SAR limits are global - they are slightly higher outside of US, Canada, Korea but 2 W/kg not 1.6W/kg, so they could go up by 25% internationally but that's 25% of not-a-lot. Part 18 etc or frequency band is irrelevant outside that.
My point was really around the band they're using is simply unavailable outside Region 2, so it can never be a global product. I don't know what restrictions Industry Canada put on the band, for example, I couldn't readily find reference to their equivalent of Part 18. Although Part 15 will be fairly commonly reflected around Region 2, with some local technical provisos, there may not be any equivalent provision at all for an equivalent of Part 18 on the 915 MHz band. Certainly the regulations I'm aware of, although admittedly in telecomms, tend to be pretty prescriptive and vary significantly.
I am somewhat surprised that despite the prescriptiveness of Part 15 (specific EIRPs in specific circumstances, channelisation, modulation methods, spread spectrum etc) as a means to allow and encourage interoperability on an inherently shared spectrum, is almost completely nullified by Part 18 which allows anything as long as the SAR requirements are met!
The different element spacing at different frequencies is just down to lambda/2 spacing as typically ideal, as lambda changes with frequency. Energous are at 0.2 lambda spacing right now, 33cm wavelength with 6cm pitch, which is on the verge of "just halve the number of elements and drive each twice as hard" as far as a phased array goes. They also only have 12 antenna total, so have very limited control over beamforming as can be seen in the plots where power seems to go everywhere but at the target.
I do mention patch antenna but there are two further issues there - first is that the impedance goes up so for any given voltage induced you have lower power, second is that they are highly directional so on receive it's hideous. It's bad for send too, you're already at 1% efficiency at best, but I doubt they are concerned about that.
The only options I can think would work would be a reflective planar array or a patch array. Planar arrays would have greater physical depth, there's a need to have some distance between the passive reflector and the driven element. Increasingly a patch array seems likely to me. My reasons for thinking this are multifold.
o Firstly, they can be fabricated using common microstrip techniques cheaply using double sided PCB, with all six driven elements fabricated on a single PCB.
o Secondly, the PCB substrate will have a permittivity that will significantly shrink the patch and spacing, with typical Er's of PCB allowing about half the size of a patch in air.
o Thirdly, driving these patches can be done very close to the driven elements, with active components including both HPAs and phase shifting. Distributing the parts to each driven element, particularly the HPAs in this way, has both thermal and loss benefits.
o Finally, polarisation. Implementing circular polarisation on a PCB fabricated patch is simple to achieve, but will need some spaghetti wiring on a reflective array. Circular polarisation has the benefit of significantly reducing fade as it's not dependent on device orientation on a given plane.
Regarding the impedance of patches, in my experience (I work on antenna designs primarily for ground and space segments in aerospace, but also work in terrestrial stuff too) that's really a non-issue particularly in narrow band applications like this. This can be done either with microstrip matching transformer techniques fabricated into the substrate, or, quite likely at 915MHz, with simple lumped fixed LC parts especially as the substrate is (as is likely) simple PCB material.
Regarding directionality of the patch, an identical issue occurs with a reflective array element. Both have broadly similar directivity and gain (about 6dBi, especially if the patch is fabricated on solid dielectric substrate).
So far I've only discussed the sending antenna. I'm not sure what physical form factor the receive side takes, I guess it's probably a sleeve. A problem here is to get something that's of a reasonable size and efficient at the frequency of interest, and, as you say, isn't too directive. In addition, achieving reasonable polarisation matching is going to help: in a linearly polarised system if you're rotated 90 degrees off in a facing plane, almost no power will be received. If the transmitter is circularly polarised instead then these nulls can be removed. If the receiver is also circularly polarised with the same sense, then minimal losses will occur.
There is however an engineering problem in that getting an efficient circularly polarised antennas in a reasonably sized phone sleeve envelope is going to be compromised. It may be better to accept that the sleeve receiver side remain linearly polarised and accept the 3dB hit incurred converting from circular to linear, as you'll get a more consistent experience that with both sides being linearly polarised. It will also mean that the receiver can harvest energy in many more three dimensional orientations.
Maintaining decent circularity with phased arrays significantly off the default centre boresight adds complexity but can be engineered if only one device is being targeted. Maintaining a reasonable axial ratio (i.e. good circularity) would be necessary to avoid nulls similar to those found using a linear-only solution.
One further concern I have on the solution as a whole is over multipath. Almost certainly there are going to be dead spots with this solution in any practical installation, and even a phased array isn't going to fix this, although it could, if you're really smart, achieve some mitigation by adjusting polarity on the fly.
Frankly all of this, while academically interesting, if I may mix metaphors, is putting lipstick on a pig that's never going to fly.