When we study the exact mode analysis of circular waveguides (Ref. Light Transmission Optics by D. Marcuse and Fundamentals of optical waveguides by Okamoto), we get an eigen value equation. If we solve this eigen value equation, we get a set of propagation constant values depending on the m(azimuthal dependence) and hence the transverse field profile. From these field patterns and propagation constant values it seems quite difficult to designate them as HE or EH. In the first reference (mentioned above) different approximations were used to get eigen values corresponding to EH and HE modes. While in the second ref. (mentioned above), the authors have considered n_core~n_cladding and differentiated the eigen value equations corresponding to HE and EH modes. My question is that "is there any other method to designate these modes" because in multi-layered structures it is very difficult to find the eigen value equation manually and separate out equations for HE and EH modes using different approximations.
I think it is possible to calculate the field distribution inside the waveguide. Then compliance of hybrid wave to one type or another, can be determined by the limiting transformation of parameters of the waveguide filling, resulting in the HE-mode converts to H-mode and EH mode converts to the E-mode of the uniformly filled (or empty) waveguide. Indices for designating types of waves usually indicate the number of field variations along the transverse coordinates.
Such a method is described in book G.I. Veselov, S.B.Raevsky Layered metal-dielectric waveguides. Unfortunately it is only in Russian.
http://en.bookfi.org/book/532886
Thanks Vladimir. It would be very helpful for me to understand it if you can outline the "transformation of parameters" in a little more detail. Thank you in advance.
Suppose you have a solution for propagation constants of your particular waveguide and those for the uniformly filled waveguied. Then you can change (in several steps) the parameters of your waveguide filling toward parameters of the uniformly filled waveguide for which modes are clearly defined to see the transformation of your dispersion curves into those of the uniformly filled waveguide.
i.e. if we have a waveguide filled with a layered dielectric we can gradually change the permittivities of layers toward the homogeneous filling controlling the transformation of the dispersion curves.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Optics