Page 265 - Fiber Bragg Gratings

242 Chapter 6 Fiber Grating Band-pass Filters

6.2 The Fabry-Perot and moire band-pass
filters

The fiber DFB grating is the simplest type of Fabry-Perot (FP) filter.
Increasing the gap between the two grating sections enables multiple
band-pass peaks to appear within the stop band. The bandwidth and the
reflectivity of the gratings determine the free-spectral range and the
finesse of the FP filter. The grating FP filter has been theoretically ana-
lyzed by Legoubin et al. [23]. Equations (6.1.4) and (6.1.5) describe the
transfer characteristics of the filter and have been used in the simulation
of the gratings in this section.
Figure 6.12 shows the structure of a Fabry-Perot filter. These filters
work in the same way as bulk FP interferometers, except that the gratings
are narrow-band and are distributed reflectors. A broader bandwidth
achieved with chirped gratings creates several band-pass peaks within
the stop band. Control of the grating length L and the separation SI allows
easy alteration of the stop-band and the free-spectral range.
At zero detuning, the peak reflectivity of a FP filter with identical
Bragg gratings is

where R is the peak reflectivity of each grating. Since the gratings are
not point reflectors, the free-spectral range (FSR) is a function of the
effective length of the grating, which in turn is dependent on the detuning.
For a bulk FP interferometer, e.g., a fiber with mirrors, the FSR is [23]

The distance between the mirrors is d, and the effective index of the mode

Figure 6.12: A schematic of a Fabry-Perot etalon filter. In the simple configu-
ration, the gratings are identical, although in a more complicated band-pass filter,
a dissimilar chirped grating may be used.