Page 348 - Fiber Bragg Gratings

7.2 Chirped and step-chirped gratings 325

is a continuously distributed reflector. Ideally, light entering into a chirped
grating from one end should be dispersed in exactly the opposite way when
entering from the other end. Early measurements on chirped gratings did
show this feature [40]. However, the gratings were short, had a large
bandwidth, and consequently had a small dispersion. Dispersion is not
generally reversible with unapodized chirped gratings. To understand this
phenomenon, we remind ourselves that light entering from the short-
wavelength end of a highly reflective chirped grating is reflected such
that only a small fraction of the short-wavelength light penetrates through
to the other end of the grating, while the long-wavelength light does. On
entering from the long-wavelength end of the grating, exactly the opposite
occurs. The detailed delay ripple is a result of the interference between
the broadband reflection due to the edge of the grating and the distributed
nature of the reflection of the grating [41].
As a crude comparison, when light enters from the long-wavelength
end of the grating, the interference is predominantly due to the large
long-wavelength reflection from the front of the grating and the small
broadband reflection due to the front edge. Short-wavelength light pene-
trates the dispersive grating and is predominantly reflected from the rear
end; it, too, interferes with the low broadband reflection from the front
end. In neither case does the rear end of the grating play a strong role.
Since the dispersion increases with greater penetration into the grating,
the delay ripple frequency increases with decreasing wavelength (see Fig.
7.5). With the launch direction reversed, exactly the opposite occurs: The
delay ripples increase in frequency with increasing wavelength. Therefore,
light dispersed by reflection from the short-wavelength end of the chirped
grating cannot be undone by reflection from the long-wavelength end! The
simulated result of this asymmetry is shown in Fig. 7.10. The sign of the
frequency chirp in the delay ripple is insensitive to the launch direction
i.e., the frequency of the chirp is always from a low to a high frequency
(Fig. 7.10, B and C) when viewed from either end.
The role played by the rear end of the grating is apparent when the
coupling constant K ac is apodized asymmetrically. In this example we
consider a grating with a profile of the refractive index modulation as
shown in Fig. 7.11a. The grating profile is half-cosine apodized so that the
light launched from the long-wavelength end sees a gradually increasing
coupling constant. The amplitude of the light reflected from the front end
of the grating is now lower than in an unapodized grating, and long-
wavelength light penetrates more deeply so that the amplitude at the