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A unified approach for representing the surface-wave fields and for computing the corresponding radiation efficiencies from arbitrarily shaped slot-type antennas on thick dielectric substrates at millimeter-wave (mm-wave) frequencies is presented. In this approach, two different representations of the surface-wave fields, i.e., the one based on the idea that the surface-wave power can be associated with a substrate radiation pattern and the other based on the cylindrical wave expansion, are linked together in a unified way. The developed theory is then applied for investigating the surface wave characteristics of printed twin offset slots and uniform linear slot arrays. Based on the developed theory, new insight into the mechanism with which surface-wave power is coupled by the slot pair is presented. Subsequently, the optimum number of elements and corresponding interelement spacing for linear, uniformly excited, slot dipole arrays is explored for achieving maximum radiation efficiency and gain. In order to provide guidance on practical mm-wave integrated slot antenna array design, supportive numerical results are presented for Substrates of dielectric constant εr = 4.0 and εr = 12.0.