Page 322 - Fiber Bragg Gratings

6.10 Mode converters 299

(4.4.12) become large with a large refractive index modulation, and multi-
ple peaks can be seen in the transmission spectrum. A FWFZ of ~5 nm
was observed. A higher-order mode stripper has to be used to observe the
loss spectrum of this filter. For the band-pass function, the higher-order
mode has to be selected. Alternatively, the higher mode can be excited
preferentially in the overcoupled filter and stripped at the output so that
the "dropped" wavelength is in the fundamental mode, with the through
state in the LP n mode.

Conversion from LP 01 mode to the leaky counterpropagating LP n
mode has been observed in depressed-clad fibers in which tilted Bragg
gratings were written [114]. In this case, the fiber supported theLP n mode
over short lengths, so that a "ghost" dip is observed in the transmission
spectrum at a wavelength slightly shorter than the Bragg reflection wave-
length. While the light is coupled into the Z/P n mode, the reflection is not
visible if the fiber on the input side of the gratings is mode stripped.
Gratings with a tilt angle of 3° have been written in standard telecommu-
nications fibers preexposed to raise the index to allow the LP U mode to
be supported [115] over the UV-exposed length. The overlap between the
LP 01 mode and the LP n mode is almost the same as the Z/P 0i mode for
this tilt angle, so that efficient reflective mode coupling is possible. The
side illumination induces a nonuniform refractive index change across
the core, breaking the LP U mode degeneracy and causing two reflections
to occur. Depressed-cladding fibers have been examined by Haggans et
al. [116] with a view to reducing the coupling to radiation and cladding
modes.
Coupling to similar order modes does not require a transverse asym-
metry in the grating (see Chapter 4). Therefore, the LP 01 mode is coupled
to the LP 02 mode for both co- and contradirectional converters with a
transversely uniform grating. The coupling constant K ac [117] is

where the subscripts refer to the mode, and u, w, and v are the normalized
waveguide parameters defined in Chapter 4. The interaction of the LP 01
—> LP 02 mode is particularly useful for narrow-band filters [118] and
for broadband dispersion compensation [119]. In the latter application,