Bottom line with any effective energy rejection filter (ERF) is to pass the wavelength of interest (in this case H alpha which is only 2A wide) and block at effective ND5 all other wavelengths from UV though to NIR (and beyond if possible)
Ha Narrow band filters (Baader, Astronomik etc) can have bandwidths from 3nm (30A) to 30nm (300A) which more than cover the Ha line. They also have very good blocking - at least up to 1100nm. The available transmission curves rarely go beyond this limit.
This is the response limit for silicon based chips ie CCD and Cmos. There is still some solar IR beyond that point but not visible to the eye but in some limited professions -glass blowing, furnace work etc long exposure can be a concern.
(I had headaches - figuratively! making an ERF for CaK wavelengths. Normal UV-IR filters cut at 400nm whereas I needed to get down to 393nm. In the end the ERF was a combo of four filters
which gave a narrow bandwidth coverage of CaK and blocking all the way through to NIR)
With the SHG for imaging visual wavelengths, a Baader ND0.9 and a Astronomik L1 UV-IR filter combo does the job.