Coherence and photon distribution function of the light generated by nonlinear effect

Abstract

The effect of the state of the atomic system to the coherence of the light generated by nonlinear effect is discussed by using the microscopic Hamiltonian of the nonlinear interaction between light and electron. The mutual interactions of electrons in the atomic system are ignored in this thesis since the very intense light source is used in the experiment of the nonlinear effect. If the atomic state can be represented by an eigenstate of an electron, the light generated in frequency up conversion process is fully coherent and has the Poisson distribution, i.e., the light is in an eigenstate of the photon annihilation operator. On the other hand, the light generated in frequency down conversion process is first order coherent and has the Gaussion ( superPoisson) distribution same as thermal source. But if the atomic state can be represented by a superposition of eigenstates of an electron, the coherence of the light generated by nonlinear effect is incoherent. The photon distribution of the light generated in frequency up conversion is the linear combination of the super-Poisson distribution for each eigenstate of an electron. The photon distribution function of the light generated by nonlinear effect in $LiNBO_3$ crystal system is calculated numerically by the computer. In this result, the effect of the state of the atomic system to the coherence of the light generated by nonlinear effect is more effective for the case of the frequency up conversion than for the frequency down conversion.