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Traveling wave antennas for the millimeter wave range face two main problems: higher metal loss at the higher frequencies, and fabrication difficulties due to the smaller wavelengths. These two problems are addressed here by a new type of leaky wave antenna, in which the fabrication problem is minimized by employing a longitudinally continuous aperture, and the higher loss reduced by basing the antenna on a low-loss waveguide, the groove guide. A longitudinally continuous asymmetric metal strip provides the mechanism that transforms the initially bound mode into a leaky mode. An accurate analysis, based on a transverse equivalent network, is presented here for the properties of this leaky structure that takes into account the mode conversion from the bound mode to the leaky mode. All the constituents of this transverse equivalent network are obtained in closed form, thus yielding a dispersion relation in closed form. Part I of these two companion papers describes the new antenna and its principle of operation, and then derives the parameters of the complete transverse equivalent network. Part II is concerned with the properties of the leaky mode and their relations to leaky wave antenna performance; design considerations together with a variety of numerical results are contained in Part II.