1      VI ème Congrès International sur les Energies Renouvelables et l’Environnement Abstract: Many devices in microwaves such as phase shifters, circulators, and isolators use the effect of propagation of electromagnetic waves in the rectangular guides with ferrites. Ferrites are characterized by a tonsorial permeability that makes the formulation of the problem starting from Maxwell equations complex. The complexity suggests the use of numerical techniques to study the inhomogeneous and anisotropic guides. We used the Transverse Operator Method (TOM) which allows to determinate the propagation constants and the electromagnetic fields. Our study is essentially based on the generalization of (TOM) which is applied for rectangular guides formed by many mediums the one at least is a ferrite and the comparison of our results with those published. A good agreement is obtained. Keywords: rectangular waveguide; longitudinally magnetized ferrites; Transverse Operator Method. 1. Introduction The electromagnetic analysis of microwave integrated circuits is an attractive subject due to the renewed interest in the use of complex materials such as anisotropic magnetic materials like ferrites as well as metamaterials. These materials are used in many microwave components (isolators, circulators, phase shifters...) especially in communications systems. The complexity of the electromagnetic problem posed in the study of nonreciprocal devices suggests the use of fairly sophisticated numerical techniques. Because of the anisotropy of the ferrite, and the fact that the rectangular waveguide can contain multiple media, the decoupling wave equation is not possible with the usual formulation. That leaves limited choices among the integral methods and we opted for the transverse operator method (TOM) followed by the Galerkin procedure. 2. Characteristic of ferrites 2.1 History Thousands of publications have been written on the subject of ferrites. Since 1947, their magnetic properties are not fully explainable. Louis Neel has played a major role in the knowledge of these materials. It shows that their properties are better than those of ferromagnetic materials. It gives a complete and quantitative interpretation of these properties based on a large number of experimental results and applied to all ferrites with success. Because of this discovery, Louis Neel won the Nobel in 1970. In addition, D. Polder has a very important role in this discovery, he was able to discover the form of the permeability tensor and find the expressions of matrix elements of the ferrite. 2.2 Definition A ferrite is a magnetic oxide whose chemical composition is of the form (MO, Fe 2 O 3 ) where M represents a divalent metal such as Zn, Cd, Fe, Ni, Cu, Co, Mg ... CONTRIBUTION TO THE MODELING OF GUIDING STRUCTURES LOADED WITH LONGITUDINALLY MAGNETIZED FERRITES USING THE TRANSVERSE OPERATOR METHOD 1. Physics Laboratory Materials and Nanomaterials applied to the Environment, cite Riadh Zirig 6072 Gabes 2. Research Unit Hatem Bettahar IRESCOMATH Gabes 3. SYSCOM laboratory-Tunis 4. LAPLACE laboratory -Toulouse E-mail: Faten85@live.fr; hafedh.benzina@enig.rnu.tn;Lassaad.Elmir@fsg.rnu.tn;saklihedi@gmail.com; Faten CHAABANE 1 ; Hafedh BENZINA 2 ; Hedi SAKLI 3 ; Lassaad ELMIR 1 ;Junwu TAO 4