where l
B
is the Bragg wavelength grating defined by l
B
¼ 2n
eff
L, l
L
is the
longest wavelength of the cladding mode, n
clad
is the cladding index, L is the
grating pitch, and n
eff
is the effective index of the propagating mode.
n
eff
can be approximated by
n
eff
n
core
þ Dn
UV
=2, (9:3)
where n
core
is the refractive index of the core and Dn
UV
is the change in the core
index caused by the UV radiation, and, such that considering the Dn, Dl
off
is
now expressed as
Dl
off
L (Dn þ Dn
UV
=2): (9:4)
Therefore, Dl
off
becomes larger as Dn is increased. A larger Dl
off
causes the
excess loss region, due to the cladding modes, to be shifted far from the Bragg
reflection wavelength. For a moderate NA of 0.25, the Dl
off
is 4.5 nm and for an
ultrahigh NA of 0.40, the Dl
off
is 12 nm. This ...