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Abstract
A novel expression has been obtained for the group velocity in metallic waveguides which are filled with media which do not induce coupling between transverse and longitudinal fields. It is shown that utilizing the expression derived for the group velocity one can express the necessary and sufficient conditions for the existence of backward waves in these waveguides. The criteria developed for the existence of backward waves do not involve evaluation of derivatives even though a backward wave mode by definition is one which has opposite signs for the propagation constant and its derivative with respect to frequency.