  Visible light integrated photonics is emerging as a promising technology for
the realization of optical devices for applications in sensing, quantum
information and communications, imaging and displays. Among the existing
photonic platforms, high-index contrast silicon nitride ($Si_{3}N_{4}$)
waveguides offer broadband transparency in the visible spectral range and a
high scale of integration. As far as the complexity of photonic integrated
circuits (PICs) increases, on-chip detectors are required to monitor their
working point for reconfiguration and stabilization operations. In this work we
present a compact in-line power monitor integrated in $Si_{3}N_{4}$ waveguides
that operates in the red-light wavelength range (660 nm). The proposed device
exploits the photoconductivity of a hydrogenated amorphous silicon (a-Si:H)
film employed as a coating layer of the optical waveguide. Experimental results
show a responsivity of 30 mA/W, a sensitivity of -45 dBm and a sub-${\mu}$s
time response. These features enable the use of the proposed photoconductor for
high-sensitivity monitoring and control of visible-light $Si_{3}N_{4}$ PICs.
