CCD measures intensity prop. to z-component of C-Poynting vector OR |E-field|^2

[omg!]

intuitively, i would say that in a CCD, the photoelectrons are being "created" only by the electric field of the incident light, so that the intensity is proportional to
$|E_x|^2+|E_y|^2$,
with the xy-plane coinciding with the CCD plane.
But I have several papers here saying that the intensity is actually proportional to
$(\textbf{E}\times\textbf{B}^*)_z$.
could someone shed some light on why this should be the case? thanks!

 

[chrisbaird]

They both basically mean the same thing. The energy flow due to electrodynamic fields in general is described by the Poynting vector S:

S = E x H

For air, the magnetic field H and the magnetic field B are related according to B = μ₀ H, leading to:

S =(1/μ₀) E x B

The intensity in a certain direction is typically defined as the time-average of the Poynting vector dotted by the direction. For sinusoidal waves, the time-average is found by complex conjugating the magnetic field and multiplying by a half:

I = (<S>_t)_z =(1/2 μ₀) (E x B*)_z

If the wave is a transverse plane wave (not always the case), then the electric field and magnetic field are related according to: B= sqrt(μ₀ε₀) z x E which leads to:

I =(1/2Z₀) |E|²

For a transverse wave, there is no z-component to the electric field, only x and y components, so we have finally:

I =(1/2Z₀)(|E_x|² +|E_y|²)

So your last expression is more general, and your first expression only applies to transverse plane waves.

 

[omg!]

thank you for your clear explanation.

forgive my ignorance, but could you point out an example of a non-transversal EM wave?

i'm trying to calculate the intensity on the CCD resulting from a focused light beam. the two formulas give slightly different values, the more general one has a complex component, do you think one should simply take the real part or the modulus?

 

[chrisbaird]

If you are close enough to light sources, the fields are not necessarily transverse. This is called the near field. Also, light in a waveguide (like a fiber optic) is not necessarily transverse. If you are using the expression I =(1/2 μ₀) (E x B*)_z, then the result should be automatically real-valued only. That is the point of the complex conjugation operation ("*").

 

[PJC01]

I understand your confusion about the relationship between intensity and the z-component of the C-Poynting vector or the squared magnitude of the electric field. At first glance, it may seem more intuitive that the intensity would be directly proportional to the squared magnitude of the electric field, as this is the component responsible for creating the photoelectrons in a CCD. However, the relationship between intensity and the z-component of the C-Poynting vector is actually more complex and can be explained through the principles of electromagnetism.

The C-Poynting vector represents the direction and magnitude of electromagnetic energy flow in a given region. It is calculated by taking the cross product of the electric field and magnetic field vectors at a specific point in space. This means that the z-component of the C-Poynting vector is not solely determined by the electric field, but also takes into account the magnetic field, which is often overlooked in discussions about intensity.

In certain situations, such as when light is polarized, the electric and magnetic fields are perpendicular to each other, and the z-component of the C-Poynting vector will be directly proportional to the squared magnitude of the electric field. However, in more complex scenarios, such as when light is circularly polarized, the z-component of the C-Poynting vector will also take into account the contribution of the magnetic field, resulting in a different relationship with intensity.

Furthermore, in a CCD, the incident light is typically focused onto the surface of the CCD, meaning that the electric and magnetic fields will not necessarily be aligned with the xy-plane of the CCD. This further complicates the relationship between intensity and the z-component of the C-Poynting vector.

In conclusion, the relationship between intensity and the z-component of the C-Poynting vector is not as straightforward as it may seem at first glance. It is important to consider the contributions of both the electric and magnetic fields in order to fully understand this relationship. I hope this explanation sheds some light on why the relationship is more complex than initially thought.