Page 464 - High Power Laser Handbook

432 Fi b er L a s er s Intr oduction to Optical Fiber Lasers 433

In silica fibers, fast heat conduction at the timescale of less than 1 ms
quickly leads to an almost uniform steady-state temperature distri-
bution across the fiber; the fiber temperature rise ∆T is dominated by
the heat transfer term [third term in the bracket in Eq. (15.25)]:

Q ρ 2
∆≈ 0 (15.26)
T
2 Rh
Equation (15.26) is plotted in Fig. 15.16 for various heat loads depos-
ited in the core (W in units of watts per meter) for a fiber with diameter
h
2R = 250 µm. Assuming 20 percent of the pump is turned into heat and a
maximum fiber temperature of 200°C, this would limit the maximum
convection heat removal to less than 70 W/m. Forced air or water cool-
ing must be used for higher output powers. When the temperature rise
is near 0, ∆T can be approximated as ∆T = 31.3 W , independent of fiber
h
diameter.
Optical Damage
The energy threshold E for optical damage is given by
th
E () = J ∆ 480 τ () cm ) (15.27)
2
ns A (
th eff
For a perfectly polished surface, the surface damage threshold is close
to that of a bulk medium. In reality, however, the surface damage

600

500
Temperature rise (°C) 400

300

200

100

0
0 10 20 30 40 50
W h (W/m)
Figure 15.16 Temperature rise in a silica fiber with diameter 2R = 250 µm
(h = 60.64 + 15.5∆T 0.25 ) versus heat load deposited in the core of the fiber,
assuming only convective heat removal from the fiber surface.