Page 475 - High Power Laser Handbook

442 Fi b er L a s er s Intr oduction to Optical Fiber Lasers 443

10 dB, though higher gain values can be obtained by propagating
the pump in the same higher-order mode as the signal. The effective
mode area of higher-order mode fibers has shown to be of smaller
compression in bent fibers.
A third approach to increasing core area is an antiguiding optical
fiber, which uses an active core doped with rare earth ions that have
49
lower index than that of the cladding. In this case, there are only a
few very leaky modes guided in the core, with higher-order modes
suffering higher losses. The concept is not fundamentally different
from many other approaches addressed earlier, except that the funda-
mental mode loss can be very high in an antiguiding fiber and becomes
only tolerable for core diameters of a few hundred micrometers (loss
scales with the inverse of the cube of the core diameter). Lasers with
fundamental mode output have been demonstrated using sufficient
gain to overcome the excessive loss of the fundamental mode, while
50
keeping the higher-order modes below threshold. It is worth noting
that these fibers are not likely to guide light through the real part of
the refractive index being modified in the presence of gain—that is,
the imaginary part of the refractive index—through the Kramers-
Kronig relation. In practice, the increase of refractive index (due to
gain) in rare-earth-doped glass is typically well below what is sufficient
to modify waveguide behavior. Gain in these fibers is likely mostly
used to compensate waveguide losses for the lower-order modes.
At large core diameters, the increasing size of the fundamental
mode makes it behave more and more like a free space beam. One
way of looking at how a guided mode navigates a bend is by imagin-
ing it continuously transforming itself into the local bent waveguide
mode adiabatically while propagating around the curve. As the mode
gets larger, it takes longer distances for the mode to make this transi-
tion adiabatically; consequently, larger coil diameters must be used to
minimize these transition losses (see Fig. 15.23). The bent fundamen-
tal modes also have a much reduced effective mode area. Effective
mode areas of bent fibers were first simulated by Fini et al. and are
plotted in Fig. 15.25, which shows the increasing effective mode area
compression at large core diameters. 51,52,53 This compression is a result
of an equivalent linear refractive index gradient introduced by bend-
ing in an optical fiber. A summary of progress of large core fiber
development in recent years is illustrated in Fig. 15.26.

Pumping of Optical Fiber Lasers and Beam Quality
Similar to high-power solid-state lasers, high-power optical fiber
lasers constructed with large core fibers can also have limited beam
quality and suffer from depolarization. Beam-quality limitations may
arise due to the presence of higher-order modes in the fiber output,
thermal stresses from fiber holders, or thermal lensing and thermal
birefringence in external components, such as collimation lenses,
polarizers, diffraction gratings, prisms, and isolators. At power levels