  We demonstrate a combination of optical and electronic feedback that
significantly narrows the linewidth of distributed Bragg reflector lasers
(DBRs). We use optical feedback from a long external fiber path to reduce the
high-frequency noise of the laser. An electro-optic modulator placed inside the
optical feedback path allows us to apply electronic feedback to the laser
frequency with very large bandwidth, enabling robust and stable locking to a
reference cavity that suppresses low-frequency components of laser noise. The
combination of optical and electronic feedback allows us to significantly lower
the frequency noise power spectral density of the laser across all frequencies
and narrow its linewidth from a free-running value of 1.1 MHz to a stabilized
value of 1.9 kHz, limited by the detection system resolution. This approach
enables the construction of robust lasers with sub-kHz linewidth based on DBRs
across a broad range of wavelengths.
