Response Of Gratings Research Articles

Intrinsically bad gratitude

This paper discusses under which circumstances grateful responses can become intrinsically bad. It is argued that gratitude should be understood as an appropriate response to value and that it is subject to the so-called recursive account of intrinsic value, according to which appropriate responses to value are intrinsically good, and inappropriate responses to value are intrinsically bad. As a result, gratitude can become intrinsically bad in two cases: i) when gratitude has the wrong object, i.e., is a pro-response to an intrinsically bad act, ii) when the grateful response is grossly disproportionate, i.e., the intensity of the response does not match the goodness of the act that it is a response to.

Fiber Bragg Sensors Embedded in Cast Aluminum Parts: Axial Strain and Temperature Response.

In this study, the response of fiber Bragg gratings (FBGs) embedded in cast aluminum parts under thermal and mechanical load were investigated. Several types of FBGs in different types of fibers were used in order to verify general applicability. To monitor a temperature-induced strain, an embedded regenerated FBG (RFBG) in a cast part was placed in a climatic chamber and heated up to 120 within several cycles. The results show good agreement with a theoretical model, which consists of a shrink-fit model and temperature-dependent material parameters. Several cast parts with different types of FBGs were machined into tensile test specimens and tensile tests were executed. For the tensile tests, a cyclic procedure was chosen, which allowed us to distinguish between the elastic and plastic deformation of the specimen. An analytical model, which described the elastic part of the tensile test, was introduced and showed good agreement with the measurements. Embedded FBGs - integrated during the casting process - showed under all mechanical and thermal load conditions no hysteresis, a reproducible sensor response, and a high reliable operation, which is very important to create metallic smart structures and packaged fiber optic sensors for harsh environments.

Adiabatic mode transformation in width-graded nano-gratings enabling multiwavelength light localization

We delineate the four principal surface plasmon polariton coupling and interaction mechanisms in subwavelength gratings, and demonstrate their significant roles in shaping the optical response of plasmonic gratings. Within the framework of width-graded metal–insulator-metal nano-gratings, electromagnetic field confinement and wave guiding result in multiwavelength light localization provided conditions of adiabatic mode transformation are satisfied. The field is enhanced further through fine tuning of the groove-width (w), groove-depth (L) and groove-to-groove-separation (d). By juxtaposing the resonance modes of width-graded and non-graded gratings and defining the adiabaticity condition, we demonstrate the criticality of w and d in achieving adiabatic mode transformation among the grooves. We observe that the resonant wavelength of a graded grating corresponds to the properties of a single groove when the grooves are adiabatically coupled. We show that L plays an important function in defining the span of localized wavelengths. Specifically, we show that multiwavelength resonant modes with intensity enhancement exceeding three orders of magnitude are possible with w < 30 nm and 300 nm < d < 900 nm for a range of fixed values of L. This study presents a novel paradigm of deep-subwavelength adiabatically-coupled width-graded gratings—illustrating its versatility in design, hence its viability for applications ranging from surface enhanced Raman spectroscopy to multispectral imaging.

Spectral-Distortionless, Flat-Top, Drop-Filter Based on Complementarily-Misaligned Multimode-Waveguide Bragg Gratings

An integrated-optics, flat-top drop-filter with low excess loss, and high sidelobe suppression ratio (SLSR), is demonstrated. The filter is based on apodized multimode waveguide Bragg grating (AMWBG) developed on a silicon-on-insulator (SOI) platform. Antisymmetric periodic refractive-index perturbations are imposed on both sides of the waveguide to couple light contra-directionally between the fundamental (TE0) and the first-order transverse electric modes (TE1). To achieve a Gaussian apodization profile, the lateral-misalignment between the two sides of the waveguide is modulated by adjusting the positions of both sides of the grating features in a complementary manner. In this way, the undesired phase errors, which exist in conventional misalignment-modulated Bragg gratings and distort the grating responses, can be eliminated. Experimental results show that our AMWBG has a high-quality flat-top response, a high SLSR of >21 dB, a 3-dB bandwidth of 8 nm, a low excess loss of 0.24 dB, and a high roll-off rate at the filter edge. We also demonstrate a dual-stage filter that has a flat-top, drop-port response with a 3-dB bandwidth > 7.5 nm, a SLSR >40 dB, and an excess loss<0.5 dB.

Enhancement of spectral response of Bragg gratings written in nanostructured and multi-stepped optical fibers with radially shaped GeO2 concentration.

