could the bend be described mathematically? Not the vector the curvature.
The bend in what? In the path of the light? That's not spacetime curvature; that's just curvature of the light's path. They're not the same thing.
Is there quantum effects at intersection? Not necessarily gravity or time. On the photon.
If you're talking about photons, you're talking about the quantum model of light. However, you don't need the quantum model of light to explain refraction; the classical model, of light as electromagnetic waves obeying Maxwell's Equations, explains refraction just fine.
Separate names with a comma.