Like there is chu and harrington limit on the size of electrically small antennas, I would like to know whether any such limit exists in absorbers? If not, then how would we define some absorber as electrically small absorbers?
I do not think there is a fundamental limit on the size of absorbers, but there may be for specific types of absorbers like metamaterial absorbers. I think it only makes sense to talk about fundamental size limits when a resonance is involved because this inherently puts the device on the same order of size as the wavelength. There are plenty of absorbing metarials out there that are based on material loss and not resonance. If you are a stickler for details, loss in materials can arise due to atomic and molecular level resonances. I am talking about circuital resonances.
Here is something else to consider. In principle, you could find an absorbing material that is lossy enough to absorb a wave at an extremely subwavelength scale. In fact, metals do this and we talk about skin depth. The problem is that if you somehow create extreme loss, you may also create extreme reflections so your wave never experiences the loss. This is the case for metals at low frequencies. Metals are so lossy that they produce very little loss! The wave is reflected before it experiences the loss. The trick to absorbers is to have high loss, but with a matched impedance. I still do not think there is a fundamental limit though, only perhaps for specific types of absorbers that are based on resonance.
There are basically four groupings of the absorber types.
Those that are based on advantages from having complex magnetic permeability and complex dielectric constant essentially equal.
Those that are 'resonant" usually a quarter wavelength thick operating over a relatively narrow frequency range.
Those that are "broad band" characterized by a gradual tapering from the impedance of free space to that of the medium over appreciable thickness (in terms of wavelengths).
Those that are very thin (in terms of wave length) that are used to attenuate surface currents on metal structures .
Thank you very much for your answers. However, I still feel that it can be a good topic to study and research as there is no empirical formula or expression governing thickness of ultra thin absorbers.