OAM) of a lightwave as a unique sensor address.

Power Phase Apodization Study on Compensation Defocusing and Chromatic Aberration in the Imaging System

We performed a detailed comparative study of the parametric high degree (cubic, fourth, and fifth) power phase apodization on compensation defocusing and chromatic aberration in the imaging system. The research results showed that increasing the power degree of the apodization function provided better independence (invariance) of the point spread function (PSF) from defocusing while reducing the depth of field (DOF). This reduction could be compensated by increasing the parameter α; however, this led to an increase in the size of the light spot. A nonlinear relationship between the increase in the DOF and spot size was shown (due to a small increase in the size of the light spot, the DOF can be significantly increased). Thus, the search for the best solution was based on a compromise of restrictions on the circle of confusion (CoC) and DOF. The modeling of color image formation under defocusing conditions for the considered apodization functions was performed. The subsequent deconvolution of the resulting color image was demonstrated.

Femtosecond Laser Fabricated Apodized Fiber Bragg Gratings Based on Energy Regulation

In this paper, an energy regulation method based on the combination of a half-wave plate (HWP) and a polarization beam splitter (PBS) is proposed for the fabrication of apodized fiber gratings, which can effectively improve the side lobe suppression ratio of high-reflectivity fiber Bragg gratings (FBGs) fabricated by femtosecond laser. The apodized FBGs prepared by this method has good repeatability and flexibility. By inputting different types of apodization functions through the program, the rotation speed of the stepping motor can be adjusted synchronously, and then the position of the HWP can be accurately controlled so that the laser energy can be distributed as an apodization function along the axial direction of the fiber. By using the energy apodization method, the gratings with a reflectivity of 75% and a side lobe suppression ratio of 25 and 32 dB are fabricated in the fiber with a core diameter of 9 and 4.4 μm, respectively. The temperature and strain sensitivities of the energy-apodized fiber gratings with a core diameter of 4.4 μm are 10.36 pm/°C and 0.9 pm/με, respectively. The high-reflectivity gratings fabricated by this energy apodization method are expected to be used in high-power narrow-linewidth lasers and wavelength division multiplexing (WDM) systems.

Basic FBG apodization functions effects on the filtered optical acoustic signal

<span>This article clarified the basic fiber Bragg grating (FBG) apodization functions effects on the filtered optical acoustic signal (AS). Max optical acoustic power variations after acousto optic filter is clarified with the spectral wavelength variations. FBG apodization functions are uniform, Gaussian, and Tanh. We have tested the max optical acoustic power variations after various apodization FBG functions with the spectral wavelength variations. The max AS power amplitude after the electrical combiner is reported based various Apodization FBG functions. The max optical AS after FBG is studied with various FBG lengths for various FBG apodization functions at the central wavelength of 1.55 μm. The max electrical power after power combiner unit is demonstrated with different FBG lengths for various FBG apodization functions at the central frequency of 193.1 THz. </span>

Spectral width reduction using apodized cascaded fiber Bragg grating for post-dispersion compensation in WDM optical networks

This paper proposes a system that aims to reduce the spectral width, Δλ, of the optical signal at transmitter for WDM system over distance 100 km. Also, a chirped fiber Bragg grating (CFBG) at the receiver is used to compensate dispersion. The proposed system consists of four cascaded FBGs connected between light source and optical fiber. Many apodization functions are investigated to enhance the performance of the FBG in the proposed system, and Δλ is obtained at every stage and apodization function. The Q-factor and bit error rate (BER) are obtained at distances 30, 40 and 50 km. It is found that Cauchy apodization function is the best one that reduces the reflective spectral width, Δλ, and achieves a maximum Q-factor and minimum BER at distances 30, 40 and 50 km at the last stage.

Complete Reduction to Amplitude Frequency Table (CRAFT)-A perspective.

