Does laser hair removal cause infertility?

There is no relationship between laser hair removal and fertility. The depth of penetration of the laser only goes a few millimeters below the skin surface, just far enough to target the root of the hair follicle. No worries. 

Hi Helen, thank you for your question!
Laser Hair Removal (LHR) has its effect on the hair follicles in the dermis (part of the skin) only. This part of the skin is far, far away, anatomically speaking, from the generative organs of the uterus, ovaries, fallopian tubes and etc. There is no physical way the light from LHR could get to the organs of reproduction in a way that would damage them, so no, LHR will not create infertility.
LHR is not recommended for women who are pregnant or who might be pregnant. This seems to be a recommendation from the manufacturers of laser equipment without any apparent basis in medical logic, however, most or all laser clinics will not perform LHR for a pregnant patient based on these recommendations for liability reasons. 
I hope this has answered your question! Thank you again for asking!