Conference Paper

Transfer matrix method for fundamental LP01 core mode coupling in a Tilted FBG sensor

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Fibre Bragg gratings (FBGs) are obtained through a permanent and periodic refractive index modulation in the core of the single-mode optical fibre. For many years, they have been employed in telecommunication industry as a passive device for wavelength division multiplexing and dispersion compensation components, or in laser apparatus for laser fibre stabilization, Erbium amplifier gain flattening device and amplifier pump reflectors. In aerospace structures, FBGs are used as sensors for structural health monitoring of composite materials as they are able to perform measurements of several parameters inside the material in an elegant and low intrusiveness way. Based on the Bragg and optical fibre structure many kind of customizations can be applied on FBG sensors during the manufacturing process. Each of them gives to the FBG sensor different proprieties and sensing abilities. In this work, we address the numerical simulation of the reflected spectrum by a special FBG sensor called tilted FBG (TFBG), in which the core refractive index modulation is performed in way to obtain a tilted Bragg superstructure. By considering the classic Coupled-Mode theory for weakly-guided waveguides, we solved the mode propagation equations with the Transfer Matrix method (TMM) obtaining the TFBG reflectivity for different tilt angles.

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The work is dedicated to a comparative analysis of the following methods for fiber Bragg grating (FBG) spectral response modeling. The Layer Sweep (LS) method, which is similar to the common layer peeling algorithm, is based on the reflectance and transmittance determination for the plane waves propagating through layered structures, which results in the solution of a system of linear equations for the transmittance and reflectance of each layer using the sweep method. Another considered method is based on the determination of transfer matrices (TM) for the FBG as a whole. Firstly, a homogeneous FBG was modeled using both methods, and the resulting reflectance spectra were compared to the one obtained via a specialized commercial software package. Secondly, modeling results of a π-phase-shifted FBG were presented and discussed. For both FBG models, the influence of the partition interval of the LS method on the simulated spectrum was studied. Based on the analysis of the simulation data, additional required modeling conditions for phase-shifted FBGs were established, which enhanced the modeling performance of the LS method.
In this paper, cascaded chirped fiber Bragg grating or CFBG based narrow-band bandpass filter capable of operating in C-band is proposed and analyzed. Cascading one linearly increasing chirp (LIC) FBG with another linearly decreasing chirp (LDC) FBG reduces the FWHM almost by five folds with a change in the normalized reflectivity. Analytical formulation based on a piecewise uniform approach (PUA) for the proposed structure(s) is also discussed. Extension of PUA approach for tilted FBGs is also presented in the paper. For the proposed structures, we have considered each CFBGs may have equal or different chirp rates keeping all other design parameters the same. As per the simulation results, the narrowest and widest FWHM achieved by the proposed structures are 1.56 nm and 1.77 nm, respectively. In such designs, the highest and lowest normalized reflectivity offered by the cascaded CFBG structures is approximately 0.81 and 0.39, respectively. The effect of temperature on the spectral characteristics for all the proposed structures is also studied. Simulation results reveal that the Bragg wavelength of the proposed cascaded structures will shift +1.701 nm for 100 °C increment in operating temperature in the absence of strain. The thermal sensitivity of all the proposed structures is estimated to be 17.01 pm/∘C.
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Fibre Bragg grating (FBG) strain sensors are not only a very well-established research field, but they are also acquiring a bigger market share due to their sensitivity and low costs. In this paper we review FBG strain sensors with high focus on the underlying physical principles, the interrogation, and the read-out techniques. Particular emphasis is given to recent advances in highly-performing, single head FBG, a category FBG strain sensors belong to. Different sensing schemes are described, including FBG strain sensors based on mode splitting. Their operation principle and performance are reported and compared with the conventional architectures. In conclusion, some advanced applications and key sectors the global fibre-optic strain sensors market are envisaged, as well as the main market players acting in this field.
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Optical fiber sensors have attracted considerable attention in health monitoring of aerospace composite structures. This paper briefly reviews our recent advancement mainly in Brillouin-based distributed sensing. Damage detection, life cycle monitoring and shape reconstruction systems applicable to large-scale composite structures are presented, and new technical concepts, “smart crack arrester” and “hierarchical sensing system”, are described as well, highlighting the great potential of optical fiber sensors for the structural health monitoring (SHM) field.
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A unified approach to obtain the characteristics of almost-periodic grating slab waveguides including gain in the waveguide is reported. In this approach the waveguides are divided into short segments, and in each segment the gratings are assumed to be periodic, that is, parameters such as coupling coefficient, grating phase, deviations from the Bragg frequency, and gain in the waveguide are independent of a propagation direction z. Then characteristics of almost-periodic grating slab waveguides can be obtained by multiplying each F matrix of a short segment with the proper grating phase conditions at the interface between two adjacent segments. The appropriateness of this approach is shown for typical aperiodic grating waveguides such as tapered, chirped, and phase-shifted gratings. The results obtained by this method are compared with others and prove to be in good agreement with the results obtained by other methods. In addition to these characteristics, it is shown that the F matrix can be used to obtain the threshold conditions for distributed feedback laser oscillations including reflections from cleaved edges.
