Page 218 - Fiber Bragg Gratings

Chapter 5

Apodization of Fiber

Gratings

Light + Light does not always give more light,
but may in certain circumstances give darkness.
—Max Born

1
Interestingly enough, apodization is a word often encountered in filter
design; a word that flows easily off the tongue. Yet many readers are not
aware of the exact meaning of the term. Etymologically, the word has its
roots firmly in Greek, a podos, meaning "private-foot," in other words,
hidden foot — footless. Curiously, any of the approximately 150 species
of the amphibian order Gymnophiona, known as caecilian, were formerly
known as Apoda. They are burrowing or swimming, secretive animals,
without limbs but with an elongate body length between 100 and 1500
mm, occurring in the Western Hemisphere [1]. Not unlike fiber gratings. . .
So what does the word mean when applied to fiber grating filter
design? Fiber gratings are not infinite in length, so they have a beginning
and an end. Thus, they begin abruptly and end abruptly. The Fourier
transform of such a "rectangular" function immediately yields the well-
known sine function, with its associated side-lobe structure apparent in
the reflection spectrum. The transform of a Gaussian function, for exam-
ple, is also a Gaussian, with no side lobes. A grating with a similar

1
Etymology: Greek, a, private,podos, a foot. Source: Chambers 20th Century Dictionary.

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