Abstract

Abstract
This paper presents the conditions required for effective sensitivity amplification in the optical harmonic Vernier effect. Two distinct cases are analyzed: in the first, the sensor cavity is the shortest, while in the second, it is the longest. Based on the proposed theoretical model, supported by experimental results, it is concluded that, in the first case, the sensitivity associated with the spectral extremes increases with the order of the harmonic states. In contrast, in the second case, the sensitivity at the spectral extremes remains constant, regardless of the harmonic order. To evaluate the effectiveness of applying the optical Vernier effect and to differentiate between the two cases, a new formulation of the magnification factor (M-factor) is introduced. This leads to the definition of a novel figure of merit for the optical Vernier effect, denoted as (FoM(Vernier)). In Case 1, where harmonics are generated by increasing the reference cavity, the figure of merit assumes a value of (m + 1). In Case 2, where harmonics are generated by increasing the sensor cavity, the figure of merit remains constant at 1, regardless of the state order (whether fundamental or harmonic). This study also concludes that the observed increase in sensitivity is apparent rather than intrinsic, as the sensitivity curve produced by the optical Vernier effect mirrors that of a conventional interferometer.

Abstract
The present letter proposes the implementation of Vernier-effect harmonics through the virtualization of different reference cavities. A Fabry-Perot interferometer (FPI), actuated by a piezoelectric transducer (PZT), was employed as the sensing element. Subsequently, the sensitivity of the dynamic range was investigated for both the individual interferometer and the implementation of the Virtual Vernier effect. A sensitivity of (8 +/- 0.05)x10(-3) nm/nm was achieved for the single sensor measurement. Considering the implementation of the Vernier effect, the following sensitivities were obtained: (65.6 +/- 0.08)x10(-3) nm/nm for the fundamental, (132 +/- 1)x10-3 nm/nm for the first harmonic, and (192 +/- 1)x10(-3) nm/nm for the second harmonic. Furthermore, a maximum dynamic range of 11.25 mu m and a maximum resolution of 5 pm were achieved. This study highlights the advantages of simultaneously measuring both a single sensor cavity and a harmonic of the Virtual Vernier effect, in order to achieve large dynamic ranges along with high resolution.

Abstract
Over the past 18 months, we have performed hundreds of temperature characterizations of fiber Bragg gratings inscribed in different germanium-doped silica glass fibers. Under experimental conditions, the main conclusions are as follows: the temperature dependence of the temperature gauge factor or the normalized temperature sensitivity, K-T, was found to be quadratic in the -50-200 degrees C range, while it may be considered linear for the -20-100 degrees C range; K-T values at 20 degrees C vary from 5.176 x 10(-6) K-1, for a B/Ge co-doped fiber up to 6.724 x 10(-6) K-1, for a highly Ge-doped fiber; K-T does not depend on the hydrogen-loading process or the gratings coupling strength; K-T is essentially independent of wavelength in the 1500-1600 nm range, its value being accurately determined with a relative error similar to 0.2%; based on the accurate value of K-T = 6.165 x 10(-6) K-1, at 20 degrees C, obtained for gratings inscribed in the SMF-28 fiber, we calculated a value of 19.4 x 10(-6) K-1 for the thermo-optic coefficient of bulk germanium glass; and gratings produced by femtosecond-laser radiation and UV-laser radiation exhibit comparable values of K-T. The previous achievements allow, by having knowledge of K-T for a single grating, the accurate determination of the temperature dependence of the Bragg wavelength for any other grating inscribed in the same fiber; the presented methodology enables one to determine the unknown gratings' temperature sensitivity, typically with an error of 0.01 pm/degrees C, being, therefore, very useful in research labs and computer simulations. Thus, expressions for the temperature dependence of K-T for gratings inscribed in several fibers are given, as well as an expression for K-T as a function of the effective refractive index. We have also fully analyzed the potential sources of error in K-T determination.

Abstract
A novel technique based on multiple amplitude wavelength modulation spectroscopy (MA-WMS) for simultaneous measurement of CH4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {CH}_4$$\end{document} gas concentration and pressure was developed and validated both through simulation and experiment, showing good agreement. To capture the spectrum broadening caused by increasing pressure and concomitantly obtain the concentration at the sensor's location, a laser centered at 1650.9 nm was subjected to multiple amplitude modulation depths while the 2fm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2f_{m}$$\end{document} signal, normalized by the DC component (an invariant quantity under optical loss), was recorded. While the use of a single and fixed modulation can introduce an ambiguity, as different pairs of pressure and concentration can yield the same value, this ambiguity is eliminated by employing multiple amplitude modulations. In this approach, the intersection point of the three level curves can provide the local pressure and concentration. The proposed system was able to measure concentrations from 5% up to 45% and pressures from 0.25 atm up to 1.75 atm, with a maximum error of 2% in concentration and 0.06 atm in pressure, respectively. The system was also tested for attenuation insensitivity, demonstrating that measurements were not significantly affected for up to 10 dB applied optical loss.