Gaussian Beam in a Symmetric Confocal Resonator. A symmetric confocal resonator

Question

Gaussian Beam in a Symmetric Confocal Resonator. A symmetric confocal resonator with mimor spacing d = 16 cm, mirror reflectances 0.995, and n-1 is used in a laser operating at 1 m (a) Find the radii of curvature of the mirrors. b) Find the waist of the (0,0) (Gaussian) mode. (c) Sketch the intensity distribution of the (1,0) modes at one of the mirrors and determine the distance between its two peaks. (d) Determine the resonance frequencies of the (0,0) and (1,0) modes. (e) Assuming that losses arise only from imperfect mirror reflectances, determine the dis- tributed resonator loss coefficient ap

Explanation / Answer

(a) For a symmetric confocal resonator, the radii of curvature of the mirrors are the same as the mirror spacing i.e. 16cm in this case.

(b) Beam waist at (0,0) is given by the relation, w0² = d*Lambda/(2*pi) = 159.577 µm

(c) Draw II (two lines) with each thickness gaussian nature.

The transverse spatial distribution is given by Hermite Polynomials. For 10 mode, it is H10 = 2*x. Here x = L/2 (on one of the mirrors)

(d) The general expression for resonance frequencies of (m,n) mode in a confocal resonator is given by

f/f0 = (q + 1) + 0.5*(m + n + 1)

where q = number of modes in a cavity (can be calculated by d/lambda)

Plugin the numbers

for (0,0) mode as q = 16cm/1µm, m = 0, n =0, and

for (1,0) mode as q = 16cm/1µm, m = 1, n =0,

calculate the final values.

(e) Mirror loss is given by alpham = (0.5/d) * ln(1/R) = 1.5664 x 10-4 cm-1

where d = cavity length, R = reflectivity of the mirror

Distributed loss coefficients due to mirror imperfections is given by alpha = 2*alpham = 3.1328 x 10-4 cm-1

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