What is the stability criteria of a laser cavity?
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Stability Criteria of a Laser Cavity
The stability of a laser cavity, often referred to as a resonator, is crucial for sustained lasing operation. It determines whether the light is confined effectively within the cavity to allow for amplification, or if it diverges and gets lost over successive round trips.
Defining the Stability Parameter
The generic stability condition of a laser resonator relies on the configuration of the cavity mirrors. A laser cavity typically consists of two mirrors facing each other at a distance 'L', with the curvatures \(R_1\) and \(R_2\). The stability criterion is expressed using the 'g-parameters', where:
g1 = 1 - (L / R1)
g2 = 1 - (L / R2)
The product of these parameters, g1*g2, yields the stability condition for the cavity.
Stability Regions
A laser cavity is stable if the following inequality is met:
0 <= g1*g2 <= 1
The stability condition can be visualized on a 'g-g' diagram where the stable and unstable regions are demarcated. The stability criteria divide the operating regimes of a laser cavity into four regions:
| Condition | g1*g2 Value | Stability |
|---|---|---|
| Both radii of curvature positive (converging) | 0 < g1*g2 <= 1 | Stable |
| One radius of curvature positive, one negative (diverging) | g1*g2 < 0 | Unstable |
| Both radii of curvature negative (both diverging) | 0 < g1*g2 <= 1 | Stable |
| Infinity radius of curvature (plane-parallel) | g1*g2 = 1 | Marginally Stable |
Conclusion
Understanding the stability criteria of a laser cavity is essential for designing lasers that can maintain mode structures and achieve the desired output with minimal losses. A cavity that does not meet the stability criteria will not support oscillation over a prolonged period, leading to inefficient laser operation.