Page 477 - High Power Laser Handbook

444 Fi b er L a s er s Intr oduction to Optical Fiber Lasers 445

relative to that of a gaussian beam. The diffraction half-angle θ can
d
be written as
 λ 
θ = M 2   (15.32)
d
 πω
2
where ω is the 1/e intensity radius of a gaussian beam. Some manufac-
turers also use the beam parameter product (BPP), which is defined as
BPPmmmrad) = ωθ (15.33)
×
×
(
d
2
For a diffraction-limited beam, M = 1 and BPP = 0.33 mm × mrad at
1 µm. Sometimes BPP is also defined as BPP = 2ω × 2θ , correspond-
d
ing to a diffraction-limited BPP of 1.3 mm × mrad at 1 µm.
High-power fiber lasers are generally pumped with high-brightness
fiber-coupled diodes, where brightness is defined as
4 P
B = (15.34)
(π dNA) 2
where P is total available pump power, NA is the fiber NA, and d is beam
diameter. Another parameter used is the etendue of a pump source,
defined as E = B/P. Current state-of-the-art fiber-coupled broad-area
2
diodes have a brightness in the range of 1.8–6.0 MW/cm , where a bright-
ness of 1.5 MW/cm corresponds to a pump power of 10 W in a 100-µm-
2
diameter fiber with NA = 0.15. Efforts are ongoing to increase the brightness
to 10 MW/cm , but such high values require simultaneous coupling of up
2
to 10 broad-area diodes into a single 100-µm-diameter fiber, which can be
accomplished with sophisticated beam-shaping techniques. Even higher
brightness values can be obtained with beam shaping of diode arrays,
where currently up to 400 W can be obtained from a 200-µm-diameter fiber
with NA = 0.22, corresponding to a brightness of 8.4 MW/cm . Efforts are
2
also ongoing to reach 1 kW from a 200-µm-diameter fiber. Even higher
power levels can be obtained by implementing wavelength multiplexing.
With present state-of-the-art diode lasers, several kilowatts of power can
be coupled into a 600-µm-diameter gain fiber. Apart from enabling higher-
power fiber laser operation, research in high-brightness diode lasers is
motivated by machining applications that can use the direct output of
semiconductor pump lasers without any intermediate fiber laser stage.

15.3 Optical Fiber Lasers

15.3.1 Continuous Wave Fiber Lasers

Background
Many configurations of fiber lasers have been studied since the mid-
1980s. Most are core-pumped lasers, with little possibility of scaling
up to higher power levels. Many of the early higher-power fiber