A theory for treating coupling between curved transmission lines is derived as an extension of the theory of coupled parallel transmission lines. It is assumed that there exists a one-to-one correspondence between the coupled points on the two transmission lines. As an example, numerical results based on the theory are included for the characteristic interaction parameters associated with directional couplers consisting of lossless semicircular and linear transmission lines. The general expressions that are derived for the interaction matrix elements are valid in these particular cases.
Masanori Matsuhara and A. Watanabe, "Coupling of curved transmission lines, and application to optical directional couplers," J. Opt. Soc. Am. 65, 163-168 (1975)