Numerical analysis on optical limiting performance of a series of phthalocyanines for nanosecond pulses

The optical limiting properties of a series of peripherally substituted phthalocyanines with different central metals and axial chloride ligand for nanosecond pulses have been studied by solving numerically the two-dimensional paraxial field equation together with the rate equations using the Crank–Nicholson method. It is shown that all of these compounds exhibit good optical limiting behaviour, and phthalocyanines with heavier central metals have better optical limiting performance due to the faster intersystem crossing caused by the enhanced spin–orbit coupling. The major mechanism of optical limiting for long pulses is the sequential (singlet–singlet)×(triplet–triplet) nonlinear absorption. Dynamics of populations is characterized mainly by the effective transfer time of the population from the ground state to the lowest triplet state. The long lifetime of the triplet state is important but not determinant. In addition, the performance of optical limiting strongly depends on the thickness and concentration of the absorber.