## 1 Introduction  
The theory of wave diffraction constitutes one of the fundamental problems in mathematical physics. Apart from its direct relevance to engineering and physics, this subject gives rise to significant methodologies in applied mathematics. Spectral methods play a crucial role in the study of electromagnetic diffraction. Notably, the Sommerfeld-Malyuzhinets (SM) method, the Kontorovich-Lebedev (KL) transform method, and the Wiener-Hopf (WH) method are fundamental and complementary in studying diffraction problems in the presence of sharp discontinuities. These methods have been extensively and effectively applied for studying wedge diffraction in isotropic regions; see [1; 2; 3; 4; 5; 6] for SM, Refs. [7; 8; 9; 10] for KL, and Refs. [11; 12] for WH, along with the references therein starting from the early 2000s literature produced by the authors of this study. Moreover, using synergy among the three methods (WH, SM, and KL), the authors obtained a complete network representation of the angular region in the presence of isotropic media [13], which helped to build a systematic methodology for analysis. The main advantage of the aforementioned techniques (SM and KL) is also a limitation, i.e., the utilization of the spectral complex angular plane derived from the Sommerfeldintegral theory [14], which, since the early 2000s, the authors of this study have also effectively used in the WH framework for Fredholm factorization [11; 12] and in the definition of rotating waves in isotropic angular regions [11; 12]. The definition of this complex plane is intricately connected to the physics of the problem, as it specifically requires spectral transformations associated with the propagation constant. Consequently, this methodology is applicable to problems involving a single propagation constant, such as isotropic media in electromagnetic fields, as well as other specific problem configurations with decoupling properties in propagation modalities. Different attempts have been developed to extend the spectral analysis to diffraction problems in more complex media, such as gyrotropic media and/or uniaxial media. For example, we recall the analysis of scattering by a perfect electrically conducting (PEC) half-plane immersed in such anisotropic media; see [15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. However, to the best of our knowledge no spectral method for scattering problems by wedges in arbitrary linear media (i.e., bianisotropic media [25; 26; 27]) characterized by multiple propagation constants has been developed to date. One of the most important results obtained in the presence of anisotropic media is the exact solution obtained by [PERSON] in the case of scattering by a PEC wedge immersed in a uniaxial medium illuminated by plane waves at normal incidence [17; 18]. However, the method used for this problem is substantially that of the separation of variables after transformations in the physical domain, which does not present the powerful characteristics of spectral methods such as asymptotic evaluation of fields and physical interpretation of field components in terms of structural and source spectral singularities. Other important works have examined the behavior of the field near the edge of a wedge immersed in a complex medium [28] and diffraction by a wedge immersed in the special case of an isotropic chiral medium with the SM method [29]. Given our experience in spectral analysis of complex electromagnetic scattering problems in isotropic media [11; 12; 30; 31; 32], and with the help of the theory proposed in [33] for the analysis of structures embedded in layered media, in this work we develop a new theory in the spectral domain with proper mathematical tools that allow for the representation of scattering problems immersed in arbitrary linear media of an angular shape. In particular, these new formulations are in the spectral domain (Laplace domain) without introducing angular complex planes, and as such are not limited to _one-propagation-constant_ problems.