Derive expressions for the resonant frequencies of these Planar mirror resonators

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  • #1
Marco Oliveira
1
0
Homework Statement
Derive expressions for the resonance frequencies and their frequency spacing for the three-mirror ring and the four-mirror ring bow-tie resonator shown below. Assume that each mirror reflection introduces a phase shift of π.
Relevant Equations
Resonator
I was trying to do the exercise from Saleh's book, but I had some doubts. Any tips on how to resolve it?

My partial solution for the three-mirror ring:

For constructive interference to occur, the total phase accumulated in a round trip must be an integer multiple of 2π. Let's denote the phase accumulated in each arm as ϕ. We have: ϕ + ϕ + ϕ = 2πn, where n is an integer representing the mode number. Since ϕ = π, then: 3π=2πn.

Now i don't know what to do.
resonator.png
 
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  • #2
Marco Oliveira said:
Since ϕ = π,
Only if d=0.
 

Related to Derive expressions for the resonant frequencies of these Planar mirror resonators

1. What is a Planar Mirror Resonator?

A Planar Mirror Resonator is a type of optical resonator that uses two parallel mirrors to trap light waves between them. This creates a standing wave pattern, allowing for the amplification and filtering of specific frequencies of light.

2. Why is it important to derive expressions for the resonant frequencies of Planar Mirror Resonators?

Deriving expressions for the resonant frequencies of Planar Mirror Resonators allows us to understand and predict the behavior of these devices. This information is crucial for designing and optimizing resonators for specific applications.

3. How do you derive expressions for the resonant frequencies of Planar Mirror Resonators?

The resonant frequencies of Planar Mirror Resonators can be derived using the boundary conditions of the electromagnetic wave equation and the properties of the mirrors, such as their reflectivity and spacing. This results in a set of equations that can be solved to determine the resonant frequencies.

4. What factors affect the resonant frequencies of Planar Mirror Resonators?

The resonant frequencies of Planar Mirror Resonators are affected by the reflectivity of the mirrors, the distance between the mirrors, and the refractive index of the medium between the mirrors. Additionally, any changes in these factors can also affect the resonant frequencies.

5. Can the resonant frequencies of Planar Mirror Resonators be tuned?

Yes, the resonant frequencies of Planar Mirror Resonators can be tuned by adjusting the properties of the mirrors, such as their reflectivity or spacing. This allows for the customization of resonators for specific applications.

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