A poem specifically designed for a man who is expecting a baby, whether this is his first child or not, is called a "father-to-be" poem. Since the baby has not been born yet, the man will be a father soon.
Since the Oxford dictionary classifies a poem as an article of writing used to express feelings through imagery, a father-to-be poem can be written by anyone. These poems are used as a method to creatively express emotions towards a father.
Several mother-to-be women write poems through the eyes of their unborn babies for their husbands. The poems also do not have to address a biological father, simply a father figure who is important to the family. A father-to-be poem can be written by hand, printed out or typed on a computer and posted to a website. As long as it reflects personal feelings towards a father figure, the writing will classify as a "father-to-be" poem.