Solving coupled wave equations

In summary, the conversation discusses difficulties understanding the solution to parametric amplifiers, specifically the undepleted pump wave and linear absorption equations. The conversation also notes a typo in equation 2.7 and 2.8 and expresses confusion about the transition from equation 2.8 to 2.9. A suggestion is made to use X = \Gamma + α+ to aid in the calculation.
  • #1
linfocus
1
0
1.
Just going through some material about parametric amplifiers but I have difficulties to see where the solution comes in given text.

In equations it is assumed undepleted pump wave and in equations there is loss caused by linear absorption for signal and idler.


2.
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p.s. There is a typo on the equation 2.7. With alpha and gamma it should be i instead of s. And in equation 2.8 the matrix element on the left and down should be E_p* instead of just E_p.


3.
For some reason I just don't get it how get from 2.8 to 2.9. Till 2.8 it was all clear. This is just bugging me badly.
 
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  • #2
welcome to pf!

hi linfocus! welcome to pf! :smile:

the vector in (2.8) is general, so the matrix must be 0, so its determinant must be 0 :wink:

(writing X = [itex]\Gamma[/itex] + α+ may help in the calculation)
 

1. What are coupled wave equations?

Coupled wave equations are a set of mathematical equations that describe the behavior of two or more interacting waves. They are used in various fields, including physics, engineering, and mathematics, to model and understand complex wave phenomena.

2. How do you solve coupled wave equations?

There are various methods for solving coupled wave equations, depending on the specific equations and boundary conditions. Some common techniques include separation of variables, Fourier transforms, and numerical methods such as finite difference or finite element methods.

3. What is the significance of solving coupled wave equations?

Solving coupled wave equations can provide valuable insights into the behavior of complex wave systems, such as the interactions between different types of waves or the propagation of waves in a particular medium. This information can be applied in many practical applications, such as designing efficient communication systems or understanding the behavior of natural phenomena like earthquakes and ocean waves.

4. What are the challenges of solving coupled wave equations?

One of the main challenges in solving coupled wave equations is the complexity of the equations themselves, which often require advanced mathematical techniques to solve. In addition, accurately modeling real-world systems can be difficult due to the presence of external factors such as non-linearities, damping, and environmental variability.

5. What are some examples of coupled wave equations in real-life applications?

Coupled wave equations can be found in various fields, including optics, acoustics, electromagnetics, and fluid dynamics. For example, the behavior of light waves in optical fibers can be described by coupled wave equations, as well as the propagation of seismic waves in the Earth's crust. They are also used in modeling the interactions between different types of waves in complex systems, such as the ocean or the atmosphere.

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