We present experimental results on fiber Bragg gratings inscription in nanostructured graded-index (nGRIN) and multi-step index (MSIN) optical fibers, both having non-uniform radial distribution of GeO2 dopant in the fiber cores. In particular, the positive role of radial shaping the GeO2 distribution in the fiber core on grating reflection efficiency is reported. We postulate that an appropriate spatial distribution of the germanium concentration that matches the fundamental mode profile improves grating spectral response due to more efficient grating-mode interaction, as compared with uniformly doped step-index optical fibers with the same overall doping level. Moreover, we show that radially shaped fibers exhibit moderately higher temperature responses than their step-index counterparts.

Saying ‘Thank You’ and Meaning It

ABSTRACT Searle held that ‘thank you’ is an expressive illocutionary act that expresses the gratitude of the speaker. Although this view has been very influential, I argue that it must be rejected because it has counterintuitive implications about when a speaker is being insincere and when she is not. A more satisfactory account can be given if we take ‘thank you’ to express the normative judgment that a grateful response is required. Although I defend the judgment account from misinterpretations and objections, I ultimately add to it to explain how ‘thank you’ can pay respect and not just communicate it. I explain this by saying that ‘thank you’ has an effective use that allows us to pay our respects even if we don’t judge that a grateful response is necessary.

Paul and Grace in Theological Perspective: A Grateful Response

AbstractThis response to the above seven articles engages with some of the significant ways in which each takes forward the theological discussion of grace. While some areas of disagreement arise, the overall sense is of a conversation that is moving beyond Paul and the Gift, using its contribution to open fresh avenues for understanding between Catholic and Protestant theologians on this deeply controversial topic, and new possibilities for conversation between biblical exegesis and theology.

Eigenmodes of a lamellar optical grating: Profile, propagation, reflection, transmission, and nonadiabatic mode coupling

We present the explicit analytic formulas for the electromagnetic (optical) eigenmodes propagating in a lamellar grating. Then, we analytically calculate a mutual transformation of the wave's spatial harmonics due to diffraction in the course of propagation through the grating as well as the matrices of the eigenmode reflectance and transmittance at the grating boundaries. Finally, we develop a theory of the nonadiabatic transformation of the eigenmodes in the inhomogeneous gratings. It allows one to disclose the effects which go beyond the geometrical optics of eigenmodes. We show that in a transition layer of a thick nonlamellar grating such effects occur due to mode coupling of just a few lower-band eigenmodes. This approach allows one to find the overall optical response of the nonlamellar gratings fully and efficiently. The results are given for both transverse electric and transverse magnetic polarizations, as well as for any absorptive permittivity.

Radiation and High Temperature Effects on Regenerated Fiber Bragg Grating

Fiber Bragg gratings (FBGs) are promising sensors for operation in harsh environments mixing temperature and radiation constraints. Regenerated FBGs (RFBGs) are suited to perform measurements at very high temperatures (up to 1295 °C) as those encountered in nuclear reactor cores. However, only a few studies have been done regarding combined effects of radiations and temperature on RFBGs. We studied the response of such gratings under X-rays at several irradiation temperatures from 25 °C to 250 °C. Tested RFBGs have been inscribed on a pre-hydrogenated Ge-doped fiber with UV laser (KrF) using a phase mask and the regeneration has been done at 750 °C. Our results show that RFBGs are relatively radiation tolerant at 25 °C with a Bragg wavelength shift (BWS) of less than 50 pm (∼5 °C error) for a total dose of 100 kGy(SiO2). However, at increased irradiation temperatures (>150 °C), the BWS is limited, remaining below 10 pm (<1 °C error). We also studied the influence of a pre-thermal treatment (300 °C for 5 h) on the RFBGs response as well as the influence of other irradiation parameters, such as the dose rate (1–20 Gy/s), the pre-irradiation (100 kGy) and the total dose (2 MGy) at 25 °C. Radiation induced-BWS increases with dose rate, whereas the pre-thermal treatment has no influence.

Quasinormal-mode analysis of grating spectra at fixed incidence angles.

Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are today used in many applications. We present a comprehensive theory of grating anomalies and develop a formalism to expand the field scattered by metallic or dielectric gratings into the basis of its natural resonances, thereby enabling the possibility to reconstruct grating spectra measured for fixed illumination angles as a sum over every individual resonance contribution with closed-form expressions. This gives physical insights into the spectral properties and direct access to the resonances to engineer the spectral response of gratings and their sensitivity to tiny perturbations.

