Page 269 - Fiber Bragg Gratings

246 Chapter 6 Fiber Grating Band-pass Filters

slightly altering the angle of the incoming beams in between the writing
of the two gratings [30]. Unless the angle can be measured accurately, it
may be difficult to reproduce the results with precision. Two gratings can
be superimposed in a fiber by writing one grating with a chirped phase
mask [31] and then stretching the fiber before writing the second [32,33].
The basic principle of moire grating formation is discussed in Chapter 5.
However, for clarity, we consider the interference due to two UV intensity
patterns to produce a grating with the refractive index profile

in which the slowly varying envelope with period A e is a result of the
difference between the two grating periods, and the chirped grating period
is A g. If the envelope has a single cosine cycle over the grating length
(the grating periods have been chosen to be such; see Chapter 5), then
the effect of the zero crossing of the envelope is equivalent to a phase
step of 77/2 at the Bragg wavelength (see Chapter 5, Section 5.2.7). This
grating is simple to simulate using the matrix method; the apodization
profile of the grating can be specified to have n cycles of a cosine function,
where n = \ is a single cycle of a cosine envelope (see Fig. 5.18). The
computed transmission spectrum of this type of a band-pass filter is shown
in Fig. 6.16. The experimentally achieved result is almost identical to
that shown in Fig. 6.16 [33], apart from the short-wavelength radiation
loss apparent just outside the band-stop spectrum in the measured result.
The problem with this type of phase-shifted grating has already been
discussed: There remains a trade-off between bandwidth and extinction,
although it is a convenient method of producing a multiple-band-pass
filter by increasing the number of cycles of the modulation envelope.

6.3 The Michelson interferometer band-
pass filter

The Michelson interferometer (MI) may be used as a fixed-wavelength
band-pass filter. Since the coupler shown in Fig. 6.17 splits the input
power equally into the two ports, the light that is reflected from a single
100% reflection grating (HR1) is again equally split between ports 1 and
2. Thus, only 25% of the light is available in the pass band at port 2.