When we couple a Gaussian beam into a Single mode fiber, then the spot size of the Gaussian beam (W) is a fiber dependent parameter which is expressed as:
W= a.*(0.65+1.619*V^-1.5+2.879*V^-6) ..............................(1)
Where a= radius of SMF V=V number of SMF. But If we couple a axicon generated Bessel-Gauss beam into a special type of hollow fiber as mentioned in your answers, then how the spot size and radial wavevector will depends on fiber parameter. That means how th.The axicon-generated Besse-Gauss beam (which is in free space) can be expressed as: A=J0(kr*r)*exp(-r.^2/W.^2) ..................................(2)
Where kr= radial wave-vector which depends on axicon angle, W is the illuminating Gaussian beam spot size and r is the radial co-ordinate of the fiber. After focusing and collimating this zeroth order Bessel-Gauss beam, this beam is to be coupled to a special fiber. Then, How the beam spot size of gaussian envelope of bessel-gauss beam and radial wave vector will change after coupling of Bessel-Gauss beam into the special guiding fiber. Is there any mathematical relationship like Gaussian beam spot size formula in a SMF as mentioned in equation(1)?