Not an expert, but we would need to have infinite thickness beam and an infinitely big axicon, for the Bessel beam to be infinite (as in, reaching infinity "lik

Not an expert, but we would need to have infinite thickness beam and an infinitely big axicon, for the Bessel beam to be infinite (as in, reaching infinity "like" regular light). Otherwise the Bessel beam is constrained to the space covered by the overlap of the radiations of both of the original waves. It makes sense since bessel beam-like radiations can be formed inside waveguides (or waveguide-like structures like optical fiber), which effectively make the wave unbound by means of bouncing it off.