Question

A laser cavity includes two mirrors: one of them a concave mirror with a radius of 86 cm, and the other one is convex with a radius of 1.42 m. The distance between two mirrors is 130 cm. The wavelength of this laser is 0.744 μm. Show if the resonator of this laser is stable or not?

Answer 1

The resonator of the laser is stable based on the calculations using the stability criterion.

Step-by-step explanation:

The stability of a laser cavity is determined by the relationship between the radii of curvature of its mirrors and the distance between them. To determine if the resonator of this laser is stable, we can use the stability criterion given by the ABCD matrix formalism:

Stability Criterion:

1. 
   
3. Calculate the stability parameter g1:
4. 
   

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• g1 = 1 - (d/f1), where d is the distance between the mirrors and f1 is the radius of curvature of the convex mirror
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• g1 = 1 - (130 cm/1.42 m) = -0.084
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Calculate the stability parameter g2:

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• g2 = 1 - (d/f2), where d is the distance between the mirrors and f2 is the radius of curvature of the concave mirror
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• g2 = 1 - (130 cm/0.86 m) = 0.349
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Check if |g1 * g2| < 1:

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• If |g1 * g2| < 1, the resonator is stable
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• If |g1 * g2| > 1, the resonator is unstable
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• |g1 * g2| = |-0.084 * 0.349| = 0.029316 < 1
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Based on the calculations, the resonator of this laser is stable.