So far the propagation of Gaussian beam in higher-order Kerr media has been investigated by using the integrals of motion. In this paper, the suitable transfer matrix for higher-order optical Kerr media is introduced. The required critical power for self-focusing in these media is presented. Using the ABCD matrix method, the propagation of Gaussian beam in higher-order Kerr media is simulated and analyzed. This method, according to its simplicity and high speed computing compared to the integral of motion method, can provide many applications in optical systems simulation programs.

Keywords: Integrals of motion, Critical power, Self-focusing, ABCD matrix method, Higer-order Kerr medium

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