“…This condition can be phrased as an integral equa-tion for the field in the plane of the bed boundary. We extracted useful information from this equation by variational techniques (Angulo, 1957;Angulo and Chang, 1959;Bresler, 1959;Reinhart et al, 1971;Hockham and Sharpe, 1972;Ikegami, 1972;Rozzi, 1978;Rozzi and Veld, 1980) Wiener-Hopf methods (Angulo and Chang, 1953;Angulo and Chang, 1959;Kay, 1959;Aoki and Miyazaki, 1982) expansion in Neuman series (Gelin et al, 1979;Gelin et al, 1981), and mode matching (Clarricoats et al, 1972;Hockham and Sharpe, 1972;Brooke and Kharadly, 1982;Mahmoud and Beal, 1975;Morishita et al, 1979). The most significant technical complication of junction problems in an open waveguide is the treatment of the continuous spectrum.…”