  The heterogeneous integration of silicon with III-V materials provides a way
to overcome silicon's limited optical properties toward a broad range of
photonic applications. Hybrid modes are a promising way to make heterogeneous
Si/III-V devices, but it is still unclear how to engineer these modes to make
photonic crystal cavities. Herein, using 3D finite-difference time-domain
simulation, a hybrid Si-GaAs photonic crystal cavity design enables cavity mode
confinement in GaAs without directly patterning that operates at telecom
wavelengths. The hybrid cavity consists of a patterned silicon waveguide
nanobeam that is evanescently coupled to a GaAs slab with quantum dots. We show
that by engineering the hybrid modes, we can control the degree of coupling to
the active material, which leads to a tradeoff between cavity quality factor
and optical gain and nonlinearity. With this design, we demonstrate a cavity
mode in the Si-GaAs heterogeneous region, which enables strong interaction with
the quantum dots in the GaAs slab for applications such as low-power-threshold
lasing and optical bistability (156 nW and 18.1 ${\mu}$W, respectively). This
heterogeneous integration of an active III-V material with silicon via a hybrid
cavity design suggests a promising approach for achieving on-chip light
generation and low-power nonlinear platforms.
