  Several applications in modern photonics require compact on-chip optical
filters with a tailored spectral response. However, achieving sub-nanometric
bandwidths and high extinction ratios is particularly challenging, especially
in low-footprint device formats. Phase shifted Bragg gratings implemented by
sidewall modulation of photonic nanowire waveguides are a good solution for
on-chip narrowband operation with reasonable requirements in fabrication and
scalability. In this work we report on their implementation and optimization in
thin film lithium niobate, a photonic platform that affords reconfigurability
by exploiting electrooptic effects. The phase-shifted Bragg grating filters
have a footprint smaller than 1 {\mu}m x 1mm and operate at telecom
wavelengths, featuring extinction ratios up to 25 dB. We demonstrate
transmission bandwidths as narrow as 14.4 pm ($Q = 1.1$ x $10^5$) and 8.8 pm
($Q = 1.76$ x $10^5$) in critically coupled structures and multi-wavelength
Fabry-Perot configurations, respectively, in full agreement with theoretical
predictions. Moreover, by taking advantage of the strong electrooptic effect in
lithium niobate, in combination with the tight light confinement of
nanophotonic wires and the ultranarrow spectral resonances of optimized grating
structures, we demonstrate a tunability of 25.1pm/V and a record modulation of
the filter transmission amounting to 1.72 dB/V at CMOS voltages. The results
pave the way for reconfigurable narrowband photonic filters in lithium niobate
with small footprint and low consumption, to be exploited towards on-chip
quantum and nonlinear optics, as well as optical sensing and microwave
photonics.
