It is shown that the plane-wave picture of a leaky mode proposed by Burg, Ewing, Press and Stulkin (1951) yields the accepted period equation for leaky modes in a water layer a half-space. The resultant mode is formed by an inhomogeneous wave with real frequency and complex wave number and phase velocity. Another form of mode considered is that formed by a homogeneous wave in the guide with real phase velocity and complex frequency and wave number. The phase-velocity dispersion curve for this case is appropriate for determining shear-wave coupling to PL waves. The procedures of the article could be readily extended to the more complicated case of a solid layer over a half-space. It is also demonstrated that the derivative of the real part of angular frequency with respect to the real part of the wave number is a good approximation to the group velocity for leaky modes with low losses.