为什么当没有主语时after要加动词ing?

从你的问题中可以感觉到,你没有完全把握after的词性和用法,常用的词性及用法：
1、作连词使用,引导句子：I went home after I had finished my work.
She became a doctor after she returned to China.
2、作介词使用,后面接名词,代词（宾格）或者动词的-ing形式：
We usually play football after school(=after school is over)
My parents watch TV after supper.
After reading Lesson One(after i had read Lesson One),I went on to read Lesson Two.

after是介词，介词后跟名词，代词，动名词

无主语的时间状语