Fabry-Perot Laser Homework: Explaining Steady State Oscillation

[zak8000]

Homework Statement

Consider a Fabry-Perot laser, length 0.1m, with an unsaturated gain coefficient, [itex]\gamma_o[/itex]=1m^-1

one of the mirrors of the Fabry-Perot cavity is perfectly reflecting, the other reflects 95% of the light and transmits 5%. wit the aid of a brief calculation explain why steady state laser oscillation is expected?

i had no idea on how to approach this question so i did some research and i found this book kind of helpful under this link:
http://books.google.co.nz/books?id=...rip gain greater than round trip loss&f=false

Homework Equations

after reading a chapter in the book the steady state condition is R1R2exp(2aL-j2wL/c)=1

The Attempt at a Solution

since i am not given any frequency value i only solved the condition for the round trip amplitude coefficent and the way i calculated it was R1R2exp(2aL)=1 --->0.95exp(2*1*0.1)=1.15
please help i cam confused on how to prove this

 

[mark726]

To approach this problem, we can use the concept of round-trip gain and loss in a Fabry-Perot laser. The round-trip gain is the total gain experienced by the light as it travels back and forth between the two mirrors of the cavity, while the round-trip loss is the total loss experienced by the light.

In this case, the round-trip gain is given by the unsaturated gain coefficient, \gammao=1m-1, multiplied by the length of the cavity, which is 0.1m. This gives us a round-trip gain of 0.1m-1.

The round-trip loss is equal to the product of the reflectivities of the two mirrors, which are 100% and 95% respectively. This gives us a round-trip loss of 0.95*0.05 = 0.0475.

To have steady state laser oscillation, the round-trip gain must be greater than the round-trip loss. In this case, 0.1m-1 > 0.0475, which means that the gain is indeed greater than the loss and steady state laser oscillation is expected.

To prove this mathematically, we can use the steady state condition for laser oscillation: R1R2exp(2aL-j2wL/c)=1. Since we are not given a specific frequency, we can ignore the term j2wL/c and solve for the round-trip amplitude coefficient, which is the product of the reflectivities of the two mirrors. This gives us the equation R1R2exp(2aL)=1.

Substituting the values we have calculated for the round-trip gain and loss, we get R1R2exp(2*0.1m-1)=1.15. This value is greater than 1, which means that the gain is indeed greater than the loss and steady state laser oscillation is expected.

In conclusion, the Fabry-Perot laser described in the problem has a round-trip gain that is greater than the round-trip loss, which means that steady state laser oscillation is expected.