Beam-Profile Measurement of Laser Pulses Using a Spatial Filter to Sample the Hermite Modes for a String of Pulses

摘要

As a first step in the development of a beam-profile measuring instrument for laser sources that is capable of determining the distribution of low-order (less than 25) Hermitian modes in a series of laser pulses, the author designed and evaluated the three key parts of such an instrument. First, there is the telescope system which allows the incident laser beam to be phase, beamwidth, and beam center matched to the optical spatial filter. Second, there is a brief error analysis of the structure of the mismatch function between the beam out of the telescope and that expected by the filter. Finally, there is the detailed analysis and design of the computer-generated spatial filter that will cause the incident-laser beam to be cross correlated with the low-order Hermite modes and will create an array of light spots in the detector (Fourier transform) plane each of which can be uniquely related to a particular Hermite mode of the original laser pulse. The principal conclusion is that the Hermite mode analysis can be done with better than 99 percent separation between modes, provided the phase between modes is uncorrelated from pulse to pulse when the filter has been fabricated with a two-level, gray-scale structure which samples the profile with either 0 percent, or 100 percent transmission.