Can photons cast a shadow?

At first glance, the answer seems to be trivially negative. But…

Light is made of photons, a fundamental particle that belongs to the so-called bosons, and that don’t have to respect the Pauli exclusion principle. For this reason, two photons do not interact directly, but simply go through each other. This is why sunlight and our radio waves do not shield each other, but travel undisturbed.

The ability of photons to occupy the same physical quantum state (position, energy, momentum, etc …) also makes it possible to pack lots of them together in a tiny region, the concept behind black holes made of light: Kugelblitz (astrophysics) — Wikipedia

If a photon hits an electron, which in turn hits another photon, then the two photons are indirectly interacting. But there is always another particle to act as an intermediary.

Another possibility is that of a high-energy photon that splits into an electron and a positron, which then unite again. When the photon is split, the particles it produces can interact and deflect other photons. So that, for all intents and purposes, two photons can influence each other.

Below, a drawing I made myself:

Colored in black, the high-energy photon that momentarily splits. In red, photons deflected by the ephemeral particles.

Sure, the likelihood of one or two photons splitting and interacting in the tiny space-time window needed is slim, but not zero.

To answer the question: for a photon to cast a shadow, it must deflect other photons, and although the probability of this happening is minimal, and high-energy photons are required, it is absolutely possible.