Investigation of third order nonlinearity in propagation of cylindrical waves in homogeneous nonlinear media

• An approximate analytical expression which contains all the main nonlinear optical effects including sum frequency generation in third order nonlinearity has been obtained.
• Results can be used for the problem of cylindrical sum frequency, difference frequency generation, third order harmonic generation and some other nonlinear effects.
• By increasing third-order susceptibility the generated wave field increases.

Four-wave mixing in propagation of cylindrical waves in a homogeneous nonlinear optical media has been investigated theoretically. An explicit analytical expression which contains all the main nonlinear optical effects, including third harmonic generation, sum and difference frequency generation has been obtained. A comparison between sum frequency efficiency for exact and approximation expression in a homogeneous nonlinear medium has been done. The effect of increasing the nonlinear optical coefficient (χeff(3)) and increasing the frequency difference between two adjacent waves (Δω)(Δω), on the efficiency of sum frequency generation in homogeneous media has been investigated.