Phase-matching for optical up-conversion with maximum angular aperture — theory and practice

Abstract

An equation of quadratic form is derived relating the phase mismatchΔk=¦k _sum −k _pump −k _slgnl ¦ in an optical sum-frequency generation process to the angle ψ between the pump and signal wave vectors. For a special value ofk _pump a solution ofΔk=0 exists having degenerate roots and consequently a single value of ψ. Because of this it is possible to choose a non-collinear phasematching situation for an optical up-converter which tolerates a much larger signal beam divergence than if a collinear-beam interaction were chosen. The case of up-conversion of 10.6μm radiation to the visible, using ruby-laser pumped proustite was chosen as an example for experimental study. Under tangential phase-matching conditions an angular acceptance angle of the infra-red beam of 300 mrad was achieved for a crystal 0.45 cm long.