Photodiode package choose

Hi, all

I have two questions about the photodiode package.

1, some of the photodiodes are packaged in plastic, for example pdb-c134f in T1 or BPV10 in T-1?.

what does this "arch? sharp package for? provide a wider angle and a optical gain? I put my understanding in the following picture. Am I right ？

2
In my application, the optical signal doesn't come in parallel, it is totally disordered like this

what kind of the package should I use to collect more photones? should I use SMD and try to put photodiode as close as possible to the light source?

It's a lens (plano-convex I guess), and provides focussing (it won't be as disordered as you think, when arriving from a distance).
You may need a lens at the transmission end too, depending on what you're trying to achieve.
For short range, sometimes a lens is not needed, just an aperture (e.g. for a slot sensor) although in that case sometimes a little
ball shaped lens (I forget what it is called, but behaves like a convex lens) is used.
For an optoisolator for instance, no lens is required, since the emission is strong enough, and the sensor is protected from ambient
light conditions.