Page 313 - Fiber Bragg Gratings

290 Chapter 6 Fiber Grating Band-pass Filters

length dependence of the loss. There are two bounds to the loss spectrum,
one on the short- and the other on the long-wavelength side: Light radiated
out of the fiber core subtends a wavelength-dependent angle #(A) to the
counterpropagation direction (STG) and copropagating (LPG), which de-
pends on the inclination of the grating and period.
For the STG, this angle of the radiated light at wavelength A in the
infinite cladding is easily shown to be

where B g is the tilt of the grating with respect to the propagation direction,
and N is the order of the grating. The angle at which the light exits from
the side of the fiber varies as a function of wavelength and therefore can
be used as a band-pass filter. The bandwidth of the radiated light can be
shown to be approximately

However, the phase-matching condition alone does not determine the
peak wavelength, in the general case when the grating is titled; the overlap
integral together with the phase matching alters the spectrum and shifts
the wavelength of maximum loss (see Chapter 4). Typical transmission
loss and reflection spectra for a strong STG are shown in Fig. 6.46a, and

Figure 6.46: The transmission loss (and reflection) of (a) a 4-mm-long side-
tap grating filter and (b) LPG filter with a 400-micron period, both written in a
boron-germania codoped fiber.