Page 253 - Fiber Bragg Gratings

230 Chapter 6 Fiber Grating Band-pass Filters

The DFB structure is used in semiconductor lasers to enable single
frequency operation [1,2]. The single /\/4 phase-shifted DFB [1] has a pass
band in the middle of the stop band. The pass band has a very narrow
Lorentzian line shape. While this narrow pass band is useful for filtering,
the need exists for broader-bandwidth, high-finesse transmission filters.
Cascading several such structures leads to an improved, broader trans-
mission bandwidth [3-5], and has been generally well known in electrical
filter design. The developments in fiber Bragg grating technology have
made it possible to fabricate direct in-fiber analogs. Low-loss, high-finesse
filters, using both a single A/4-shifted and cascaded phase-shifted DFB
structures have been reported in the literature [6,7]. Rare-earth-doped
fiber DFB lasers (see Chapter 8) have also been demonstrated [8].
Coupled-mode analysis developed in Chapter 4 leads directly to the
fields in each grating. The matrix method provides a simple route to the
transfer function of the DFB structure. Recalling Eq. (4.8.22), the transfer
matrix of the DFB is

S
where TP is the phase shift matrix shown in Eq. (4.8.19)

6
l
Remembering that the transfer matrix elements of T and T are
described by Eqs. (4.8.18M4.8.21) immediately leads to the solution for
the DFB transfer function, T DFB:

The transmitted power according to Eq. (4.8.8) is

where * indicates the complex conjugate, and