  Bessel beams, known for their unique non-diffracting property, maintain their
shape and intensity over long distances, making them invaluable for
applications in optical trapping, imaging, and communications. This work
presents a comprehensive theoretical analysis of micro-photonic antennas
designed to generate Bessel beams within the Terahertz (THz) and optical
frequency ranges. The technique is demonstrated by generating far-field
patterns of Bessel waves at these frequencies. The design employs metasurface
patterns arranged as arrays of concentric rings atop rectangular silicon
waveguides, collectively creating a Bessel beam. Dyadic Greens function
integral equation techniques are used to model the transverse electric (TE) and
transverse magnetic (TM) fields in the metasurface radiation zone. Utilizing
orthogonal vector wave functions, Bloch theorem, Floquet harmonics, and the
transverse resonance technique, a photonic chip is designed to achieve a
non-diffracting range of 500 um at the optical telecom wavelength of 1.5 um for
a metasurface radius of 25 um. A radiation efficiency exceeding 80% is achieved
by optimizing the attenuation constant (alpha) along the structure. The
theoretical models are validated through simulations for both optical 1.5 um
and Terahertz 14 um wavelengths, demonstrating significant alignment between
predictions and simulation results.
