Three-dimensional light sculpting using a geometric analysis

Phase-only spatial light modulators (SLM) have been a staple in laser beam shaping research and applications due to their efficiency and programmability. An SLM's capability to shape three-dimensional distributions of light has interesting applications in optical micromanipulation and microscopy. Since these SLMs operate by modifying the phase of incident light, it is common to model their operation using scalar diffraction theory or Fourier optics. In this work, we show how utilizing a ray tracing or geometric optics analysis can produce both interesting and practical results. We have previously shown how to generate laterally shaped beams that do not have the characteristic noise or discontinuities typical of the output generated with iteratively or numerically derived phase distributions. In this work, we extend the geometric approach to three dimensions to form interesting distributions that behave like non-diffracting beams, light sheets and beams that follow spiraling or diagonal paths as they propagate. The analytically derived input phase functions for these beams can be calculated in a straightforward manner. Hence, they are easily encoded and re-configured for SLM applications. Experiments demonstrate these 3D light distributions on a typical 2f holographic configuration, verifying its applicability on existing holographic setups.