  Fibre Bragg grating sensors have emerged as a simple, inexpensive, accurate,
sensitive and reliable platform, a viable alternative to the traditional
bulkier optical sensor platforms. In this work we present an extensive
theoretical analysis of the tilted fibre Bragg grating sensor (TFBG) with a
particular focus on its polarization-dependent properties.
  We have developed a highly efficient computer model capable of providing the
full characterization of the TFBG device in less then $3$~minutes for a given
state of incident light polarization. As a result, the polarization-dependent
spectral response, the field distribution at the sensor surface as well as the
fine structure of particular resonances have become accessible for theoretical
analysis. As a part of this computer model we have developed a blazingly fast
full-vector complex mode solver, capable of handling cylindrical waveguides of
an arbitrary complex refractive index profile.
  Along with the theoretical study we have investigated optical properties of
the TFBG sensor with application to polarisation-resolved sensing. We proposed
a new method of the TFBG data analysis based on tracking the grating
transmission spectra along its principle axes, which were extracted from the
Jones matrix.
  In this work we also propose a new method of enhancing the TFBG sensor
refractometric sensitivity limits, based on resonant coupling between the TFBG
structure resonances and the local resonances of nanoparticles deposited on the
sensor surface. The $3.5$-fold increase in the TFBG sensor sensitivity was
observed experimentally.
