You can generally make a loop detector work with carbon fiber bikes by just making sure the chainring/chain are over one corner of the loop. The chain is usually made of steel, so should be detected if the loop is sensitive enough.
The ingenious device to trip the loop detector may be coming just in time to become obsolete. I see more and more intersections have the cameras set up to trip the lights (the technology has gotten a lot cheaper, and they no longer have to dig into the asphalt and lay a wire). I find they are even less likely to work with bikes, since we present such a narrow head-on profile, about the same as a ped crossing the street, and they wouldn't want peds to be able to trip the lights. I have tried placing the bike sideways, but it could be risky if the light changes just as a motor vehicle approaches, having to get the bike straightened out, with the driver wondering why the heck you've got the bike sideways. At night, you cannot trip them by aiming your headlight beam at the camera (I've tried).
Luis