Diffractive gratings with varying period’s shape

Diffractive gratings with varying period’s shape

Deduced Refractive Index Profile Changes of Type I and Type II Gratings When Subjected to Ionizing Radiation

Type I and type II Bragg grating arrays in silica fiber have been irradiated at the Ohio State University Nuclear Reactor Laboratory in the gamma facility and the pool-type reactor, to receive a relatively small gamma dose (2.82 Mrad) and a relatively large gamma–neutron dose (638 Mrad, ${6\times }{10}^{17}\rm {({n}/{cm^{2}})}$ ), respectively. The Bragg grating fibers were first irradiated in the gamma facility and those same fibers were then subsequently irradiated in the reactor, while being monitored in situ by optical frequency domain reflectometry. The response of the Bragg gratings, in terms of reflected amplitude, was analyzed, both in the frequency and spatial domains. A Bragg grating modeling code, written in MATLAB, was then used to generate modeled fiber Bragg grating (FBG) responses to match the experimental responses, based on some fundamental assumptions. With the modeled responses, we were able to deduce the alterations to the refractive index profile of the Bragg grating inscribed fibers as a result of the irradiation.

Reducing Residual Strain in Fiber Bragg Grating Temperature Sensors Embedded in Carbon Fiber Reinforced Polymers

The temperature response of fiber Bragg gratings (FBGs) embedded in carbon fiber reinforce polymers (CFRPs) is investigated in this paper. To provide strain-free temperature measurements, two pieces of anti-sticking materials are placed at both sides of the embedded optical fiber and between carbon fiber prepregs; thus, providing slippery surfaces that minimize the strain transfer to the FBG sensor. In particular, the impact of different anti-stick materials on the temperature and residual bending strain response of the embedded FBGs is experimentally investigated. Results demonstrate that although some materials can allow for minimum residual strain being transferred to the FBG, their thermal conductivity does not always fulfill the requirements for reliable temperature sensing. It is found out that, among the tested materials, aluminum and copper foils can provide both reliable temperature response (with negligible delay and bias) and minimum residual strain. Using such anti-stick materials, the error induced by the residual strain on FBG temperature measurements is also experimentally evaluated by applying temperature and bending loads (strain) simultaneously to the CFRP packaging. While the study is here performed for FBG-based point sensors, most of the results and conclusions are also expected to be valid for applications of embedded distributed optical fiber sensors being affected by strain-temperature cross-sensitivity issues.

Performance Improvement of Refractometric Sensors Through Hybrid Plasmonic–Fano Resonances

In this paper, we present a plasmonic refractometric sensor that works under normal incidence; allowing its integration on a fiber tip. The sensor's material and geometry exploit the large scattering cross-section given by high-contrast of the index of refraction subwavelength dielectric gratings. Our design generates a hybrid plasmonic-Fano resonance due to the interference between the surface plasmon resonance and the grating response. We optimize the sensor with a merit function that combines the quality parameter of the resonance and the field enhancement at the interaction volume where the plasmon propagates. Our device shows a high sensitivity (1000 nm/RIU) and a high Figure of Merit (775 RIU$^{-1}$). Degradation in performance is negligible through a wide dynamic range up to 0.7 RIU. These quantitative parameters overperform compared to similar plasmonic sensors.

Characterization and compensation of apodization phase noise in silicon integrated Bragg gratings.

Precise and reliable apodization of silicon integrated Bragg gratings (IBGs) is the key to realizing their spectral tailoring for many optical applications such as optical signal processing and wavelength-division multiplexing systems. However, apodization in a silicon IBG that is typically realized by modifying the physical waveguide grating structure can also introduce unwanted grating phase variations that can affect the grating response. In this paper, we present a model to characterize apodized silicon IBGs which can take such apodization phase noise (APN) into account, based on direct synthesis of the physical grating structure. The model is used to characterize a set of different silicon IBGs apodized by lateral misalignment (ΔL) and duty-cycle (DC) modulations and designed with different responses, and the results show that the APN can greatly distort the complex responses of the gratings. Then, we develop a methodology to compensate the APN and thus to correct the distorted grating responses. The designed silicon IBGs were fabricated and tested experimentally. The accuracy of the model is examined by comparing the measured grating spectra with those predicted by the model. Spectral corrections are then demonstrated in Gaussian-apodized gratings based on ΔL- and DC-modulated silicon IBGs and a square-shaped filter developed on a ΔL-modulated IBG. Finally, a complex spectral correction of a photonic Hilbert transformer developed on a ΔL-modulated silicon IBG is achieved.

