Laser Electronics: Solutions for Chapter 6 Problems in 3rd Edition

[hmdsaeedy]

I am study in this term Laser Physics course from engineering book
"Laser Electronics" by "Joseph T. Verdeyen"
and I need the solution for this problem in 3rd edition:
problems in chapter 6(Resonant Optical Cavities):20,13,12

 

[antoker]

I think that everyone is capable of reading fonts in normal size ;) Homework questions should be posted in homework section. Before asking for help we'll need you to show, what were your attempts at a solution.

 

[ravenprp]

Hello! It's great to hear that you are studying Laser Physics and using the book "Laser Electronics" by Joseph T. Verdeyen. I am happy to provide the solutions for the problems in Chapter 6 (Resonant Optical Cavities) in the 3rd edition of the book.

Problem 20:
The problem states that a laser cavity has two mirrors with reflectivities of 99.9% and 99.8%. The separation between the mirrors is 1 cm and the gain medium has a length of 2 cm. The gain coefficient for the medium is 0.1 cm^-1. The question is asking for the round-trip gain and the threshold gain.

Solution:
To find the round-trip gain, we can use the formula G = (1-R1)(1-R2)e^(2αL), where R1 and R2 are the reflectivities of the mirrors, α is the gain coefficient, and L is the length of the gain medium.

Substituting the given values, we get:
G = (1-0.999)(1-0.998)e^(2*0.1*2) = 0.0036

The threshold gain is the minimum gain required for lasing to occur. It can be calculated using the formula Gth = αL/(ln(R1R2)), where R1 and R2 are the reflectivities of the mirrors, α is the gain coefficient, and L is the length of the gain medium.

Substituting the given values, we get:
Gth = 0.1*2/(ln(0.999*0.998)) = 0.0066

Therefore, the round-trip gain is 0.0036 and the threshold gain is 0.0066.

Problem 13:
This problem deals with a laser cavity with two mirrors. The first mirror has a reflectivity of 99.8% and the second mirror has a reflectivity of 99.5%. The separation between the mirrors is 10 cm and the gain medium has a length of 2 cm. The question is asking for the round-trip gain and the threshold gain.

Solution:
Using the same formulas as in Problem 20, we get:
G = (1-0.998)(1-0.995)e^(2*0.1*2) = 0.0003

Gth = 0.1*