Proving Vector Potential Pump Amplitude-Intensity Relationship

In summary, the relationship between the dimensionless amplitude a of a wave and the intensity I of the wave is given by I = c*B^2 / (magnetic permeability of free space), where B is the magnetic field and A is defined as [mass of electron * c / e ]*a*e^[i*(kx-wt)], with k as the wavenumber given by 2pi / wavelength of laser. The hint suggests taking the divergence of A to find a unique solution for B, but the specific method is not specified.
  • #1
cetmoimonsieur
2
0

Homework Statement


Prove that the relationship between the dimensionless amplitude a of a wave and the intensity I of the wave is given by:

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Homework Equations


B = curl (A)
B: Magnetic Field
A = [mass of electron * c / e ]*a*e^[i*(kx-wt)]
where k is the wavenumber and is given by: 2pi / wavelength of laser
I = c*B^2 / (magnetic permeability of free space)
Hint: div(A) = 0 will give a unique solution for B

The Attempt at a Solution


Honestly I do not know where to begin. Take the divergence of the equation of A and find a solution for B? I am not sure.
 
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  • #2
Sorry to bump this thread, but does anyone have an idea?
 

Related to Proving Vector Potential Pump Amplitude-Intensity Relationship

What is a vector potential pump amplitude-intensity relationship?

A vector potential pump amplitude-intensity relationship refers to the mathematical relationship between the amplitude of a vector potential and the resulting intensity of a pump laser.

Why is it important to prove this relationship?

Proving this relationship is important because it helps to understand the behavior of vector potentials and how they affect the intensity of a pump laser. This information can be useful in various fields such as optics, materials science, and quantum mechanics.

How is the vector potential pump amplitude-intensity relationship measured and verified?

The relationship can be measured and verified experimentally by using a pump laser and measuring the resulting intensity at different vector potential amplitudes. The data can then be analyzed and compared to the predicted relationship from mathematical models.

What factors can affect the vector potential pump amplitude-intensity relationship?

The relationship can be affected by various factors such as the properties of the material being pumped, the wavelength of the pump laser, and the angle of incidence. It is important to consider these factors when studying and verifying the relationship.

What are the potential applications of understanding the vector potential pump amplitude-intensity relationship?

Understanding this relationship can have applications in various fields such as laser technology, materials science, and quantum computing. It can also help in developing more efficient and precise laser systems for industrial and medical purposes.

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