Cassinian Waveguides [Keynote Speeches: Speech 1]

Summary form only given. Cassinian curve as shown below has been in existence for quite a long time yet not used in applications of practical interest since engineers do not know them well. No hand book gives the result of K (1//spl sqrt/2) as the perimeter of the Cassinian when β = 1. Greenhill discusses this curve five times in his book [1892] and gives different results that might have confused the readers. To solve this problem we introduce a series of elegant transformations and change the variable ρ
⁴
into d
²
COS
²
θ + e
²
sin
²
θ throughout and end with a perturbation formula from our provious work. In this way we developed a new class of waveguides named as Cassinian Waveguides. The merits of these waveguides are listed.