The objective of this Small Grant for Exploratory Research is to improve and generalize the present characterization and description of laser beam properties or laser beam figures of merit to cover a broader range of laser beams and pulses, and to describe their propagation through ideal and real optical systems. The new point of view is to use the phase-space approach for describing the beam completely in both space and time, and to derive important figures of merit for the beam from this phase-space description. This language relates different characteristics to each other, leading to a few overall measurable quantities for characterizing even a pulsed beam. It follows that a description of the laser beams and pulses in phase-space will provide new, more general overall information. The experimental objective is to design and develop a device for measuring the overall laser beam characteristics in a new fashion by providing direct access to phase-space characteristics, using suitable optical transforms and digital acquisition of phase- space information. Such a device would present more complete information about either a pulsed or cw laser beam. The main significance of the project is that: it will provide a better description than presently available for laser beams, laser pulses and their propagation; it will generalize to beams with lower symmetry and also to pulsed laser beams the existing results for cw symmetric beams; and it will provide an experimental set-up for measuring the beam factors of merit directly in phase-space terms.