Hot water-assisted fabrication of chirped polymer optical fiber Bragg gratings.

We obtained chirped gratings by performing hot water gradient thermal annealing of uniform poly (methylmethacrylate) (PMMA) microstructured polymer optical fiber Bragg gratings (POFBGs). The proposed method's simplicity is one of its main advantages because no special phase mask or additional etching are needed. It not only enables easy control tuning of the central wavelength and chirp characteristics, but it also leads to obtain flexible grating response, compared with tapered chirped POFBGs. Therefore, a flexible and low-cost chirped POFBG devices fabrication technique has been presented by using a single uniform phase mask.

Computational analysis of dispersive and nonlinear 2D materials by using a GS-FDTD method

In this paper, we propose a novel numerical method for modeling nanostructures containing dispersive and nonlinear two-dimensional (2D) materials, by incorporating a nonlinear generalized source (GS) into the finite-difference time-domain (FDTD) method. Starting from the expressions of nonlinear currents characterizing nonlinear processes in 2D materials, such as second- and third-harmonic generation, we prove that the nonlinear response of such nanostructures can be rigorously determined using two linear simulations. In the first simulation, one computes the linear response of the system upon its excitation by a pulsed incoming wave, whereas in the second one the system is excited by a nonlinear GS, which is determined by the linear near-field calculated in the first linear simulation. This new method is particularly suitable for the analysis of dispersive and nonlinear 2D materials, such as graphene and transition-metal dichalcogenides, chiefly because, unlike the case of most alternative approaches, it does not require the thickness of the 2D material. To investigate the accuracy of the proposed GS-FDTD method and illustrate its versatility, the linear and nonlinear responses of graphene gratings have been calculated and compared to results obtained using alternative methods. Importantly, the proposed GS-FDTD can be extended to three-dimensional bulk nonlinearities, rendering it a powerful tool for the design and analysis of more complicated nanodevices.

Distinguishing the Imago Dei from the Soul

This article contends that the ‘structural’ view of the imago Dei, which identifies the image of God with (or as being a property of) the human soul, requires revision in light of exegesis of Genesis 1, and that philosophical reflection following aftersuch exegesis reveals that the imago Dei needs to be distinguishedconceptually from the soul. In dialogue with, and (grateful) response to, Joshua Farris ‐ the most recent proponent of the (or ‘a’) structural view, the article counters the position, arguing that instead of the image of God being (a property of) the human soul(entailing a human having a body contingently), the emphasis of Scripture is that the image of God is a human in their entirety (a view entailing their having an immaterial soul).

Compensation Method for Temperature Cross-Sensitivity in Transverse Force Applications With FBG Sensors in POFs

In this paper, we investigate the influence of temperature on the transverse force response of polymer optical fiber Bragg gratings (POFBGs) inscribed in cyclic transparent fluoropolymers (CYTOPs). The gratings are imprinted in the fiber using the direct-write, plane-by-plane femtosecond laser inscription method. The temperature increase leads to a decrease in the polymer Young's modulus, which causes a sensitivity variation in the POFBG sensor for transverse force applications. The proposed technique is based on the characterization of both the sensor's response offset and the material's Young's modulus variation due to the temperature increase. Transverse force tests were performed at different temperatures (30 °C, 40 °C, 50 °C, and 60 °C) and the compensated and uncompensated responses are compared in terms of root mean squared error (RMSE). The compensated results show an RMSE lower than 3% (mean value between all tested temperatures), which is 6.7 times lower compared with the uncompensated response. In addition, the proposed compensation technique presents a maximum RMSE reduction of 16 times at 60 °C.

Sampled Bragg gratings formed in helically twisted fibers and their potential application for the simultaneous measurement of mechanical torsion and temperature.

We propose and demonstrate a novel type of sampled Bragg gratings by combining a helically twisted fiber and a Bragg grating. A comb-like spectrum with a series of harmonic narrow resonances is observed, and the influence of geometrical parameters on the resonances is studied. As a special application, the intrinsic nature of the device that contains the Bragg grating and helical fiber spectral responses permits the temperature to be detected from the former, whereas the mechanical torsion is extracted from the latter, suggesting a potential for the simultaneous measurement of these two parameters. The proposed configuration features simplification, easy fabrication, high flexibility, stability, and low cost, and therefore has good prospects for sensor applications, as well as other applications, such as multi-channel filters, distributed Bragg reflectors, etc.