You should be looking for some material that is transparent to IR light. Glass is not and most plastic is not. Some device that is active all the time and battery powered will certainly need constant battery charging for operation at night and recharge during the day.
The problem is that power is needed to power the sensor at all time .
An Arduino too , will take power to supply its on board regulator and other parts . You need to look into that to work out what sized battery you need , how often to replace it , and if project is workable for you.
If you were just to use a bare 328 processor etc and make your own board you could get the power right down , not sure if that’s within your ability ( google minimum Arduino)
Is there no way you can get power to your sensor ??
It may be better to use a passive infrared sensor (PIR) instead of a beam break arrangement. A PIR sensor can have a quiescent power consumption around 30 micro amps , so would be suitable for battery operation. Examples are HC-SR505 and AM312. You may be able to shield the sensor in such a way that it behaves like a narrow beam break system.
Thanks everyone for lending support. The application is actually for my Mom who is 93 and has cognitive issues with wandering off.
The current system of cameras over doors gives a overload of emails.
I just wanted to let all know that this has helped a lot.
Last note there is no outside system like this and has other applications with garages and other applications.
If you can leave one end at the home there are several possibilities. Have you looked at retro reflective photo detectors? The RCWL RADAR module is good for several feet. These are just a few. Hint: the RADAR can go through walls.