Hi Hossein:

That's a pretty detailed and well thought out question/evaluation.  I don't have time to go into all my thoughts on the subject, but it might give you some insight to drop your frequency a few orders of magnitude.  At RF and microwave frequencies, the same conceptual rules apply in terms of dielectric and magnetic properties, but the "photon" like behavior can generally be ignored.  At these frequencies, you can much more easily think of the electron (and to a lesser extent, atomic core) interactions with a quasi-static electromagnetic field.  It is easy to envision the electronic "drag" that a wave would have as it attempted to accelerate/decelerate electrons in the medium.  The net effect would generally be a transfer of energy from a leading edge of a wave front to a trailing edge of a wave front (in my Ph.D. dissertation I actually demonstrated that electrons on the Fermi surface of a metal could transfer energy forward or backwards in an acoustic wave, since the electron moved faster than the wave, thereby speeding or slowing it, depending on the orbit diameters due to an applied magnetic field; i.e. the magneto-acoustic effect.  Anyway, back to EM waves!).  

A more macroscopic way of looking at the problem at these frequencies is just capacitively and inductively.  Essentially you're charging a capacitor and/or inductor and releasing the energy a bit later.  

Dear Hossein,

Probably, it is impossible to answer your question better than it did Richard Feynman in his course of lectures on physics: Richard P. Feynman, Robert B. Leighton, Matthew Sands. The Feynman Lectures on Physics, Addison-Wesley Publishing Company, Inc. Reading, Massachusetts, Palo Alto, London, 1963 (vol. 1, chapter 31-1).

In particular, Feynman writes that " It is approximately true that light or any electrical wave does appear to travel at the speed c/n through a material whose index of refraction is n… Our problem is to understand how the apparently slower velocity comes about”.

Therefore, I advise you to refer to this source:

http://selfdefinition.org/science/25-greatest-science-books-of-all-time/20.%20Feynman%20et%20al.%20-%20The%20Feynman%20Lectures%20on%20Physics%20Volumes%201%20-%203%20(1963).pdf

Best regards, Leonid A. Skvortsov

Have a look at this paper  which explains how photons propagate : A. Vatarescu, “Photonic coupling between quadrature states of light in a homogeneous and optically linear dielectric medium,” J. Opt. Soc. Am. B 31, 1741–1745 (2014).

Some great answers already but I would just add a simple way to think about it. Light is an electromagnetic wave. The speed of propagation of the wave is where c is c2=1/uo eo. In a dielectric material the local value is eo is modified and the speed of propagation is changed. 

Dear Hossein,

In order to give an appropriate answer to this question, we have to know what matter is and how it works and we have to know what a photon is and how it works. The book in the 3rd attachment provides this information. The text below gives brief statements on matter and photons, but please review the book for further understanding of these statements. After this, a few statements are given to conceptually explain why the velocity of a photon may decrease as it passes through matter; but please review the book for further understanding of this presentation. The 1st and 2nd attachments are excerpted from the book for your convenience.

MATTER:  Per Figure 2, in any of the three attachments, a view of the electron is given; it shows photon fibers combining to form two half cylindrical B-fields, which together is an electron. Thus, electrons are tiny fields, not hard particles. The two half fields oscillate inward and outward along their common z-axis. The reason why fibers (photons) combine to form a cylindrical B-field is given by Maxwell’s equations; please see the 2nd or 3rd attachment for the electron’s derivation. This tiny field has both particle and wave characteristics. The construction of other particles, such as protons and neutrons, consist of cylindrical B-fields also, similar to the electron. See Section 4 in the book for example. Thus, all matter is a compilation of cylindrical B-fields, which consist of oscillating and twirling photon fibers. Explanation of the photon fiber is given in the next paragraph. The charge of an electron is negative because its circumferential B-field is left-handed, while that of the proton is right-handed. A neutron has no charge because it consists of a mixture of left-handed and right-handed twirling fibers.

PHOTONS:  Figure 1, in any of the three attachments, provides a view of the photon fiber, which is also called heat fiber sometimes. The energy of a photon (heat fiber), given by Planck’s law E = hν, arises from its light-speed oscillatory motion along its length and about its origin (which is at its mid-length), rather than its translational motion. Its oscillatory motion is perpendicular to its translation; thus, a waveform develops as it translate. Hence, light and radiation, in general, are not waves but are photon fibers that translate in a waveform. See Figure 10 in Section 6 of the book to see how an electromagnetic wave is formed when the fiber translates. Per Figure 1, perpendicular elements develop along the fiber length, due to Lorentz length contraction, as it oscillates back and forth at light-like speed along its length. These perpendicular elements give its B-field as it twirls about its origin. The energy given by the fiber oscillation is related to its oscillation range or stroke; shorter strokes yield shorter wavelengths and higher frequencies, and thus greater energies. The fiber energy hν is the limit of the external work that may be performed by a fiber during an interaction with a system or the internal energy contribution, the fiber gives to a macroscopic body, of which it is part of. The fiber’s intrinsic perpetual oscillating motion gives rise to the laws of energy conservation; that is, without such motion, energy would not be conserved in any process.

