Page 480 - High Power Laser Handbook

448 Fi b er L a s er s Intr oduction to Optical Fiber Lasers 449

The detuning factor δ is given by δ = 2πn (1/λ – 1/λ ). The peak
0
0
reflectivity is given by
2
R = tan h (κ L) (15.39)
The FWHM bandwidth of a FBG is given by

 ∆n  2  1  2
∆= λ g + (15.40)
λ
0   2n     N  
0
For weak gratings, FBG bandwidth is inversely proportional to the
number of grating periods, N = L/Λ. For strong FBGs, it becomes
proportional to the relative index modulation and is independent of
FBG length. Reflections from weak FBGs of 10 percent peak reflec-
tion at various lengths are plotted in Fig. 15.28a, while those from
FBGs of 10 mm length at various coupling coefficients κ are plotted
in Fig. 15.28b. Frequency detuning from the peak frequency is used
as the horizontal axis.
In a fiber laser with an output mirror of transmission T and total
0
round cavity loss α , the laser output can be written as 59
t
Tf
P = o s P ( − P ) (15.41)
out α f abs th
t p

0.1

0.08
L = 1 mm
0.06
Reflection 5 mm

0.04
10 mm
0.02 20 mm

0
−100 −75 −50 −25 0 25 50 75 100
Frequency detuning (GHz)
(a)
Figure 15.28 FBG reflection (a) at various lengths and 10% reflection and
(b) at various κ and L = 10 mm.