Gaussian Beam in a Symmetric Confocal Resonator.

[mogul28]

λ

Homework Statement

A symmetric confocal resonator with mirror spacing d =16 cm, mirror reflectances 0.995, and n = 1 is used in a laser operating at λ[o] = 1 μm.
(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 distributed resonator loss coefficient Qr.

Homework Equations

The Attempt at a Solution

a) symmetric confocal ==> R1=R2=-d=-16cm.

Zo = d/2=8cm
b) W0=√(λ*d/2*pi) = 0.1596 mm

d)v[q]=qv[F] + (Δζ/pi) v[F]

 

[member 553083]

v[F]=c/n = 3x10^8 /1 = 3x10^8 m/sΔζ(q,p) = (p+1/2)*pi - arctan(2*pi*(2*q+p+1)*z0/λo) for (0,0): Δζ (0,0)= pi-arctan(2*pi*z0/λo)= pi- arctan(16*pi/1x10^-6) = 3.1415 rad for (1,0): Δζ (1,0)= 3/2*pi - arctan(2*pi*3*z0/λo)= 4.7122 radv[q,p]=(1+1/2)*v[F] + (Δζ/pi)* v[F] ==> v (0,0)= 1.5*v[F] + (3.1415/pi)*v[F]=4.913x10^8 m/s and v (1,0)= 2.5*v[F] + (4.7123/pi)*v[F]= 8.042x10^8 m/s e) Qr = (π*v[F])/((1-R^2)*A) where A = 4*pi*W0^2 Qr = (π*v[F]) / ((1-0.995^2)*4*pi*(0.1596x10^-3)^2) Qr= 0.2351x10^11 s^-1