Engineering structures are often subjected to the conditions of cyclic-loading, which onsets material fatigue, detrimentally affecting the service-life and damage tolerance of components and joints. Carbon fibre reinforced plastics (CFRP) are high-strength, low-weight composites that are gaining ubiquity in place of metals and glass fibre reinforced plastics (GFRP) not only due to their outstanding strength-to-weight properties, but also because carbon fibres are relatively inert to environmental degradation and as such, show potential as corrosion resistant materials. The effects of cyclic loading on the fatigue of CFRP are detailed in several papers. As such, collating research on CFRP fatigue into a single document is a worthwhile exercise, as it will benefit the engineering-readership interested in designing fatigue resistant structures and components using CFRP. This review article aims to provide the most relevant and up-to-date information on the fatigue of CFRP. The review focuses in particular on defining fatigue and the mechanics of cyclically-loaded composites, elucidating the fatigue response and fatigue properties of CFRP in different forms, discussing the importance of environmental factors on the fatigue performance and service-life, and summarising the different approaches taken to modelling fatigue in CFRP.
A detailed theoretical treatment is presented of bound-mode to bound-mode Bragg reflection and bound-mode to radiation-mode coupling loss in a tilted optical-fiber phase grating. Numerical predictions of the effects of grating tilt on the spectral characteristics of such a grating are calculated. These predictions are compared with experimentally measured spectra of strong gratings written by ultraviolet irradiation of deuteriumsensitized fiber with grating tilt angles ranging from 0° to 15°. Good agreement is obtained between the theoretical predictions and the experimental results.
Optical fiber gratings have developed into a mature technology with a wide range of applications in various areas, including physical sensing for temperature, strain, acoustic waves and pressure. All of these applications rely on the perturbation of the period or refractive index of a grating inscribed in the fiber core as a transducing mechanism between a quantity to be measured and the optical spectral response of the fiber grating. This paper presents a relatively recent variant of the fiber grating concept, whereby a small tilt of the grating fringes causes coupling of the optical power from the core mode into a multitude of cladding modes, each with its own wavevector and mode field shape. The main consequence of doing so is that the differential response of the modes can then be used to multiply the sensing modalities available for a single fiber grating and also to increase the sensor resolution by taking advantage of the large amount of data available. In particular, the temperature cross-sensitivity and power source fluctuation noise inherent in all fiber grating designs can be completely eliminated by referencing all the spectral measurements to the wavelength and power level of the core mode back-reflection. The mode resonances have quality factor of 10(5), and they can be observed in reflection or transmission. A thorough review of experimental and theoretical results will show that tilted fiber Bragg gratings can be used for high resolution refractometry, surface plasmon resonance applications, and multiparameter physical sensing (strain, vibration, curvature, and temperature).
A theoretical model for studying the outgoing radiation from a uniform-tilted fiber-Bragg grating has been developed. This model allows for calculation of the radiated fields in the vicinity of the fiber. Good agreement was found between the simulation and experimental results, which validates the proposed model. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 124–127, 2003; Published online in Wiley InterScience ( DOI 10.1002/mop.10843
Drilling cooling holes in aerospace materials with a neodymium-doped: yttrium aluminum garnet (Nd:YAG) laser is an established technique used in the aerospace industry. However, there are new challenges as the industry begins to use materials that can witstand higher temperatures and pressures. In this paper, the mechanisms of some laser-drilling processes, the types of laser used, the quality characteristics of a laser-drilled hole, the effects of drilling parameters, and the advantages and limitations of the laser hole-drilling operation are reviewed.
A full vector complex coupled mode theory (CMT) for the analysis of tilted fiber gratings is presented. With the combination of the perfectly matched layer (PML) and the perfectly reflecting boundary (PRB), the continuous radiation modes are well represented by a set of discrete complex modes. Simulation of coupling to radiation modes is greatly simplified and may be treated in the same fashion as guided modes. Numerical results of the tilted fiber Bragg gratings (TFBGs) with outer-cladding index equal, lower and higher than that of the inner-cladding indicate that the complex coupled mode approach is highly effective in the simulation of couplings to cladding and radiation modes in tilted fiber gratings. The reflective TFBGs are investigated by the proposed approach in detail.
Presents theoretical and experimental results on the wavelength properties of sidetap grating filters written in single-mode optical fibers. A simple theoretical model based on Fraunhofer diffraction and antenna theory is used, modified to take into account the longitudinal variation of the incident field. Expressions are derived for the filter attenuation and bandwidth, and good agreement is demonstrated with experiment. The results show that the shape of the attenuation spectrum does not change with the filter length or index modulation, but that the magnitude of the attenuation increases with both parameters. The results also show that the effect of decreasing the fiber core-cladding index difference is to increase the peak attenuation and reduce the filter bandwidth. The existence of a strict longitudinal phase-matching condition is shown to cause asymmetry in the shape of the spectrum. Comparison with the properties of bulk sidetap gratings shows there to be a shift in the peak wavelength and apodization of the filter sidelobes. A simple diagram for the design of sidetap filters is presented for the first time
The volume current method for the analysis of tilted fiber gratings was discussed. The radiation patterns including the wavelength dependence, azimuthal distribution and polarization dependence of tilted fiber phase gratings were calculated. The analysis was developed for both uniform and apodized fiber gratings. The results focused on phase matching condition, wavelength dependence, angular distributions and polarization dependence. The comparisons between the experimental measurements and the theoretical prediction verified the validity of the analysis.
In this paper, we describe the spectral characteristics that can be achieved in fiber reflection (Bragg) and transmission gratings. Both principles for understanding and tools for designing fiber gratings are emphasized. Examples are given to illustrate the wide variety of optical properties that are possible in fiber gratings. The types of gratings considered include uniform, apodized, chirped, discrete phase-shifted, and superstructure gratings; short-period and long-period gratings; symmetric and tilted gratings; and cladding-mode and radiation-mode coupling gratings
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