|
If the period L or the DC refractive index
Dndc
changes within the grating, different Bragg conditions exist and a larger
bandwidth of wavelengths is reflected (at the price of smaller reflectivity).
Both cases of chirping are presented in Fig. 2-8. The two chirping
effects are independent and then they can be combined to reduce or enhance the
total grating chirp.
Fig. 2-8 Chirped FBG index profile : period chirp (left), index chirp
(right)
The spectral reflection response of
these gratings is also presented in Fig. 2-7. The grating parameters are
the same as the homogeneous FBG, but the grating is divided in 100 layers for
which the period function linearly varies from a Bragg condition of 1299.8 to
1300.2 nm. We observe a reduction of the maximal reflection to 92 %
and an important relative increase of the side-lobes. The Fabry-Perot effect is
also reduced due to the fact that the both sides of the grating reflects
different wavelengths. For a larger chirp the reflectivity spectrum becomes much
more complicated and not so easily predictable. We observe for the delay time a
completely different behavior. Singularities appear and an anti-symmetric delay
time is found. Chirped gratings can be used as dispersion compensators to
compress temporally broadened pulses, it can also be used (broadband chirped
grating) for pump rejection and recycling of unabsorbed pump light from an
erbium-doped fiber amplifier.
Fig. 2-9 Blazed fiber Bragg grating
When the grating planes are not
orthogonal to the fiber axis (Fig. 2-9), the grating is called blazed or
tilted. For a tilt angle q and a phase mask period of Lg/2, the effective period L that determines the Bragg condition is given
by L =
Lg/cos(q). The overall effects are
a reduced fringe visibility factor and transfer of a part of the energy to the
cladding modes [2-17]. It is important to note that the energy coupled in
the cladding modes is considered as excess loss.
The tilt of the grating planes and the
strength of the index modulation determines the coupling efficiency and the
bandwidth of the light that is tapped out. Multiple blazed gratings can be used
to flatten the gain spectrum of erbium-doped fiber amplifiers. Another
application of blazed gratings is in mode conversion.
e) FBG with phase shifts
Phase shifts in FBG consist of some
discontinuities in the functions Dndc or q(z). The fiber grating can
be designed as a narrow-band transmission filter with the introduction of phase
shift across the fiber grating whose location and magnitude can be adjusted to
design a specific transmission spectrum.
An arbitrary FBG can be characterized
by any kind of functions Dnac(z), Dndc(z) and L(z), and thus have simultaneously apodization,
period and refractive index chirp, phase shifts and tilt. The design of
complicated FBG is required when specific spectral responses are expected, for
example limited delay time over a large wavelength bandwidth. Sometimes the Dnac, Dndc
and L functions are not completely under control, due to fabrication
problems or specific grating environment (temperature or strain). Arbitrary FBGs
are difficult to characterize since three different distributions need to be
known to fully determine the grating (if we neglect the tilt effects).
|