The CRAFT (Complete Reduction to Amplitude Frequency Table) technique, based on Bayesian analysis approach, converts FID and/or interferogram (time domain) to a frequency-amplitude table (tabular domain) in a robust, automated, and time-efficient fashion. This mini review/perspective presents an introduction to CRAFT as a processing workflow followed by a discussion of several practical 1D and 2D examples of its applicability and associated benefit. CRAFT provides high quality quantitative results for complex systems without any need for conventional preprocessing steps, such as phase and baseline corrections. Two-dimensional time domain data are typically truncated, particularly in the evolution dimension, and conventional processing after zero-filling and t1max -matched apodization masks potentially available peak resolution. The line broadening introduced by extensive zero-filling and severe apodization functions leads to the lack of clear resolution of cross peaks. CRAFT decimation of interferograms, on the other hand, requires minimal or no apodization prior to extraction of the NMR parameters and significantly improves the spectral linewidth of the cross peaks along F1 dimension compared to conventional (FT) processing. The tabular representation of the CRAFT2d cross peaks information can be visualized in a variety of frequency domain formats for conventional spectral interpretation as well as quantitative applications. A simple workflow to generate in silico oversampled interferogram (iSOS) is presented, and its potential benefit in CRAFT decimation of highly crowded 2D NMR is demonstrated. This report is meant as a collective thesis to present a potentially new paradigm in data processing that questions the need for hitherto unchallenged preprocessing steps, such as phase and baseline correction in 1D and zero-fill/severe apodization in 2D.

Performance evaluation and enhancement of apodized fiber Bragg grating for dispersion compensation

The apodization function has a significant impact on the state of the art of group delay, dispersion compensation, and acceptable decrease in side lobes in the spectrum of Fiber Bragg Grating (FBG) reflection. Accordingly, the Bragg grating length would be considered the backbone parameter in order to achieve a distinguishable performance. Here, the utilization influence of the presence of FBG is considered a dispersion compensator. In addition, we have implemented a tuned uniform-apodized FBG methodology according to various apodization functions. Common apodization functions have been studied and tested effectively. Experimental results show that the proposed raised cosine apodized function has scored the highest reflectivity with 50% reduction in the side lobe level and the narrowest bandwidth among all tested functions. Moreover, simulations for this function were performed with various lengths of grating. It is demonstrated that the reflection spectrum value is fixed at 100% at grating lengths greater than or equal to 28 mm and the minimum dispersion value is realized.

Comparative analysis of silica fiber Bragg grating and chalcogenide fiber Bragg grating

Sensing performance of silica fiber Bragg grating (FBG) and chalcogenide FBG are compared in presence of apodization functions. The Bessel and Gaussian apodization functions are chosen in this analysis. These fibers are compared on the basis of their sensitivity, detection accuracy, quality parameter and sidelobe suppression ability. Reflectivity equations established from couple modes equations by matching fields at interfaces. For considered apodization profiles, it is observed that the sidelobe suppression ability and sensitivities are nearly same in both chalcogenide and silica fiber Bragg grating. Chalcogenide-based fiber Bragg grating with Bessel apodization function have narrower full width half maxima (FWHM) value that’s why its detection accuracy and quality parameter is maximum in comparison of other considered cases. Hence for sensing application purpose chalcogenide-based fiber Bragg grating in presence of Bessel apodization function is appropriate.

Performance Analysis of Apodized Fiber Bragg Gratings for Sensing Applications

Sensing performance of fiber Bragg grating in presence of various apodization functions are studied and compared. Using couple modes theory and matching the fields at various boundaries, the equation of reflectivity of fiber Bragg grating sensors are obtained. The sensors are optimized to get maximum reflectivity with narrow full width half maximum of the resonance peak. It is observed that all considered apodization functions suppress the sidelobes. The suppression of dominating sidelobe is maximum −141.29 dB for Blackman apodization function in all considered cases. The larger sensitivity 6.07 AU/RIU and 6.06 AU/RIU is obtained in Bessel apodization function and Barthann apodization function, respectively. Since, Bessel apodization function shows lower (0.1500 nm) fullwidth half maximum value in comparison to the Barthann apodization function, therefore it gives maximum detection accuracy10329 and quality parameter 40.47 AU/nm-RIU. Followed by Bessel apodization function the Gaussian apodization function also shows high detection accuracy10030 and quality parameter 38.18 AU/nm-RIU due to its lower (0.1545) fullwidth half maximum value. Here the considered Bessel apodization function is recommended for sensing applications.

Constructing feed-forward artificial neural networks to fit potential energy surfaces for molecular simulation of high-temperature gas flows.

