Ultrasonic imaging technologies possess extensive applications in modern medical diagnosis and treatment. In this paper, a designed artificial bubble array is utilized to establish a multi-scattering sound field model to describe the nonlinear vibration of the artificial bubble array, combining nonlinear acoustics and multi-scattering theory. With the results of the effective medium model, the correctness and reliability of the multi-scattering model are verified. Furthermore, under different incident frequencies and different bubble array parameters, the distributions of fundamental and second harmonic sound pressure fields produced by nonlinear vibration of the artificial bubble array are investigated. Via a judicious design of structural parameters, both fundamental and second harmonic acoustic focusing at specific locations inside the bubble array and second harmonic acoustic focusing outside the array under a specific incident frequency are realized.