Page 479 - High Power Laser Handbook

446 Fi b er L a s er s Intr oduction to Optical Fiber Lasers 447

Ultraviolet photosensitivity in the germanium-doped core of an
optical fiber originates from germanium oxygen-deficient centers
with well-defined absorption of around 240 nm, accessible by KrF
excimer lasers, frequency-doubled argon ion lasers, or frequency-
quadrupled Nd:YAG lasers. In addition to the depletion of the ger-
manium oxygen-deficient centers upon UV exposure, there is also
evidence of stress relaxation and sometimes compaction. All these
effects are believed to contribute to the observed refractive index
change. It was eventually found that hydrogen loading in a high-
pressure cell near room temperature prior to UV exposure leads to
a significant improvement of photosensitivity. This discovery has
57
enabled FBG writing in some germanium-free glasses. Large
amounts of hydroxyls are found in the glass after UV exposure, and
the significant composition modification is believed, in this case, to
play a role in the refractive index change. FBGs are found to be
highly stable at room temperature, though they can be erased at
elevated temperatures. Most FBGs will be erased at temperatures
58
above 400°C, and FBGs with improved temperature stability can be
made using special writing processes. One unique aspect that makes
FBGs possible is that silica glass in the cladding is not photosensi-
tive, which allows the UV beam to reach the core glass without
being absorbed.
In an FBG, due to momentum conservation, we have
k = k − k (15.35)
g f b

This leads to a relation between peak wavelength λ and grating
0
pitch Λ.
λ = 2n Λ (15.36)
0 0
where n is effective mode index. For a uniform grating, reflectivity
0
can be analytically determined:

κ 2 h κ sin 2 ( L)
R = (15.37)
2
2
δ 2 h ( L +κ sin 2 − κ )( δ 2 )cos h κ ( L)
where L is grating length. The coupling coefficient is defined as

π ∆n
κ= g η (15.38)
g
λ 0
where η is the spatial modal overlap with the grating. It is also the
g
proportion of modal power in the core if the FBG is written uniformly
over the core; 2∆n is the peak-to-peak refractive index modulation.
g