Demonstration of a general scaling law for far-field propagation

This paper conducts experiments that demonstrate the utility of a general scaling law (GSL) for far-field propagation. In practice, the GSL accurately predicts the diffraction-limited peak irradiance in a far-field plane, regardless of the beam shape in a near-field plane.Within the experimental setup, we use a reflective, phase-only spatial light modulator to generate various beam shapes from expanded and collimated laser-source illumination, including both flattop and Gaussian beams with obscurations, in addition to phased arrays with these beam shapes. We then focus the resulting near-field source plane to a far-field target plane and measure the peak target irradiance to compare to the associated GSL prediction. Overall, the results show excellent agreement with less than 1% error for all test cases. Such experiments present a convenient and relatively inexpensive approach to demonstrating laser-system architectures (of varying complexity) that involve far-field propagation.