Giant non-linear susceptibility of hydrogenic donors in silicon and germanium

Implicit summation is a technique for the conversion of sums over intermediate states in multiphoton absorption and the high-order susceptibility in hydrogen into simple integrals.Here,we derive the equivalent technique for hydrogenic impurities in multi-valley semiconductors.While the absorption has useful applications,it is primarily a loss process;conversely,the non-linear susceptibility is a crucial parameter for active photonic devices.For Si:P,we predict the hyperpolarizability ranges from χ^((3))/n_(3D)=2.9 to 580×10^(−38 )m^(5)/V^(2) depending on the frequency,even while avoiding resonance.Using samples of a reasonable density,n3D,and thickness,L,to produce thirdharmonic generation at 9 THz,a frequency that is difficult to produce with existing solid-state sources,we predict that χ^((3)) should exceed that of bulk InSb and χ^((3))L should exceed that of graphene and resonantly enhanced quantum wells.