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, KT, was found to be quadratic in the -50–200 °C range, while it may be considered linear for the -20–100 °C range; KT values at 20 °C vary from 5.176 × 10-6 K-1, for a B/Ge co-doped fiber up to 6.724 × 10-6 K-1, for a highly Ge-doped fiber; KT does not depend on the hydrogen-loading process or the gratings coupling strength; KT is essentially independent of wavelength in the 1500–1600 nm range, its value being accurately determined with a relative error ~0.2%; based on the accurate value of KT = 6.165 × 10-6 K-1, at 20 °C, obtained for gratings inscribed in the SMF-28 fiber, we calculated a value of 19.4 × 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 KT. The previous achievements allow, by having knowledge of KT 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/°C, being, therefore, very useful in research labs and computer simulations. Thus, expressions for the temperature dependence of KT for gratings inscribed in several fibers are given, as well as an expression for KT as a function of the effective refractive index. We have also fully analyzed the potential sources of error in KT determination.

Abstract