Light, aka electromagnetic radiation, is said to have electric and magnetic fields as it propagates thru space. When I hold a 1 Tesla rare earth magnet next to a beam of red laser light, nothing happens. Why?
Maxwell's equations are linear and there is therefore no interaction between magnetic fields. The magnetic field of the dipole magnet satisfies the Maxwell equations. The electromagnetic waves from your laser is another solution. Add them up and the sum of the two solutions is another solution.
So, this suggests that there shouldn't be a deflection. This is not 100% true. The most important effect that does lead to a deflection is the fact that the magnet induces changes in the air that the laser light moves through. Even though the full problem is linear, if you pretend that the medium isn't there, then it is effectivel nonlinear.
But even in a perfect vacuum there are QED effects due to virtual electron positron pairs. The magnet effectively changes the QED vacuum and then the laserlight that moves through it will be deflected. When light enters a region with a magnetic field, then it behaves as if there is an index of fraction. This effect is largest if the light enters the region orthogonal to the magnetic field. The two polarizations states of the light with the magnetic component parallel or orthogonal to the external field have different indices of refraction. That causes the so-called vacuum birefringence effect.