Space-time odd-symmetric Butterfly wave packets with multidimensional modulation properties

It is a highly significant research area to investigate how to achieve multidimensional modulation and analysis of breathers in a local nonlinear medium. We present the first investigation of space-time odd-symmetric Butterfly (STOSB) wave packets in a local nonlinear medium, focusing on their odd-symmetric focus and focal length control. Meanwhile, a completely new modulation method for breathers is proposed that can alter the intensity distribution of breathers in the X-Y plane at the focus while maintaining the intensity distribution in the X-T and Y-T planes unchanged. Furthermore, both the unique self-healing capability of breathers in STOSB wave packets when obstructed by barriers and the variation trend of the waist diameter are discussed. Our work develops spatiotemporal wave packets with multidimensional modulation and self-healing functions, and advances the basic research on breathers in fields such as optical communication.