I don't have a hard scientific explanation for this but I interpreted these 4 mediums of communication as follows.
Long membrane: a long, low-frequency wave form; gravitation
Medium membrane: middle of the spectrum and what we call radio waves; electromagnetism
We also know from elsewhere in the series that there is neutrino-based communication (maybe neutron-based and I'm misremembering). Neutrinos interact via the weak subatomic force, and if that is the force-field through which these communications are transmitted, we now have 3/4 of the fundamental physical forces listed as a medium for communication. Because the weak force has such a short range, I presume it could be thought of as a "short medium" as communications transfer through this force field of very short-ranged forces.
This leaves the last communication medium listed, light medium, and the last fundamental physical force, the strong subatomic force. This is the force explaining the Trisolaran droplet's odd qualities. I'm not sure of the physics basis for calling communications via the strong fundamental force's field "light medium" and I'd be interested in more information. I validated this medium type on the basis that the droplet had some odd physical properties related to light and other phenomenon. Here's a description of it from https://forums.spacebattles.com/threads/weakest-sci-fi-weapon-that-can-destroy-the-droplet.331222/ with emphasis added:
It's the size of a small truck, weighs ten tons, and has a perfectly smooth surface that reflects every wavelength of radiation,
temperature at almost absolute zero.
The truth is it's made of Strong Interaction Material. The Trisolarans
altered physical constants, making nuclear strong force have longer
effective range, creating this material that is as dense as normal
material, but as tough as a neutron star. It's said that it can
penetrate earth like a bullet through butter. [...]
Propulsion data: It can go from 0 to 31.7 km/s in 50 seconds. Maximum
speed 15% lightspeed. It's shown to take a 15 degree sharp angle turn
at 31.7 km/s, without any deceleration. Whether it can perform the
same turn at 15% lightspeed is unknown. It's energy source is unknown.
It's controlled through quantum communication, so there is no range
limit of control.
It's not a perfect match, but there is some hint that the droplet is as far removed from ordinary matter as light is as far removed from ordinary matter, potentially considered as a membrane of of spacetime. There's also the hint that "light membrane" won't be as directly 'translated' as we humans think it is, because 'light membrane' as we know it is electromagnetism, but electromagnetism is already referred to as 'medium membrane' aka radio telecommunications. Thus, I figure light membrane could be communications via the strong fundamental force's field.
For that matter, what communication membrane do the sophons work through?