Transmission characteristics related to Laplacian mode-field half-width of noncircular single-mode waveguides

For weakly guiding noncircular single-mode waveguides, we define the generalized frequency v and find that the four parameters [v, b(v), d(vb)/dv, vd(2)(vb)/dv(2)] play an important role in the theory of noncircular waveguides. We also derive the relations between the Laplacian mode-field half-width (MFHW) and the propagation constant, normalized propagation constant, group delay time/unit length, composite material dispersion, composite waveguide dispersion, composite profile dispersion, modal birefringence, beat length, polarization-mode dispersion, Rayleigh scattering loss, and MFHW W(infinity). We also derive Brown's identity by a new and simple method. Finally, we use our analytical theory to design a new periodic fiber system.