Theory of SN function wave guides

We study the conformal transformation z = sn ω to see how the constant u and constant v lines are transformed into the Z-plane curves to be utilized as boundaries of EM Waveguides. We give two sample curves for the lines v = K′/2 and u = K/2. The latter is believed to be new: a Cassinian oval curve of α = 1/k and β = 1/k √k′. Many curves can be drawn as boundaries of EM ware guides. We give formulas for drawing these curves and show that we can also use a good table of 4 significant figures to draw these curves, (11) and (17c) are new.