Page 430 - Tunable Lasers Handbook

390 Paul Zorabedian

For the Littrow geometry, the grating resolution can be expressed in terms of the
filled depth as

-
RVHXI(Lil1rouI - (54)
XL, .

For the grazing-incidence geometry. the resolution is

h’
= 2 (55)
‘LWH,,,,,, KL, .

In terms of optical frequency. the grating reflectance function for a Gaussian
beam is given by [63]

where the band width is given by

AVRVHkl = C (57)
KL,.
~

7.2.1.2 Distributed Bragg Reflector
7.2.1.2.1 Principle of Operation
Periodic modulation of the index of refraction along the length of an optical
waveguide results in a structure known as a distributed Bragg reflector. The
reflection is maximized at a wavelength for which the period of the modulation
is equal to h/3. If the modulation period can be varied, then the reflected wave-
length can be tuned.

7.2.1.2.2 Embodiment in Optical Fiber
A variable-wavelength distributed Bragg reflector for single-mode optical
fiber has been realized in the following form [64]. An optical fiber was placed in
a groove in a fused silica substrate. The substrate was then polished until part of
the cladding of the fiber was removed. On a separate substrate, a fan-shaped
grating consisting of slowly diverging lines of sputtered amorphous silicon was
fabricated. The grating was placed face-down on the side-polished fiber with a
small amount of index-matching oil between the substrates. The grating then
was able to interact with the evanescent field in the fiber. The grating substrate
was able to slide over the fiber substrate, thus changing the pitch of the grating