Page 241 - Fiber Bragg Gratings

218 Chapter 5 Apodization of Fiber Gratings

both gratings receive the same UV dose is overcome by stretching the fiber
back and forth continuously, e.g., by using two piezoelectric transducers,
oscillating out of phase. If the fiber is periodically stretched at a high
enough frequency, a perfectly apodized grating will result. The apodization
function has a pure half-sinusoidal period as an envelope.
For a scanning phase mask interferometer, it is necessary to ensure
that the scan speed is such that each point of the fiber is exposed to the
UV beam for at least a single stretching cycle, for each scan. This is easily
achieved by adjusting the scan speed to be slow enough, depending on
the frequency of the stretcher. For a given UV beam width, W^, and scan
speed, Vjjy m/sec, the frequency f of the stretching oscillator is

Apodization works for a variety of situations: If the UV beam is static,
the stretching scheme frequency is really not that important, so long as
the UV power is low enough to enable the grating to form in a time
frame much greater than a single period of the oscillator frequency. This
condition is generally met unless the grating is written in a single shot
from a pulsed laser. A certain amount of care does need to be taken if the
apodization is to be performed with a pulsed laser source. It is important
that the grating be inscribed over many pulses so that pulse averaging
takes place, as well as than every possible position of the stretch of the
fiber be inscribed with a grating. One exception is if the grating is inscribed
in two uniform pulses of identical intensity, one for each extreme position
of the stretch.
Apodization of the grating is continuous and not stepped, since each
part of the fiber is stretched exactly the correct amount for apodization.
This is not true of the MPM technique, in which a whole subgrating
length is "smeared" out by the same amount, so that only quasi-continuous
apodization is possible. The same applies to the MPF technique. The
reason both techniques work is because some of the index change is
sacrificed over the finite length of the subgrating. In the case of the MPF
scheme, each subgrating tries to print the new grating on what was
printed before, but slightly altered. In the MPM, it continuously builds
on the regions that have been "wrongly" printed, the result of a finite
length of subgrating. There is normally enough refractive index change
available for this limitation not to be a problem.