## 3 Interrogation Techniques
### Interferometric Detection Schemes  
Previously in the polarimetric detection scheme, the rotation of the plane of polarization of linear polarized light was analyzed. This rotation can also be analyzed in terms of circular polarization, corresponding to a phase difference between the two circular orthogonal modes (left-handed and right-handed circular polarization). This can be done using an interferometric detection scheme where a modulation frequency carrier is generated, and the optical phase variation that is modulated by time delay induced between arms of the interferometer, will contain the electric current information. This phase carrier can be generated by using an unbalanced Michelson or Mach-Zehnder interferometer, or other interferometric configuration, such as Sagnac interferometer [1,3]. Figure 5 shows schematically a current sensing Sagnac interferometer, which is commonly used in gyroscopes and it is sensitive to non-reciprocal effects [4]. This interferometer is interrogated by using a heterodyne detection scheme. In this particular application, light from an optical broadband source, is linearly polarized with a fiber polarizer and is injected into the Sagnac loop with crossed \(\lambda\)/4-wave plates mounted at an angle of \(45^{\circ}\) and \(-45^{\circ}\) relative to the plane of polarization of the linearly polarized inputs, for the upper and lower plate, respectively. In this arrangement each of the counter propagating waves are converted to  
Figure 5: Sagnac loop interferometer current sensor. orthogonal circular states. These two counter-propagating waves travel the Sagnac loop with different velocities, due to the external magnetic field induced circular birefringence. After crossing the loop they are converted again into linear polarization modes and interfere after crossing the output linear polarizer. The phase information is retrieved with the introduction of the phase modulator on the unbalanced Mach-Zehnder interferometer, which can be used to generate the phase carrier. Using either Pseudo-Heterodyne or Heterodyne processing schemes, the relative phase accumulated in the Sagnac loop, which is proportional to the magnetic field generated by the electric current on the conductor, can be recovered. Some disadvantages of using this type of interferometer include temperature and vibration dependent sensitivities. An improved version of the above system can be done in a reflection configuration, as shown in Figure 6.  
Between the optical source and the \(\lambda\)/4-wave plate, the polarized light is injected at 45\({}^{\circ}\) into a polarization maintaining fiber (PMF). After crossing the PMF, the \(\lambda\)/4-wave plate which is oriented at 45\({}^{\circ}\) with respect to the birefringence axis of the PMF, transforms the two orthogonal polarization modes into circular polarization modes with opposite rotation directions. At the end of the fiber, reflection occurs and the reverse process occurs. Due to reflection configuration, the states of polarization swaps and each polarization component travels the optical path made by the other polarization. At the end, both polarization pass through the same optical path and compensate all reciprocal effects, but still maintaining a phase difference proportional to the electric current to be measured. Due to the operation in reflection this scheme also doubles the sensitivity in relation to the first one, for the same number of fiber turns around the wire. The modulation introduced in the polarization interferometer (the length of PMF), near the 45\({}^{\circ}\) splice enhances the ability to detect the small phase differences, produced by small currents. Although the two schemes described permit a certain degree of immunity to reciprocal perturbations, time-varying disturbances which alter the birefringence of the PM fiber, affect counter-propagating waves differently and are not compensated [4].