
APPENDIX G 503
9.1b How big is the beam at the back mirror?
Solution:
d = d
0
1 +
z
b
2
= 0.7 mm ×
1 +
20
61
2
= 0.74 mm (G.85)
9.1c I now wish to launch the beam into a ber whose core is best matched to a Gaussian
beam with a diameter of 5 μm. Figure out how to do this, using one or more lenses in a
reasonable space.
Solution:
There are a number of good solutions. The easiest is to start from the waist of the beam
entering the ber. Find where the beam is 0.7 mm in diameter.
d = d
0
1 +
z
b
2
(G.86)
z
b
=
d
d
0
2
−1 (G.87)
z =±b
d
d
0
2
−1 =±
πd
2
0
4λ
d
d
0
2
−1. (G.88)
With all distances in micrometers,
z =±
π5
2
4 ×0.633
700
5
2
−1 ≈±
π5
2
4 ×0.633
700
5
=±4.4 × 10
3
. (G.89)
We