Solving paraxial equation (to get cavity modes)

In summary, when analyzing transverse modes in a cavity, the general solutions to the paraxial equation (HG, LG, IG modes) can be used, but for more accurate results, specific solutions for the particular cavity can be obtained by using the dimensions of the cavity as inputs. This can be done by solving the paraxial equation with the boundary conditions of the cavity or by using numerical methods such as finite element analysis.
  • #1
hangainlover
83
0
Hello,

I've been going through some cavity material and attempted analyses regarding transverse modes.

Invariably, they always deal with general solutions of paraxial equation and do not have solutions specific to specific cavities

I do know that general solutions to paraxial equation are HG, LG , IG modes.

What do you do if you want to know what transverse modes you will get for a given cavity a priori? I mean.. cavity specific solutions will depend on dimensions of your cavity. So, shouldn't those dimensions be your inputs ??
 
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  • #2
You can use the dimensions of your cavity to estimate the transverse modes in the cavity. The paraxial equation can be used to calculate the exact transverse modes for a given cavity. To do this, you need to solve the equation for the particular boundary conditions of the cavity. This will give you the exact solutions for the transverse modes in the cavity. Additionally, you can use numerical methods such as finite element analysis to find the transverse modes in a cavity. This method is usually more accurate than solving the paraxial equation.
 

Related to Solving paraxial equation (to get cavity modes)

1. What is the paraxial equation?

The paraxial equation is a mathematical equation that describes the propagation of electromagnetic waves in a paraxial approximation. In other words, it is a simplified version of the wave equation that is valid for waves propagating in a specific direction with small angles of divergence.

2. Why is the paraxial equation important for solving cavity modes?

The paraxial equation is important for solving cavity modes because it allows us to accurately model the behavior of electromagnetic waves in a cavity. By solving this equation, we can determine the resonant frequencies and modes of the cavity, which are crucial for understanding and designing optical devices such as lasers and optical filters.

3. What are cavity modes?

Cavity modes are standing waves that are formed inside an optical cavity, which is an enclosed space between two reflective surfaces. These modes correspond to specific frequencies at which the electromagnetic waves can resonate inside the cavity, creating a stable and amplified output.

4. How is the paraxial equation solved to obtain cavity modes?

To obtain the cavity modes, the paraxial equation is usually solved using numerical methods such as the finite difference method or the finite element method. These methods involve discretizing the equation and solving it iteratively to obtain the eigenvalues and eigenvectors, which correspond to the resonant frequencies and modes of the cavity.

5. What are the practical applications of solving the paraxial equation for cavity modes?

The practical applications of solving the paraxial equation for cavity modes include the design and optimization of various optical devices such as lasers, optical filters, and resonators. It also plays a crucial role in understanding and analyzing the behavior of light in optical systems, which has important applications in telecommunications, imaging, and sensing technologies.

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