## 1 Introduction  
The method of resonant transmission lines (RTL) has evolved from some original observations around the generic theme of transverse resonance in direct association with the standard theory of the solutions of the general telegrapher's equation in transmission lines. The particular advantage of the method is that it offers the possibility of reducing even full three-dimensional problems into one its dimensional equivalent, at least wherever a full variable separation is possible due to the particular symmetries of a given coordinate system. A full historical review of the use of transmission lines for modeling electromagnetic problems would require too much space but we can provide some important milestones in chronological order in brief. The transmission line theme can be traced as far back as in the old treatise by [PERSON] [1]. Further physical justification is offered by a seminal paper by [PERSON] and [PERSON] [2] where we find a first version of the transverse resonance condition as a means to satisfy certain boundary conditions via appropriate impedance matching. Extensive use of the telegrapher's equation is also found in [PERSON] [3], [PERSON] [4], [PERSON] and [PERSON] [5,6], [PERSON] [7], [PERSON] and [PERSON] [8], [PERSON] [9], [PERSON] and [PERSON] [10] as well as [PERSON] et al. [11]. More recently, [PERSON] et al. [12] also used transmission line methods for the study of photovoltaic cells. An important comparison between transverse stationary modes and their similarity with quantum wells is mentioned by [PERSON] [13] and has led to the application of the RTL method by some of the authors in Schrodinger type and general Sturm-Liouville problems [14, 15, 16]. An early application of similar ideas in optical fibers can be traced in a paper by [PERSON] and [PERSON] [17]. [PERSON] also discussed guided waves based on impedance matching in Reference [18], while later [PERSON] and [PERSON] [19] applied transfer matrix methods for inhomogeneous fibers. More recently, [PERSON] and [PERSON] [20] used transverse resonance for studying multilayered photonic crystals. The modern RTL method was originally introduced by [PERSON] and [PERSON] [21; 22; 23; 24; 25; 26] in simple cases of standard step index and radial index profiles. Lately, it was also applied successfully in the case of superlattices with periodic potentials [27] which are similar to a certain class of photonic crystal fibers (PCFs) or Bragg fibers in general. Several other cases of unusual refractive index profiles have been successfully treated with the same method [28; 29; 30; 31]. In the present work, we expose more recent developments in an effort to expand the validity of the RTL method in all unconventional fiber models. We shall heretofore refer to all the cylindrical optical fibers as the class of conventional optical fibers (COFs) for as long as they can be separated in a set of \(n\) very thin successive cylindrical layers of average radius \(r\) with uniform refractive index values given as \(n_{i}\). Indices of successive layers will be allowed in general to be different for each step varying as \(n_{i}=n(r_{i})\). The resulting, total index profile \(n(r)\) variation from the center of the fiber up to the limit outer air medium, completely defines the propagation properties inside the fiber. We shall also separate another class of unconventional optical fibers (UOFs) as the ones in which at least in some of its successive thin cylindrical layers present an additional variation of the total index profile along its radial coordinate \(\varphi\) in the form \(\eta(r,\varphi)\). Such cases include elliptic core, non-symmetric or eccentric core fibers, and in general, all cases of not strictly circular core fibers. In these cases, any discretization into thin cylindrical layers that \"cuts\" through the core and cladding, results in a variation of the refractive index along \(\varphi\). In Figure 1, we show such a case of a thin, circular cylindrical layer cutting an elliptic core fiber.