## 4 State of Art
### Magnetic Force Sensors
#### 4.3.1 Magnetocristive Sensors  
During the 80's decade a great effort done for detecting magnetic fields and/or electric current using optical fibers in combination with materials that exhibit magnetostriction effects. In 1980, [PERSON] _et al_[43] studied the possibility of detecting weak magnetic fields by using magnetostrictive perturbation in optical fibers. A low loss optical fiber of length \(L\) was wrapped around a nickel jacket that suffers a longitudinal mechanical strain when immersed in a magnetic field. The first experimental evidence of the magnetic field sensing characteristics of optical fibers jacketed with either nickel or metallic glass magnetostrictive materials was reported by [PERSON] _et al_. [44]. Both bulk magnetic stretchers, as well as, thin films directly deposited on a single mode fiber (SMF) were analyzed. An all-fiber Mach-Zehnder interferometer was used to detect the magnetically induced mechanical changes in the optical path length that contained the magnetostrictive jacket. Figure 11 shows the schematic diagram of the magnetometer proposed by [PERSON] _et al_. The sensor sensitivity achieved with the bulk nickel material was \(6.37\times 10^{-6}\) A/m\({}^{2}\). The response of the first generation thin film coated fiber optic sensors was about two orders of magnitude lower and was ruled by the thin-film thickness. [PERSON] _et al._[48] investigated the mechanical strain induced by a weak axial magnetic field in an optical fiber with magnetostrictive jacket with different thickness. The sensitivity was calculated as function of jacket thickness for a variety of magnetostrictive materials. These configurations could be sensitive to magnetic fields, but unfortunately also sensitive to all other parameters that influence the optical path length of the fiber, such as, temperature [52]. [PERSON] proposed a non-magnetostrictive metal-coated element in one arm of the interferometer to directly detect temperature, improving this way the sensitivity to magnetic field of fiber optic interferometers. A SMF wounded under tension around a magnetically sensitive nickel cylindrical piece was proposed by [PERSON] [53]. The magnetic field changed the state of polarization (SOP) of light in the fiber. An optical phase sensitivity of 1.76 \(\times\) 10\({}^{-2}\) rad/m Oe was achieved, allowing a detection of magnetic fields as small as \(3.5\times 10^{-4}\) A/m\({}^{2}\) of fiber. Figure 11: Experimental scheme of fiber optic magnetic sensor. The magneto-optic coupling coefficient as function of frequency for a Mach-Zehnder interferometer incorporating a nickel toroid was measured by [PERSON] _et al._[54]. They observed that the frequency response of the coupling coefficient was found to be essentially smooth in a range between 15 and 600 Hz. [PERSON] _et al._[55] reported the fabrication and characterization of optical fibers coated with nickel thin-film. The thickest coating was greater than 90 \(\upmu\)m and was fabricated by chemical vapor deposition (CVD). The optical phase sensitivity obtained by the fiber Mach-Zehnder interferometer was \(1.9\times 10^{-8}\) rad.m/A. The use of a metallic glass as sensing element for detection of very low magnetic fields was described by [PERSON] and [PERSON] [45]. In their experiment, different metallic glasses were used on an all fiber Mach-Zehnder interferometer in order to measure their magnetic field detection sensitivities. A minimum detectable magnetic field of \(3.98\times 10^{-7}\) A/m\({}^{2}\) was reported. A configuration for measuring DC magnetic fields using an optical fiber coated with amorphous Fe\({}_{0.8}\)B\({}_{0.2}\) alloy in one arm of a modified magnetometer was developed by [PERSON] and [PERSON] [56]. In order to obtain a maximum sensitivity, the system was analyzed in quadrature allowing the elimination of polarizations fluctuations. A linear region was analyzed and a sensitivity of 102 rad/T-m was obtained.