The generation of focused beams in the millimeter- and submillimeter-wave ranges, with transverse-electric (TE) polarization, is investigated in the radiative near-field region. The desired field distribution is achieved through a leaky-wave beam launcher consisting of a grounded dielectric slab with an annular strip grating on top excited by a circular slot on the bottom ground plane. The latter is fed by a Marié transducer, which converts the input, fundamental TE10 mode of a standard rectangular waveguide into the higher-order TE01 mode propagating in the circular waveguide connected to the device. The generation of TE-polarized diffraction-limited Bessel and Bessel–Gauss distributions is achieved by suitably synthesizing the annular strip grating. Simulated results are in excellent agreement with those predicted by leaky-wave analysis providing a proof-of-concept for the generation of TE-polarized Bessel and Bessel–Gauss beams at 300 GHz with a beam size of 1.7 and 1.9 mm up to the nondiffractive range of about 25 and 15 mm from an aperture plane with radius of 12.75 mm, respectively.