Hi, Thanks for the reply, but I believe there is some misunderstanding. The terminology might have been bit confusing due to gaussian source object and gaussian input beams.
On the first part I am talking about a plane wave incident on the lens producing diffraction limited beam (non gaussian). I was already using the diffraction limited equation that you have pasted in your reply. From the equation that you pasted for the airy pattern, the first dark ring ( first minima) should be where the J1(k a sin(theta)) goes to zero, which corresponds to a beam diameter of the diffracted spot to be 1.22*lambda/NA. For 1360nm input beam with an NA of 0.14 this corresponds to 11.85um. But the FDTD simulated version for fully vectorial calculation gives 2.17um, which is confusing!!! This should be what is simulated by lumerical.
On the second part I show that this is not explained by assuming a gaussian input beam instead of a plane wave. If the input to a lens is gaussian instead of plane wave, the diffraction limited beam (which is non gaussian) is expected to be 6.18um based on the same diffraction limit arguments. So I am confused why the simple fully vectorial FDTD simulation doesnt match any of these.