Use Green's Function calculate photonic density of state

In summary, the author is trying to explain how the imaginary part of Green's function can be negative, depending on the dielectric function. The process of calculating the Green's function using the volume-integral method can be difficult to understand, and the author suggests readers look into Landau damping and the Bromwich contour to understand the origin of the imaginary part.
  • #1
Jeffrey Yang
39
0
Hi Everyone:

I think some of you who familiar with quantum-optics know that the local photonic density of state can be calculated by the imaginary part of electromagnetic Green's function.

The Green's function can be further presented by the dipole's mode pattern as

G = E(r)*p0*ε(r)*c^2/ω^2

, where E(r) is the electric field profile, p0 is the dipole moment, ε is the dielectric function, ω is the frequency

You can find these formulas in Lukas' book "Principle of nano-optics"

However, I'm confused by the calculation's process. E(r) contain both the real and imaginary part, and so dose ε. Therefore, the final imaginary part of G will contain the cross-product item.

The dielectric function will have a negative real part if there has metal material. But this will lead a negative imaginary part of Green's function in metal area, as also a "NEGATIVE DENSITY OF STATE"!

Dose this reasonable?
 
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  • #2
Looking at equation 8.111, 8.113, 8.114, I don't see how it could be negative.
However, the track from 8.111 to 8.114 seems a little bit obscure.
IMHO, I think the author tried to avoid handling the singularity from the beginning (near 8.109).
IMHO, solving for the Green function must be done by using the Bromwich coutour properly in order to account for the imaginary part.
(this is similar to the way Landau damping in plasma physics is derived)

My best advice is to read about Landau damping and about the Bromwhich contour.
In this way, you will probably be able to clarify the origin of the imaginary part and see why it is always positive.
(in a stable media)
 
  • #3
maajdl said:
Looking at equation 8.111, 8.113, 8.114, I don't see how it could be negative.
However, the track from 8.111 to 8.114 seems a little bit obscure.
IMHO, I think the author tried to avoid handling the singularity from the beginning (near 8.109).
IMHO, solving for the Green function must be done by using the Bromwich coutour properly in order to account for the imaginary part.
(this is similar to the way Landau damping in plasma physics is derived)

My best advice is to read about Landau damping and about the Bromwhich contour.
In this way, you will probably be able to clarify the origin of the imaginary part and see why it is always positive.
(in a stable media)

Thanks for your comments

My problem came from equation 16.29 which use the volume-integral method to calculate Green's Function. In this method, the system's Green's Function can be linked to the electric mode excited by a electric dipole. However, the dielectric function can be negative, if there is a metal material, and finally you will get a negative imaginary part of Green's function.

Of course, these negative imaginary part of Green's function will only exist in the region of metal.
Photonic density of state is negative in metal??
 
Last edited:

FAQ: Use Green's Function calculate photonic density of state

What is the purpose of using Green's Function to calculate the photonic density of state?

Green's Function is a mathematical tool that helps us understand the behavior of waves in a given system. By using it to calculate the photonic density of state, we can gain insight into the distribution of electromagnetic modes in a particular material or structure.

How does Green's Function differ from other methods of calculating the photonic density of state?

Unlike other methods, which often require complex simulations or assumptions about the system, Green's Function provides a more direct and accurate approach to calculating the photonic density of state. It takes into account the specific properties and geometry of the system, making it a more reliable tool.

Can Green's Function be used for any type of material or structure?

Yes, Green's Function can be applied to any system that exhibits wave-like behavior, including photonic crystals, metamaterials, and even biological systems. However, the level of complexity and accuracy of the calculations may vary depending on the specific system.

How does the photonic density of state affect the properties of a material or structure?

The photonic density of state plays a crucial role in determining the optical properties of a material or structure. It affects phenomena such as light absorption, emission, and scattering, and can also impact the performance of devices such as solar cells, lasers, and photodetectors.

Are there any limitations to using Green's Function to calculate the photonic density of state?

While Green's Function is a powerful tool, its use may be limited by the complexity of the system being studied. In some cases, it may be necessary to use approximations or combine it with other methods to accurately calculate the photonic density of state. Additionally, experimental measurements are often needed to validate the results obtained from Green's Function calculations.

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