Theory for the Faraday effect in optical fiber

The theoretical study of the fiber optic Faraday effect based on the mode theory is conducted for the first time, to my knowledge. An analytical formula that represents the Faraday effect in a single-mode fiber under the appropriate approximation is given as an explicit function of the refractive indices and Verdet constants of the core and cladding, the upsi-value of the fiber, the magnetic field, and the fiber length. The difference between the fiber optic and bulk-optic Faraday effects is made clear. The effect of the modal field spreading in the core and cladding on the fiber optic Faraday effect is examined both analytically and numerically.