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This section presents different results
obtained by the simulations of the spectral response of lossless FBGs by
T-matrix and the corresponding impulse responses calculated by Fourier
transformation. A Bragg condition in the 1300 nm range has been chosen as
for the experimental FBGs fabricated and characterized in chapter 4. The used
algorithm is based on the T-matrix formalism of Erdogan [3-1], where the
overlap integral h is not considered. The effective refractive index is adapted to
keep the average refractive index constant to a value of 1.45.
The representation of the impulse
responses has been chosen to be as close as possible from OLCR measurements.
For this reason, we have used a distance scale OPLD instead of a time scale t. The relation
between OPLD and t is simply OPLD = c0×t (c0
is the light speed in vacuum), that is, the
OPLD corresponds to the traveled distance in vacuum during a time t (in the context
of OLCR, the OPLD corresponds to the optical path length difference in vacuum
between the reference and test arms). Moreover, the representation of the
impulse response amplitude in decibel scale is preferred, but in this case, a
reference illumination light source needs to be defined. In order to remain
consistent with the experiments presented in Chapter 4, a Gaussian light source
with 40 nm spectral bandwidth and centered at the Bragg wavelength is
used. The influence of the source bandwidth and the wavelength detuning between
the FBG and the source central source wavelength is nevertheless described at
the end of this section.
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