If I understand your question you are asking how light up the background?

I use a flash on the floor, a small stand, or a short light stand, directly behind the subject probably at or below the waist.

I use manual flash and and take several test shots to achieve the desired effect.

I may use max power if I want to white out the background.

You can use a gel if you want to create a color change to the background.

You can also focus or spread the beam by its distance from the background or changing the flash setting.

These also look as if they have a hair light in which case you might want to use a grid on those to keep them from spilling onto the background.

Hope that helps.