Let's say we have perfected a meta-material that is invisible to the complete range of electromagnetic radiation. I reckon that since light (ionizing or not) entering the material is simply being bend/redirected instead of passing through without being absorbed too much power can still hurt.
Using known science, would the perfect invisibility cloak truly be invincible to energy based weapon? If not, how to build one that would be invincible to energy based weapons?
Kinetic energy weapons will not care at all about meta-materials, they will simply transfer kinetic energy to it, like they would do on any other target. I presume you mean EM energy weapon.
Meta-materials work thanks to a carefully arranged geometry. Though they are chosen to be as much transparent as possible (there is no perfect transparency) for the light they are supposed to work with, EM weapons have such an high power that even a small absorbance yields noticeable effects. (absorbing 0.1% of a 100 kW beam is still 100 W, not peanuts...)
Such effects can be:
If you're taking the technology to perfection then any detectable energy has to apparently pass through volume covered by the cloak entirely unchanged from any angle.
If that's not the case, then the technology isn't perfect.
An energy weapon, being detectable energy, would hence have to apparently pass through without being affected. I fire from one side, the person standing beyond gets fried, volume within cloak doesn't even get warm.
Using known science? No chance. But then known science barely provides energy weapons so I wouldn't worry that much.
It would also be very dark inside the cloak and, if fully concealed by it, you wouldn't be able to see what was going on outside. After all, all detectable energy passes you by.
If you want to be able to see from the inside then the cloak is no longer "perfect", it's now a point along the scale and L.Dutch's calculations for how much energy from weapons penetrates apply along with visible light.
The problem is (AFAIK) that metamaterials are capable of bending/redirecting specific wavelengths to a specific degree. So a metamaterial that could (for a simplified example) bend green light perfectly around a human-sized bubble would have trouble with red light, and so on. Even if you would manage to get one that bends all visible light around it (a rather impressive range of wavelengths), there's still a lot of range below (infrared...) and above (ultraviolet) that.
Overall, a metamaterial-based invisibility is - using current tech - highly unlikely, and even if you somehow (through VERY creative use of geometry to make a suit out of several metamaterials, each redirecting a range of wavelenghts along specific paths around the body?) got it to work I really doubt you could get it to work on all wavelengths. Especially since - as L.Dutch mentioned - even a small percentage of imperfection would already lead to heating and damaging of the complex, and likely fragile, arrangement of metamaterials.
As for the second part, "how to build one that do"(sic)... if you want to stick with current science, "not". Invulnerability to energy weapons is a thing for handwavium force fields, handwavium sci-fi materials, magic, thick bunker walls or "not being where they shoot".
If you are physically present, then you are physically vulnerable.
The main advantage of an invisibility cloak is that you cannot be seen and are therefore unlikely to be directly attacked. However your invisibility cloak works, bending or otherwise manipulating normal incident light cannot be the same as handling an energy blast, whatever form that energy blast might take - even if it is simply light energy, it is unlikely to be simply 'visible' light.
I can think of one energy-based weapon that does not rely on radiation: an electrical arc. If the attacker can generate enough positive potential on one side of the target, and enough negative potential on the other, a discharge will follow the path of least resistance between them in traveling to ground. Even an advanced metamaterial likely has better conductivity than air.
This may be very difficult to achieve under most circumstances, and of course invisibility would hinder targeting. But with the right setup--an armed trap within a security system, for instance--the electrical arc would not only be able to "seek" the user of the cloak, but presumably deliver a great deal of energy that would not be affected by refraction.
