Why don't you accept explanations based on Maxwell wave theory? A photon is both a particle and a wave. Maxwell wave theory applies to photons directly. Here is a brief explanation from Wikipedia:

At the microscale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the electric susceptibility of the medium. (Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility.) As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency. The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with a phase delay, as the charges may move out of phase with the force driving them (see sinusoidally driven harmonic oscillator). The light wave traveling in the medium is the macroscopic superposition (sum) of all such contributions in the material: the original wave plus the waves radiated by all the moving charges. This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies (see scattering) [http://en.wikipedia.org/wiki/Refractive_index#Microscopic_explanation].

Thanks for your answer. 

I didn't said that''I don't accept answers based on Maxwell wave theory''. 

I just said that I am looking for explanations which answer the question without maxwell theory. I was wondered if there is any other explanation or not. An explanation which is easy to imagine and 

This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. I did not understand clearly with this line. Is It mean the amplitude because the frequency is inversely proportional to wavelength? If the frequency is same, how the wavelength be shorter ? Please explain.

 Dear harish

What you said is a macroscopic explanation of what happens microscopically. But here the question is that what is the mechanical of this effect in microscopically scales.

I think it is all based on how the objects (cristals or liquids or whatever) modify the impedance of the vacuum. It Is the vacuum which drives the electromagnetic waves, not materials, unlike what we are brought to think, since vacuum is 99,9% of the volume of any atom.

Whilst I agree with Alexander's original comment (perfectly valid classical explanation for refraction..... why do you want the microscopic one).. I would suggest you pick up R. P. Feynamn's QED: A strange theory of light and matter.  This is a very short book explaining QED as only Feynman could.  I beliieve that videos of this 4-part lecture given in New Zealand should be available for free online. 

In there Feynman gives exactly what you are looking for.  A microscopic description of light bending or reflecting off surfaces that is ``intuitive''.

I've answered this question in a paper published in OSA in 2017. You can find it in the following link Article Analytical and graphical ray-tracing techniques based on a c...

This answer is classical.

Good-luck

Hassan Elagha