Vernier effect of two cascaded in-fiber Mach-Zehnder interferometers based on a spherical-shaped structure.

The Vernier effect of two cascaded in-fiber Mach-Zehnder interferometers (MZIs) based on a spherical-shaped structure has been investigated. The envelope based on the Vernier effect is actually formed by a frequency component of the superimposed spectrum, and the frequency value is determined by the subtraction between the optical path differences of two cascaded MZIs. A method based on band-pass filtering is put forward to extract the envelope efficiently; strain and curvature measurements are carried out to verify the validity of the method. The results show that the strain and curvature sensitivities are enhanced to -8.47  pm/με and -33.70  nm/m-1 with magnification factors of 5.4 and -5.4, respectively. The detection limit of the sensors with the Vernier effect is also discussed.