Yes they do couple directly. It's called two-photon physics. SLAC have done the experiments. And go and read
Light bends itself into an arc. What do you think's going to happen if that arc is so very curved that it forms a closed path?
a) Because we know two-photon physics, we know
extremely precisely that there is no light-light bound state. Go ahead, work it out. I'll wait. According to the laws of photon-photon interactions, write down the binding energy of a photon-photon bound state.
There is no bound state.
In ordinary, nonrelativistic QM, there's is a standard (advanced) undergrad homework problem: find the ground state energy of an electron bound to a spherically-symmetric "square well" of finite depth. For shallow wells,
there is no bound state. None. Zero. An electron can scatter off such a well, but never stick to it. Go ahead, learn QM and see for yourself. I'll wait.
Same with neutrinos. Neutrinos can scatter off one another---indeed, the weak force provides an
attractive potential---but there's no neutrino-neutrino bound state.
I repeat:
there is no light-light bound state. If you want to invent one, you're going to have to
throw out the "two photon physics" you keep citing, because that physics tells you you're wrong.
b) You have misunderstood the "arc" paper to an absolutely comical extent. There is no light-light scattering in this paper; it's just a cleverly-constructed set of ordinary, noninteracting waves.
ETA:
http://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.108.163901 said:
These beams are the full vector solutions of Maxwell’s equation for shape-preserving accelerating beams. Moreover, in their scalar form, these beams are the exact solutions for nondispersive accelerating wave packets of the simple and most common wave equation describing time-harmonic waves. As such, the work pre- sented in this Letter has profound implications to almost any linear wave system in nature, ranging from sound waves and surface waves in fluids to many kinds of clas- sical waves. In this spirit, it is now clear that the phenome- non of accelerating waves is not the result of a specific unusual behavior of the Schro ̈dinger equation (which is equivalent to the paraxial wave equation), as one may think from reading the first paper pioneering this subject [17].
My bold. There's no light-light scattering (a nonlinear and non-Maxwell's equation phenomenon) in this paper.