Finding Total Number of Optical Field Modes for Visible Light

In summary, the conversation discusses the equation ρ_kdk = k^2/π^2 dk, which represents the density of field modes. By rearranging the equation, ρ_λdλ = 8π/λ^4dλ, the number of modes per volume for frequencies between λ and λ+dλ can be calculated. To find the number of optical field modes per unit volume for a given frequency range, integration is necessary. The result of the integration is 1.06x10^20, which represents the number of modes for a specific range of frequencies.
  • #1
freddie123
2
0
Homework Statement
Calculate the total number of optical field modes per unit volume for visible light (i.e. in the range 400-700nm).
Relevant Equations
ρ_kdk = k^2/π^2 dk
k=2π/λ
ρ_kdk = k^2/π^2 dk is the density of field modes (what we are trying to solve for here), and as ρ_kdk = ρ_λdλ, and k=2π/λ, we can rearrange this to get ρ_λdλ = 8π/λ^4dλ
This is where my confusion lies. I am not sure what to do next. I know this equation physically means the number of modes per volume for frequencies between λ and λ+dλ, so do we just take λ as 400nm and then dλ is 300nm? Or are we meant to integrate to get
-8π/3[(1/(700x10^-9)^3 - 1/(400x10^-9)^3)] = 1.06x10^20 number of modes??

I don't know how to use this equation to get the number of optical field modes per unit volume for the given frequency range.

Help would be much appreciated.

Thanks!
 
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  • #2
Yes, you need to integrate. Your result appears correct.
 
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Likes freddie123
  • #3
DrClaude said:
Yes, you need to integrate. Your result appears correct.
Awesome. Thank you! ☺️
 

1. What is the definition of optical field modes?

Optical field modes refer to the different possible configurations of the electromagnetic field in a given space, which can be described by different frequencies, polarizations, and spatial patterns.

2. How is the total number of optical field modes for visible light calculated?

The total number of optical field modes for visible light can be calculated using the formula: N = (2L+1)^2, where L is the maximum angular momentum of the light and N represents the total number of modes.

3. What is the significance of finding the total number of optical field modes for visible light?

Finding the total number of optical field modes for visible light is important in understanding the behavior and properties of light in different environments. It can also aid in the design and optimization of optical devices and systems.

4. How does the total number of optical field modes for visible light vary with different wavelengths?

The total number of optical field modes for visible light increases with shorter wavelengths. This is because shorter wavelengths have higher frequencies, which results in a larger number of possible configurations of the electromagnetic field.

5. Can the total number of optical field modes for visible light be experimentally measured?

Yes, the total number of optical field modes for visible light can be experimentally measured using techniques such as Fourier transform spectroscopy or Fabry-Perot interferometry.

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