D.3     Matlab FFT and Gaussian example

D.3.2     Example

A SLD light source with Gaussian shape is chosen with Dl_FWHM = 40 nm and centered at l_c = 1318 nm. The SLD intensity I(n) is

The relations between n_c, b, Dl and l_c are

where c₀ is the light speed in vacuum (2.9979×10⁸ m/s). The discrete intensity between 1210 and 1410 nm with 5000 points is presented in Fig. D-1.

Fig. D-1 : Gaussian light source intensity in linear (left) and dB scale (right)

The Fourier transform of the light spectrum, which is the impulse response h(t) of the light source and the pulse width Dt_FWHM are given by

The pulse width Dt_FWHM is found to be 38.3mm/c₀. The calculated impulse response amplitude is presented in Fig. D-2. The impulse axis is the optical path difference between -120 and 120 mm corresponding to the travel distance in vacuum for the corresponding impulse time.

Fig. D-2 : Impulse response amplitude of the Gaussian light source intensity in linear scale (left) and in dB scale (right)

The impulse response outside the ±95 mm is no more the expected Gaussian function due to roundings in the calculation process.