Page 321 - Fiber Bragg Gratings

298 Chapter 6 Fiber Grating Band-pass Filters

(4.3.16), (4.4.11), and (4.4.12) govern the coupling of counter- and copropa-
gating guided modes. Coupling of the modes of the same order is always
possible, provided the phase-matching condition is met. The overlap inte-
gral, Eq. (4.4.5), for the coupling of dissimilar modes is zero, unless the
transverse distribution of the refractive index modulation is not constant,
breaking the symmetry. Thus, a slanted grating will increase the overlap
integral between modes of different order, since the transverse refractive
index modulation profile is no longer uniform. This was first reported by
Park and Kim [107] using a novel internal mode-beat grating, by exciting
a bimoded fiber at a wavelength of 514.5 nm from a CW argon laser. The
beating of the modes automatically creates a blazed grating with the
intensity of the laser radiation varying transversely across the core with
the mode-beat period. This intensity grating induced a photoinduced grat-
ing, which created the mode converter. This principle has been extended
by Ouellette [108] by recognizing that the phase-matching condition is
met by more than one set of modes due to the nondegeneracy of the modes,
but at longer wavelengths. Thus, a grating written at 488 nm by exciting
a chosen pair of modes allowed the "reading" of the holographic grating
at around 720 nm. Further experiments have demonstrated the sensitivity
of the mode beat length to the applied strain [109], since the propagation
constants of the fundamental and higher-order modes change differen-
tially. These types of converters have applications in strain sensing and
as nonlinear optical switches [110]. A phase-matching condition is also
possible where the beat length L b —> oo [111,112], allowing very long period
gratings to be used.
A principle similar to the one reported by Park and Kim [107] has
been used to fabricate mode converters at different wavelengths. The
coupling between the LP n and LP 01 modes was made possible by slanting
the grating using an external, point-by-point UV exposure technique [113],
details of which may be found in Chapter 3.
A slit (12 /urn) at an angle of 2-3° was used to expose the fiber at the
first-order period of 590 /urn (N = 1) mode beat length, 27rf[N(f3 LPQi -
/3 Lpu)]y resulting in a mode converter at a wavelength of 820 nm in a
Corning Telecommunications fiber with a higher-order mode cutoff of 1.1
/mm [113]. The grating had typically 200-300 steps for 100% coupling,
while overcoupled converters with 1000 periods were also reported. These
convert the LP 01 to the LPn and then back again to the LP 0i- Unlike
polarization rocking filters, mode-converting gratings can be very strongly
coupled, so that the side lobes of the sine function in Eqs. (4.4.11) and