Page 117 - Fiber Bragg Gratings

96 Chapter 3 Fabrication of Bragg Gratings

effect of unchirping the grating. If the relieved strain is too large, the
grating becomes chirped once again but with an opposite sign of chirp:
i.e., the narrower diameter end has a shorter wavelength than the larger
diameter end. The method is capable of high reproducibility, is simple
to implement, and allows nonlinear chirps to be programmed into the
grating [80]. There are two factors that affect the Bragg wavelength
in strained etched fibers: the change in the physical length of the fiber,
and the effective index of the mode through the stress-optic effect,

where the change in the Bragg wavelength is AA under zero stress, after
the grating has been written under local strain of e t, and 8n eff is the
change in the effective index of the mode due to the strain-optic coefficient.
The two quantities on the RHS in Eq. (3.1.26) have opposite signs, with
the strain term being much larger than the stress-optic coefficient. Never-
theless, when a grating is written in a tapered fiber under strain, it
appears chirped, although the period of the grating is uniform. Because
of the stress-optic effect, the local effective index of the mode is not uniform
along the length of the grating. On removal of the strain after the grating
has been inscribed, the effective index of the mode becomes uniform, but
the period is altered because of the change in local strain, and the grating
becomes uniform at some lower strain value and chirped with the opposite
sign when fully relaxed.
Etched linear tapers produce nonlinear chirp, since the chirp is in-
versely proportional to the square of the radius of the section according
to Eq. (3.1.25). Since the Bragg wavelength is directly proportional to the
applied strain [see Eq. (3.1.14)], the induced chirp becomes nonlinear. To
compensate for this disparity, a nonlinear etching profile [99] can be used,
resulting in a linear chirp. In order to fabricate a predetermined etch
profile, the time of immersion of the fiber in the etching solution (usually
buffered hydrofluoric acid) must be controlled, since the etch rate at con-
stant temperature is highly reproducible. A three-section vessel with a
layer A of a mixture of decahydronaphthalene and dichlorotoluene (10%)
floating above layer B of 32% HF and with a third layer C of trichloroethyl-
ene below it may be used. This allows the acid to come into contact only
with a small section of the fiber when it is immersed vertically into it. With
the fiber remaining in position, the vessel is lowered at a programmed rate
to expose another part of the fiber in section B, while the top layer A
immediately stops the fiber from etching any further. Using this method,
highly repeatable tapers have been produced and linear chirps of 4.8 nm