I would call post-1945 literature "contemporary", and describe some of the works produced during that period as "post-modernist".
Thus (to my mind) the poems of Larkin are "contemporary"; but the later stories of Borges or Calvino are both "contemporary" and "post-modern".
By the way, you could also add the Edwardian (1901-1910) and Georgian periods (1910-1914).
(Of course, these periods are only for convenience: "Victorian" authors continued to write in a Victorian style into the early years of the 20th century, and Georgian writers continued to Georgianize into the 1920s.)
All the best,