Detecting lateral misalignment of Laguerre Gaussian beams via spatial mode projection
We propose a technique to detect lateral misalignment of Laguerre Gaussian(LG) beams via spatial mode projection. We analytically solve the intensity of the misaligned beam projected on two different basis beams--a Gaussian beam and an aligned LG beam with the same topological charge l. We verify the analytical calculations by doing numerical simulations. Results show that the probability amplitudes follow a quadratic behavior for the Gaussian basis beam and a quartic trend for the LG basis beam with respect to increasing lateral misalignment. This study can be applied in determining minute beam displacements such as beamshift measurements.