Focusing geometries for constant fluence in infrared multiple-photon dissociation

Generalized mathematical expressions are presented that describe the fluence distribution of a laser beam focused properly into an optically thick gas medium so that the axial fluence distribution is made nearly constant. The laser-beam focusing parameters are optimized such that they compensate for the decrease in pulse energy along the beam axis. Two cases are taken into account for optical absorption. These cases are linear and nonlinear absorption, of which the latter is often met in infrared multiple-photon dissociation and applied widely to laser-isotope separation. It is demonstrated that an optimized focusing is effective in achieving almost constant axial fluence distribution, thereby maximizing reaction yields of a target isotopic component without the loss of isotopic selectivities in laser-isotope separation.