Focusing effect of a laser beam on the power dependence of multiphoton processes

The effect of focusing a laser beam on the intensity (I) dependence of multiphoton processes was examined. A general method is given to deduce a genuine intensity dependence from the focused-beam experiment. In addition, some typical examples were examined in detail. For the dependence of the type ofI ⁿ, an apparent relation ofI ^3/2 appears only when there is a change of dependence asI ⁿI^m, withn>3/2 andm<3/2. A genuine intensity dependence can be obtained directly from the focused beam experiment ifn does not change throughout the irradiated volume, or if the conditionn>3/2>m does not hold. The case of gradually decreasingn, as is common for the infrared multiphoton reaction probability (P), was also analyzed taking the Arrhenius-type dependence,P exp(–/I), as an example. A simple method is proposed to obtain a genuine relation betweenP andI for this type of intensity dependence.