in the case of two-photon and three-photon absorption, in most of the papers, the absorption cross-section values follow with absorption coeffcint. whether is there any exceptional case is there? if so what causes it?
The absorption cross section is proportional to the absorption coefficient as long as the the absorption of the particles is not coupled, which means that there must be a certain distance between them (e.g. molecules in a gas at low pressure, diluted solutions etc.). Otherwise, larger deviations are possible, see, e.g., Article Deviations from Beer's law on the microscale - Nonadditivity...
Pradeep kumar Vasudevan - as Thomas Mayerhöfer says, in principle the absorption co-efficient is proportional to the absorption cross-section, but is your question whether the absorption cross section of a 2 or 3 photon transition is proportional to the absorption co-efficient of a single photon transition?
In this case, no - as for example a 2 photon transition accesses states of different parity than a single photon transition.
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