Percolation and lasing in real 3D crystals with inhomogeneous distributed random pores

We systematically study the percolation phase transition in real 3D crystals where not only the state of pores but also their radius r and displacement s are random valued numbers. The mean values R=〈r〉R=〈r〉 and S=〈s〉S=〈s〉 emerge as additional spatial scales in such an extended network. This leads to variations of the threshold (critical) percolation probability pC and the percolation order parameter P that become to be the intricate functions of R and S. Our numerical simulations have shown that in such extended system the incipient spanning cluster can arise even for situations where for simple periodical system the percolation does not exist. We analyzed the validity of the nearest neighbor׳s approximation and found that such approximation is not valid for materials with large dispersivity of pores. The lasing of nanoemitters incorporated in such percolating spanning cluster is studied too. This effect can open interesting perspectives in modern nano- and micro-information technologies.