Quantum theoretical approach basis on notion of PHOTON , which is an elementary unit of electromagnetic radiation. This notion has been invented by M. Planck and enabled A. Einstein to explain  photo-effect phenomenon. Now a day the quantum theory of radiation is fundamental approach to the modern theoretical physics.

For reading I recommend the following:

Quantum Statistical Properties of Radiation by W.H. LOUISELL.

Ed. John Wiley & Sons 

You need to narrow the question. You meant light propagation in free space or in presence of a light-guiding structure? Nonlinearity of medium which light passes is another important issue as well as light interaction with the medium.

Fourier optics is a powerful and intuitive alternative to ray optics and naturally handles light propagation through both conventional and diffractive optical elements.  An excellent reference is

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005)

Like ray optics, Fourier optics works in the paraxial approximation, which means that it treats the electromagnetic field as a scalar function.  The payoff for this loss of generality is comparatively straightforward computation.

The Debye-Wolf-Richards integral formalism is useful for a fully vectorial treatment of light propagation.  The relevant integrals typically have to be worked out numerically.  A very effective framework for these computations is the finite-difference time domain (FDTD) algorithm.

Quantum phenomena of light considering light as a particle i.e photon so the distribution of energy of photons might be helpful to represent the images....

it might be helpful to you

ftp://ftp.cordis.europa.eu/pub/ist/docs/fet/qip2-eu-32.pdf

Dear Vladimir,

I agree with David : Fourier optics is a powerfull mean to describe light propagation, available for free space, guided propagation and image propagation throught optical components like lens, prism and others.

I recommend the McLeod Research Group web site which introduce several approaches for light propagation :

http://ecee.colorado.edu/~mcleod/index.html

and more specifically the Teaching pages.

Regards,

Francois

Fourier optics is not only limited to the paraxial approximation. It can be used exactly in completely non-paraxial regimes. In a linear isotropic homogenous medium with no free charges, the scalar wave equation is exact, one only needs to performed for each polarization component.

The approximation comes from the initial conditions imposed on the electric fiedl: e.g. the divergence of the field is zero, thus for linearly polarized light (e.g. Ex0, Ey=0) then there must be a component of the electric field in the longitudinal direction (i.e. Ez0), but this term is normally neglected. This only becomes apparent when focusing tightly because the intensity distribution cannot be fully described by the singe Ex component of the electric field since the Ez component will be significant.

For anisotropic medium, the scalar equation can also be used but its a little more complicated.

When free charges are included, inhomogenous or nonlinear medium are considered, coupling between polarization components are requried, and the 'standard' Maxwell's wave equation is not valid because one is required to take into account the gradient of the material properties (see Born and Wolf, principles of optics).

At high intensities, the magnetic field component is important, introducing more nonlinear corrections. Constrained geometry also changes the situation (e.g. waveguides).

A truly alternative approach, which in some special case may be advantageous, is to solve Maxwells equations in the time domain. I^m not an expert in this, and to my best knowledge there is no standard reference to this approach, but I know a person, who has deveöpped an interest in it: Rudolf Morf ([email protected]).

Approach that a corpuscle of light is combination of 3D matter-core surrounded by distorted region in universal medium may be of interest to you. Check out http://vixra.org/abs/1312.0130 

Nainan

Still in the ray domain, but instead of Snell's law you can use the codington equations

Similar to this but in time domain, you may use Fresnel principle of least time

Wavefront propagation

Fourier optics

Gaussian propagation algorithms (related to Fourier optics)

Monte Carlo Green's function formalism for the propagation of partially coherent light

Transfer Matrices

Hi,

There is no short answer, but a good starting point to learn how a light wave (or any EM wave) works is in Post #4 on this site.  This much can be said here: a light wave is a fiber (photon) that oscillates up and down perpendicular to its direction of travel. The two movements (oscillation and translation) gives the waveform derived by Maxwell. I hope this helps.

Regards,

Dan S. Correnti

Please check if these are of any use. http://vixra.org/abs/1312.0130 and http://vixra.org/abs/1103.0026 

Nainan

This may or may not be of interest. We have developed a new form of illusionary space called Vision-Space. The space that occurs to us within the phenomenon of vision. This includes a field potential that's set out radially when we either make a fixation or centre it on ourselves. The point being that it has nothing to do with the fundamentals of optics. The irritating thing for physics is that this field structure is generating proximity cues that relate to the real distances between objects and surfaces in the environment. So the field structure is provisioning an implicit form of spatial awareness even on a monocular basis (this is quite wrongly referred to a 'peripheral vision'). Nothing to do with 'depth' perception through occlusion or perspective cues. Vision is actually entirely non-photographically rendered. I attach a list of presentations.  Why is this of interest here? Because this field structure appears to derived from information in noise. We appear to be unfolding a data potential from noise that's emanating from the environment. A form of decoherence at the retina with the pays element being preserved and streamed? A function for rods at photopic levels working with ipRGC on something other than light intensity? Environmental signal in radiance? There are articles on my page. "Having the courage of your perceptions" attempts to cover the physics angle.