As predicted by Huygens' principle it seems obvious that light can produce light. Is it true or I have a misconception?
I asked this question because what I have learnt till now is that light can only be produced by accelerated charges but Huygens' principle gives whole different concepts. It says that each point of wavefront can behave as source for new wavelets. It means light can produce light. Is it so?
No. The most reasonable way to think about what it means to “produce” light is to consider “production” to be the transformation of some other form of energy into light energy. Thus the kinetic and electrostatic potential energy of an excited electron in an atom does produce light, but light does not produce light. Huygens' principle helps explain how light propagates, not how it is produced. When light propagates in space, its energy just moves around; no additional light energy gets created.
No. Fundamentally, for light to be able to produce light, photons should couple to photons. In QED, there is no such interaction. In other words, a photon is not electrically charged. So, there is no Feynman vertex where a photon can decay into two or more photons. So, there is no process in which light can produce more light by itself.
That said, there are loop diagrams where, effectively, it would look like $n_1$ photons scatter into $n_2$ photons where $n_1$ may or may not be the same as $n_2$. (See this famous box diagram where two photons scatter into two photons in a one-loop process.) If one wishes, one can say that in this scenario, effectively, the light produced more light. (Of course, the momentum and energy would be conserved!) However, notice that fundamentally, light didn't produce more light "by itself". The loop processes involve the decay of a photon into an electron-positron pair and there still isn't any direct interaction between a photon and a photon.
