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
A refractive index sensor was designed using a novel approach to sensing based on a cleaved standard fiber Bragg grating (FBG) at the grating region, which enables the FBG to interact with its surrounding environment. The sliced-FBG (SFBG) exhibits a variable phase shift in the reflection response due to the length of the last grating's pitch, which differs from the rest. At the SFBG, the signal is the result of interference between the reflected wave from the grating and the transmitted spectrum returned due to Fresnel reflection at the final pitch, and the intensity of this signal depends on the refractive index of the surrounding medium. Based on this phenomenon, an intensity-based refractive index sensor with self- referencing technique was employed in this experiment, whereby the grating peak maximum point served as the signal reference, while the minimum of the Fresnel peak from each measurement functioned as the signal input. The proposed sensor demonstrated the ability to measure refractive indices within the range of 1.333-1.339, with a resolution of approximate to 10(-3), and a minimum detectable value of 6x10(-4) RIU (the data yielded a linear response with R-2=0.990). This study presents an innovative data sensing approach compared to existing techniques found in literature, which typically employ wavelength variation in the reflected wave to extract the desired information.

Abstract
This work analyzes the sensitivity of an optical system consisting of two fiber Fabry-Perot ( FP) interferometers and the apparent increase in sensitivity due to the harmonics of the Vernier effect. Two scenarios are examined: (1) when the larger FP cavity acts as the sensor, and (2) when the smaller FP cavity acts as the sensor. The computation analysis reveals that in the first scenario, higher-order spectral harmonics yield greater sensitivity for maxima and minima of the same order. In the second scenario, however, the sensitivity remains constant and does not depend on the harmonic order. Moreover, it is demonstrated that the sensitivity curve is identical for both scenarios, regardless of the harmonic order. This outcome occurs because the use of spectral harmonics simply reduces the free-spectral range in certain situations, bringing the extrema closer to the maximum sensitivity condition (i.e., Delta L = 0) and thereby increasing sensitivity. Consequently, if points on the envelope other than maxima or minima are used, the sensitivity achieved is the same for both scenarios.

Abstract
In this letter, we propose a method for utilizing the internal cavities of optical circulator devices-commonly referred to as parasitic cavities-as optical reference cavities. The method involves using an optical circulator operating at 1550 nm, illuminated by a light source at 1330 nm, thereby enhancing the amplitude of the interferometric signals generated by the internal optical cavities. The system was characterized by using both an Optical Spectrum Analyzer (OSA) and the Low-Coherence Interferometry (LCI) technique. Experimental results indicate that the Optical Path Difference (OPD) remains constant with varying aperture sizes, thereby confirming the feasibility of employing the optical circulator as a reference sensor. Finally, its performance as a reference sensor is demonstrated through its integration with an external cavity that functions as a displacement sensor.