In the case when the incident light is sufficiently intense so that a significant population accumulates in the excited state and if the material has an excited state absorption cross section sex that is larger than the ground state cross section s0, the effective absorption coefficient of the material increases. To achieve the largest nonlinear absorption, both a large excited state absorption cross section and a long excited state lifetime are required. When the lifetime of the excited state being pumped is longer than the pulse width of the incident light, the changes in the absorbance and the refractive index are fluence (J/cm2), not intensity (W/cm2) dependent. Thus, in materials with long upper state lifetimes, it is the fluence rather than the intensity that is limited. Limiting the fluence is usually desirable, since damage to optical devices is also often fluence dependent. This sequential two-photon absorption process has also been called reverse saturable absorption (RSA) or excited state absorption.
Some criteria necessary for a large, positive nonlinear absorption are apparent including a large excited state cross section sigma(ex) and a large difference between the ground and excited state absorption cross sections (sigma(ex) - sigma(0)). A variety of organic and organometallic materials have been found to fulfil these conditions. Materials known to possess a positive nonlinear absorption in the visible besides phthalocyanines include porphyrins, organometallic cluster compounds [18-23], and other materials.
The condition that sigma(ex) is greater than sigma(0) is necessary, but it is not sufficient for a useful optical limiting material. A practical optical limiter must operate over the wide range of incident intensities that might be encountered. The nonlinear response should possess a low threshold and remain large over a large range of fluences before the nonlinearity saturates. A high saturation fluence normally requires a high concentration of the nonlinear material in the optical beam. For an organic material, this means it is highly soluble in common organic solvents, or it is a pure liquid or a solid film that can be prepared with good optical quality.
Many of the dyes used as nonlinear absorbers tend to aggregate at high concentration. The intermolecular interactions caused by aggregation are often deleterious. Extensive aggregation needs to be suppressed by modification of the molecular shape and electronic effects, to suppress the Van-der-Waals interaction between the large pi-systems. In addition, the material must possess a high linear transmission and a large nonlinear absorption over a broad spectral bandwidth as well as a high threshold for damage. Furthermore, the nonlinear absorption must appear with a sub-nanosecond response time. Meeting all these criteria is a significant chemical challenge in synthesis.
We developed different strategies to synthesize indium(III) and titanium(IV) phthalo- and naphthalocyanines suitable as optical limiting materials.