Influence of saturable absorber on critical phenomenon analogies in single mode laser driven by external coherent field

The influence of the existence of absorbing atoms in a laser cavity on the critical exponents of abrupt transitions between steady states in the system of single mode onephoton laser driven by an external coherent field is discussed. An isolated threshold when ,and a kind of threshold when, where is the pump parameter of the absorbing atoms, is obtained. The asymptotic forms of the families of potential functions for the system near these threshold are also found. The well-known scaling hypothesis in the general homogeneous function form is shown to be a characteristic of these asymptotic families. Four threshold exponents, , , and and four threshold amplitudes,B, D, andA, near each of these thresholds, are obtained. The threshold exponents near each threshold obey the scaling laws of critical phenomena, while the corresponding amplitudes obey the definite relations between exponents and amplitudes.