Are photons just electromagnetic waves? I really can't say that. As we know, electromagnetic waves come from changes in electromagnetic fields; therefore, electromagnetic waves typically have different amplitudes to reflect the different changes in electromagnetic fields. One of the most critical questions is: do photons have different amplitudes? Obviously not, which means, photons are not electromagnetic waves.
There is another indicator that photons are not electromagnetic waves. Anyone who has done the secondary quantization of electromagnetic fields knows that it is more complicated than the quantization of other particle fields. Since the electromagnetic field naturally satisfies the Lorenz covariance, there is no reason to be more difficult to quantize it than the wave function of a particle. Actually, this just proves that the electromagnetic field is not a photon quantum field, and Maxwell's equations should not be the object for quantization. Therefore, the quantization of electromagnetic fields is very far-fetched, and the object of quantization should be the photon quantum field.
Then, what's the relationship between photons and electromagnetic waves? Electromagnetic waves are the fluctuations of electromagnetic fields in classical physics, but they have the appearance of photons. So how can the fluctuations of continuous electromagnetic fields become quantized photons? Leaving aside those "beautiful" generation & annihilation operators for photons, what actually happened in the physical process? This question may not have been asked in the early days of quantum mechanics, but it definitely needs to be explored now.
At the beginning of the last century, Hilbert, the famous mathematician who made Einstein jealous, once said "Physics is too hard for physicists" which ridiculed the limited mathematical knowledge of physicists at that time. After that, physicists worked hard to study mathematics, and the requirements for mathematics in physics research became higher and higher. In any case, after Einstein, the requirements of mathematics in physics research are getting higher and higher. This is of course a good thing. The precise description of physical phenomena is inseparable from rigorous mathematical support. However, entering the new century, I personally feel that the influence of mathematics on physics is a bit overcorrected. Many results of physics research in these years can tell that physics is becoming more and more mathematical. Actually, mathematics has made many physicists forget the original intention of physics research.
Back to the above question, what is the physical process of the quantization of electromagnetic waves into photons? The answer to this question may be found in the quantum field theory (QFT), where photons are regarded as excited states of photon quantum fields. Maybe, it's the electromagnetic waves that activates the photon quantum fields. When the electromagnetic wave propagates, it resonates with the photon quantum harmonic oscillator of the same frequency and is activated as photons; the amplitude of the electromagnetic wave is converted into the number of activated photons. The stronger the electromagnetic wave, the more activated photons. From the black body radiation formula to the latest research in quantum mechanics, it has revealed the truth of "vacuum is not empty", and this non-empty vacuum must have something that we don't know about. It is likely to help us reveal how electromagnetic waves are quantized into photons. It should be the most reasonable prediction that the zero-point energy (ZPE) in vacuum is actually the photon quantum harmonic oscillator which represents the ground state of the photon quantum field that can be activated by electromagnetic waves, let us wait and see.
Although Einstein proposed many years ago that there is no need to assume the existence of ether for the propagation of light, quantum field theory tells us that the propagation of light waves may really require a "medium"-a photon quantum field. Seeing these, do you still think that photons are electromagnetic waves?