PHOTON   FIBER   INTERACTION  WITH  MATTER  (ATOMIC  PARTICLES): As a incoming photon fiber interacts with matter’s atomic particles (which are tiny cylindrical B-fields consisting of photon fibers as explained above), it will either be admitted into the medium, be repelled by the medium, or pass through the medium. The reason why incoming fibers (photons) undergo one of these reactions with matter is given by Maxwell’s equations, which is the same mechanism that gives the formation of matter. Please see the 2nd or 3rd attachment for the electron’s derivation. To gain admission into one of the B-fields of matter, the rotational direction of the incoming photon fiber has to be the same as those fibers in the portion of the B-field it is interacting with, and also be fairly resonant with these fibers; one example is the oscillation ranges of the fibers should be nearly the same. When the incoming photon fiber interacts with a fiber(s) in one of the B-fields of matter that has opposite rotational direction, then it will be repelled and reflected from the medium, unless it is intercepted by another fiber in the medium that is resonant with it. When the incoming photon fiber passes through the medium, its velocity will decrease due to net attractive forces between such fiber and the nearby photon fibers of the B-fields of the medium, which it passes. The sum of the net instantaneous forces is attractive because the photon fiber passing through will do so nearer the attractive fibers of the B-fields than those that are repulsive to it.

 We hope this helps; please let me know if you have any comments

 Regards,

Dan S. Correnti

Article UNVEILING of the ELECTRON (Post #1) [A Proposed Electron Structure]

Article DERIVATION of the ELECTRON (Post #2)

Book New Physics Framework (Post 5.1)

The slowing of photons occurs through coupling of modes of vibration, electronic excitation, or other types which are excited by the E-field through their attendant polarization.  This polarization then re-radiates back into the E-field.  Overall, the effects are governed by conservation of energy and k-vector or momentum. For optical phonons, as an instance, the strength of the coupling is governed by the Faust-Henry constant.

Well, there are many treatments with varying complexity and depth to answer your questions. We will avoid quantizing the Electromagnetic field and rather treat the problem classically.

If we model each atom as a simple harmonic oscillator, the electric field will induce a force to separate the positive and negative charge apart where there also exist a counteracting coulomb restoring force . Now because electric field can drive and oscillate a charge, an oscillating charge can generate an electric field (Maxwell Equations). Depending on the frequency of the driving EM field and the system resonance frequency, the generated wave may lead or lag. If you are comfortable with LC circuit, the analogy still applies. (More about this here https://en.wikipedia.org/wiki/Harmonic_oscillator).

Now if you have a volume of these dipole scatterers dancing within the driving electric field and generating their own, the total EM field in the volume will be the superposition (interference) of the incident field + sum(all dipoles scattered fields). This process collectively will define the wavefronts and it is speed (phase velocity). The microscopic process is still governed by the speed of causality (c), but the macroscopic total wave tends to look slower/faster.

Two important things. One: there is nothing special about the speed of light. c fundamentally is the speed of causality and photons happen to travel at that speed (Nice video by PBS https://www.youtube.com/watch?v=msVuCEs8Ydo). You have also mentioned that “Material is mostly empty, the light will still travel with c in the empty spacing”. Although volume-wise it is true, the scattering cross section between electron and EM field is much larger than the geometrical cross section. (more about this here https://en.wikipedia.org/wiki/Cross_section_(physics))

For your question about absorption-emission process. The process is indeed quantized, but you still have broadening in absorption due to many reasons (Doppler broadening. Pressure broadening, etc ). Even In its simplest form, a single electron in only two allowed energy states separated by E, you will still have broadening in absorption around E to satisfy the Heisenberg uncertainty principle: that is delta E * delta t

There are number of thoughts that clerify discusson made by Dr. Hossein Jafarzadeh

However, in my opinion when an electromagnetic field incident on any material, it produces oscillations in the system. These oscillations are due to interaction of EM wave with material and produces polarization in accordance with ε = ε0 + P/E. As can be seen with that effect permittivity of material changes. Slow down of phase velocity in material comes due to response time of polarized material against incident wave. That is the reason for different value of permittivity that will lead to different phase velocity in the material. It also should be noted that any perturbation in the material may cause back-forth motion of wave and it may again increase the slow light effect in the material. However, it will be only valid for certain wavelength range that participate in that back-forth phenomenon.