Coupled-mode theory for magneto-optical fiber Bragg grating under non-uniform magnetic field

Abstract

CAccording to the perturbation theory, the coupled-mode equations for guided optical waves in the magneto-optical fiber Bragg gratings (MFBGs) under non-uniform magnetic field are derived. The equivalent relation between the magneticallyinduced non-uniform fiber Bragg grating (MnFBG) and the corresponding non-magnetic chirped grating is expressed and verified by the piecewise-uniform MFBG model under linear magnetic field. On the basis of the equivalent relation, the MnFBGs can be effectively investigated by means of simulations. The characteristics of the MnFBGs under three typical magnetic field distributions with application to optical pulse compression are simulated, and the minimal pulse width can be achieved for the same magneto-optical coupling parameter of 2.2 10 3 m -1 .The chirped fiber Bragg gratings (FBGs) have been widely used in the dispersion management [1][2][3][4] for optical fiber communications. The tunable chirped optical fiber grating becomes a trend, especially for the dynamic and flexible optical networks [5,6] . The theoretical model of uniform magneto-optical FBG (MFBG) with linear birefringence has been put forward [7,8] , and the magnetic control of the MFBG's photonic bandgap for use in optical signal processing has been also investigated [9,10] . However, to our knowledge, the non-uniformly magnetized MFBG, also named magnetically-induced non-uniform FBG (MnFBG), has not been taken into account based on the coupled-mode theory until now. In this paper, it will be shown that a chirped MnFBG may be equivalent to a non-magnetic chirped FBG, whose chirp phase is the sum of the initial phase of the MnFBG and the integral of the magneto-optical (MO) coupling coefficients along the whole grating. And then, one can easily establish the MnFBG's simulation model by means of the commercially available simulation softwares for optical communication. As an example, the pulse compression characteristics of the MnFBGs under three typical magnetic field distributions are discussed.The MFBGs with large MO coefficient can be achieved by writing grating in terbium-doped or yttrium iron garnet *