Kinetic rates for thermochemical nonequilibrium models are generally computed from quasiclassical trajectory (QCT) calculations on accurate ab initio potential energy surfaces (PES). In this article, we use a feed-forward artificial neural network (ANN) to fit existing single-point energies for N_{2}+N_{2} interactions [Bender et al., J. Chem. Phys. 143, 054304 (2015)JCPSA60021-960610.1063/1.4927571] to construct a PES suitable for molecular simulation of high-temperature gas flows. We then perform detailed comparisons with a widely used N_{4} PES that was built using the permutation invariant polynomials (PIP) method. Specific physical considerations in the construction of the ANN for this application are detailed. Translation, rotation, and permutation invariance are precisely satisfied by mapping the interatomic distances onto a set of permutation invariant inputs, known as fundamental invariants (FI) that generate the permutation invariant polynomial ring. The diatomic energy is imposed by decomposing the total potential energy into a sum of a two-body and a many-body energy contribution. To obtain the correct dynamical behavior with the most basic, yet computationally efficient ANN, spurious long-distance interactions must be removed to avoid incorrect physical behavior at the dissociation threshold. We use a simple apodization function to smoothly taper off to zero any residual many-body interaction at large separations. Both accuracy and performance of the FI-ANN PES are assessed. QCT calculations are used to compute dissociation probabilities and vibrational energy distributions at various equilibrium temperatures. Excellent agreement with the results obtained from the PIP PES is found. For our test case, the ANN PES is also significantly more computationally efficient than the PIP PES at comparable root-mean-square error levels.

Apodized chirped fiber Bragg grating for postdispersion compensation in wavelength division multiplexing optical networks

SummaryIn this paper, a postdispersion compensation unit is proposed leading to a better performance for the optical communication systems. This unit utilizes a chirped fiber Bragg grating (CFBG). For enhanced performance of the CFBG, a proper apodization function is chosen to improve the quality factor (Q‐factor) and the bit error rate (BER) of the system. A 110‐km wavelength division multiplexing (WDM) optical link is investigated. The system performance is evaluated through its Q‐factor, eye diagram, and BER showing best performance when using the Hamming apodization function.

New simulation and analysis fiber Bragg grating: narrow bandwidth without side lobes

The purpose of this paper is to simulate and analyze the spectral characteristics of the fiber Bragg grating (FBG) to obtain narrow bandwidth and minimization side lobes in reflectivity. Fiber Bragg grating has made a big revolution in telecommunication systems. The existence of fiber Bragg grating is needed when an optical fiber amplifier and filter are used. They can be used as band reject filter or band pass filter for optical devices. The model equations of the cascaded uniform fiber Bragg grating and different cascaded apodization functions such as, Hamming apodized fiber Bragg grating, Barthan apodized fiber Bragg grating, Nuttal apodized fiber Bragg grating, Sinc apodized fiber Bragg grating and Proposed apodized fiber Bragg grating are numerically handled and processed via specially cast software to achieve maximum Reflectivity, narrow bandwidth without side lobes.

Efficient Photonic Beamforming System Incorporating a Unique Featured Tunable Chirped Fiber Bragg Grating for Application Extended to the Ku-Band

This article demonstrates a photonic-based wideband true-time delay (TTD) beamforming network employing a raised cosine apodized linearly chirped fiber Bragg grating (FBG) of varying lengths, such as $50\,\,{\times \,\,10^{-3}}$ m, $45\,\,{\times \,\,10^{-3}}$ m, $40\,\,{\times \,\,10^{-3}}$ m, and $35\,\,{\times \,\, 10^{-3}}$ m, and different chirp parameters $25\,\,{\times \,\, 10^{-9}}$ m, $35\,\,{\times \,\, 10^{-9}}$ m, $6\,\,{\times \,\, 10^{-8}}$ m, and $8{\,\,\times \,\,10^{-8}}$ m. The proposed scheme can be used as variable TTD lines having a much lower ripple factor compared with the previously studied apodized linearly CFBG for controlling the radiation angle of phased-array antenna (PAA), i.e., the main lobe radiated by the PAA can be steered squint-free from 0° to ±36.8° suitable for continuous beam forming at microwave frequencies 8–12 GHz extended up to Ku-band. To the best of our knowledge, this is the first experimental demonstration that shows the impact of tuning wavelength on delay change due to raised cosine apodized CFBG in the RF signal fed to the respective element of the antenna array. Four sets of $1\times4$ PAAs have been fabricated with the required electrical parameters, such as reflection coefficient ( $S_{11}$ ), voltage standing wave ratio, gain, far-field radiation pattern, and so on, to show the photonic feed idea. In addition, FBG’s having raised cosine apodization function is fabricated in our collaborative laboratory.

基于零阶贝塞尔函数加权的三角窗切趾函数

基于零阶贝塞尔函数加权的三角窗切趾函数