  We present an integrated semiconductor-dielectric hybrid dual-frequency laser
operating in the 1.5 $\mu$m wavelength range for microwave and terahertz (THz)
generation. Generating a microwave beat frequency near 11 GHz, we observe a
record-narrow intrinsic linewidth as low as about 2 kHz. This is realized by
hybrid integration of a single diode amplifier based on indium phosphide (InP)
with a long, low-loss silicon nitride (Si$_3$N$_4$) feedback circuit to extend
the cavity photon lifetime, resulting in a cavity optical roundtrip length of
about 30 cm on a chip. Simultaneous lasing at two frequencies is enabled by
introducing an external control parameter for balancing the feedback from two
tunable, frequency-selective Vernier mirrors on the Si$_3$N$_4$ chip. Each
frequency can be tuned with a wavelength coverage of about 80 nm, potentially
allowing for the generation of a broad range of frequencies in the microwave
range up to the THz range.
