Mode matching

Literature

Laser Beams and Resonators H. Kogelnik et al., Applied Optics 5, 1550 (1966)

Determination and optimization of mode matching into optical cavities by heterodyne detectionG. Mueller et al., Optics Letters, Vol. 25, No. 4 (2000)

Mirror configuration

Parameter

Radius of curvature of mirror R1: R1= 1 m

Radius of curvature of mirror R2: R2= infinity (Incoupling side)

Wavelength: λ= 1.55×10^-6 m

Length between the resonator mirrors: L= 485 mm

Beam radius at waist: w0

Beam radius at mirror: w1, w2

Stability parameter of the resonator: g1, g2

Distance between mirror and the waist: t1, t2

Beam waist calculation from resonator

Step 1: Calculate the stability parameters

Step 2: Calculate the beam waist radii on the mirrors
From thesis of Sana:

Beam Radii, 1/e^2 of the intensity

Alternative from rom Appl. Opt. 5, 1550 (1966):
In our case:
Step 3: Calculate the distance of beam waists on the mirrors and focus
Position of the beam waist on the two mirrors:
In our case: and t_2 is ≈0
Step 4: Calculate the focal length of your collimator
Take the radii on the plane w_2=w_0=496.567µm and curve mirror w_1=691.95µm and calculate the focal length f: D is the beam waist diameter of the collimated beam after the collimator and w is mode beam diameter of the fiber output. In our case is: The diameter from the light, which comes out of the fiber (1550 nm) is w= 10.5+/-0.5µm. That gives us a focal length f= 5.32044mm.
Step 4b
We did the calculation wrong. We used D=w_0 and got f=2.66022mm.