  We present a digitized adjoint method for realizing efficient inverse design
of "digital" subwavelength nanophotonic devices. We design a single-mode 3-dB
power divider and a dual-mode demultiplexer to demonstrate the digitized
adjoint method for single-object and dual-object optimizations, respectively.
The optimization comprises three stages, a first stage of continuous variation
for an "analog" pattern, a second stage of forced permittivity biasing for a
"quasi-digital" pattern, and a third stage for a multi-level digital pattern.
Compared with conventional brute-force method, the proposed digitized adjoint
method can improve the design efficiency by about 5 times, and the performance
optimization can reach approximately the same level using the ternary pattern.
The digitized adjoint method takes the advantages of adjoint sensitivity
analysis and digital subwavelength structure and creates a new way for
efficient and high-performance design of compact digital subwavelength
nanophotonic devices. This method could overcome the efficiency bottleneck of
the brute-force method that is restricted by the number of pixels of a digital
pattern and improve the device performance by extending a conventional binary
pattern to a multi-level one, which may be attractive for inverse design of
large-scale digital nanophotonic devices.
