Example where photon acts only as a wave I've heard photon can act both as a wave and as a particle. In the photoelectric effect it acts as a particle.
Is there any example where photon acts only as a wave?
 A: Interference and diffraction are phenomena where photon exhibits its wave nature purely. Polarization is another phenomenon, where photons act exclusively as waves.
A: Individual photons are fundamental particles, and act as particles, although they behave as quantum particles, not as classical/ macroscopic particles.
A population of many photons with the same energy/frequency/wavelength can be treated as if it is a classical wave - this allows the classical analysis of phenomena such as polarisation, refraction and reflection.
A: It is not true to say that a photon acts in some circumstances as a classical particle and in other circumstances as a classical wave. Rather, it acts in all circumstances like a quantum thing, which is neither a classical point particle nor a classical wave. Having said that, some of the behaviours are reminiscent of classical particles and others are reminiscent of classical waves, and it is good to draw attention to this.
The most direct way to see where the wavelike behaviours arise is to examine interference phenenomena, where each photon has more than one route from a source to a detector. The Young's slits experiment is the standard example. One finds there is a pattern of bright and dark fringes; this pattern is in the probability of arrival of the photons at one place or another. This pattern corresponds precisely to the classical wave optics prediction for such experiments.
A stream of photons will exhibit behaviours that match the classical wave optics most fully when there are many photons and one looks at statistical averages. The classical monochromatic wave, for example, corresponds to a collection of photons with frequencies distributed close to some given frequency, and such that the number of photons is in a superposition state described statistically by a poissonian distribution. Such a state is called a coherent state of the electromagnetic field.
A: There is a misconception in the question, a photon by axiomatic definition in the standard model of particle physics, where it is defined in the table is always a point particle, and its kinematics is tied up with quantum mechanics. In quantum mechanics it is the wave function $Ψ$  whose complex conjugate form $Ψ^*Ψ$ is equal to the probability of seeing a photon at (x,y,z) at time t.
See here how single photons added up with the same boundary conditions end up giving distributions  that show the interference patterns associated with light, electromagnetic waves.



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*Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.


The dots are the individual footprints of photons, and a single photon is never a wave, as it is a point particle. It can be shown mathematically that the classical electromagnetic field with the light waves emerges from the quantum mechanical level of photons, but it needs quantum field theory to follow the proof (example ).
A: A photon, just like an electron, a proton or a molecule is a particle. Its behavior is however statistical, also just like that of an electron, a proton or a molecule. This statistical behavior is described by a wave function. In the case of photons this is the electromagnetic potential. It is this potential or its derivative the electromagnetic field that exhibits the wave behavior including interference. Photons themselves do not exhibit interference nor wave behaviour. They do not have a frequency or a wavelength, unlike their wave function, but they do have energy and momentum.
A: I think the best way to describe the wave-particle duality is to note three things.
First, a "photon" (or any quantum object) behaves like a photon. The labels "wave" and "particle" are given by experimenters but the photon isn't bound by names.
Second, a "photon" behaves like a particle in an experiment designed to measure particle-like properties.
Third, (really part 2-A) a "photon" behaves like a wave in an experiment designed to measure wave-like properties.
A: There is a nice answer by @annav, I would like to add something the other answer do not mention, that is the example of Rayleigh scattering.

Rayleigh scattering (/ˈreɪli/ RAY-lee), named after the nineteenth-century British physicist Lord Rayleigh (John William Strutt),[1] is the predominantly elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the radiation.

https://en.wikipedia.org/wiki/Rayleigh_scattering
Individual photons are quantum objects (and they are defined in the SM as point particles), though, they do build up the classical EM waves that travel from the Sun and scatter on the atoms in our atmosphere. These light waves have a wavelength that is much bigger then the atoms in the atmosphere, but the scattering process itself is wavelength dependent. Blue light has higher frequency and shorter wavelength, thus, those photons of higher energy (blue) scatter with higher probability. This is a beautiful example of how light's wave properties dominate throughout the scattering process and create the colors of our skies.
Your question is about individual photons, and though these are quantum objects, that are defined as point particles in the SM, when they beautifully build up the classical EM waves, and scatter on the atoms in the atmosphere, the wave properties manifest and the wavelength dependency of the process emerges from the fundamental (quantum) properties of the universe.
