See if this helps
Huygens' Principle geometric derivation and elimination of the wake and backward wave
https://www.nature.com/articles/s41598-021-99049-7
It shows elimination of the backward wave without the obliquity factor.
I am interested in any discussions about wave propagation. I authored:
Huygens' Principle geometric derivation and elimination of the wake and backward wave
https://www.nature.com/articles/s41598-021-99049-7