  The integration of miniaturized optical spectrometers into mobile platforms
will have an unprecedented impact on applications ranging from unmanned aerial
vehicles (UAVs) to mobile phones. To address this demand, silicon photonics
stands out as a platform capable of delivering compact and cost-effective
devices. The Fourier transform spectrometer (FTS) is largely used in free-space
spectroscopy, and its implementation in silicon photonics will contribute to
bringing broadband operation and fine resolution to the chip scale. The
implementation of an integrated silicon photonics FTS (Si-FTS) must nonetheless
take into account effects such as waveguide dispersion and non-linearity of
refractive index tuning mechanisms. Here we present the modeling and
experimental demonstration of a silicon-on-insulator (SOI) Si-FTS with
integrated microheaters. We show how the power spectral density (PSD) of a
light source and the interferogram measured with the Si-FTS can be related
through a simple Fourier transform (FT), provided the optical frequency and
time delay are corrected to account for dispersion, thermo-optic non-linearity
and thermal expansion. We calibrate the Si-FTS, including the correction
parameters, using a tunable laser source and we successfully retrieve the PSD
of a broadband source. The aforementioned effects are shown to effectively
enhance the Si-FTS resolution when properly accounted for. Finally, we discuss
the Si-FTS resilience to chip-scale fabrication variations, a major advantage
for large-scale manufacturing. Providing design flexibility and robustness, the
Si-FTS is poised to become a fundamental building-block for on-chip
spectroscopy
