Effective Photon Wavelength of an Incident Wave?

[RuthlessOptimism]

Hello,

 

I have a problem where I have a 1 dimensional Finite Difference Time Domain program simulating an electromagnetic wave, classically using Maxwell's Equations and the Yee Algorithm. What I would like to do is define an "effective" photon wavelength at every grid point (I don't know if it even makes sense to do so). The way I am trying to do this is;

 

1.) I have the electric and magnetic field magnitudes at every grid point: Ex, Hy (the simulation is Transverse Magnetic).

2.) I calculate the energy density of the wave at each grid point: EnergyDensity = ((Ex^2)+(Hy^2))/2

3.) I multiply the energy density by my spatial unit step cubed to get the total energy at each grid point: EnergyTotal = EnergyDensity*(Delta_z^3)

4.) Since E = h*f, and c/f = wavelength I calculate the effective incident photon wavelength as: Wavelength = c/(EnergyTotal/h) .

 

where c is the local speed of light.

 

This gives me values of wavelength in the range of (9.22x10^9) meters. Which is obviously wrong.

 

So my question is how do you take a classical electromagnetic wave and then "chop" / or portion it into photons so that you get the correct number of them with the correct wavelength and frequency? Is that even possible?

 

Thank you.

[Sensei]

I would start from checking units whether they match.

Electric field is in Volts/m,

Energy density is in J/m^3,

etc. etc.

[RuthlessOptimism]

Well after doing some reading I finally found out how to correctly calculate the energy of an EM wave, its: EnergyDensity = {[(epsilon)*E*E]+[(mu)*H*H]}/2 . But this doesn't solve the additional part of my question. I can use this to define an "effective" photon wavelength, but what doing that does is say that there is basically one photon within that volume. If the volume is extremely small that is probably ok. But how do I even try to attempt to correct for the possibility of having multiple photons in that unit volume if it is large?