Nikkhah V, Pirmoradi A, Ashtiani F, Edwards B, Aflatouni F, Engheta N, “Inverse-designed low-index-contrast structures on silicon photonics platform for vector-matrix multiplication”, Nature Photonics 18, (2024).
INVERSE-DESIGNED Analog Computing at Optical Frequencies
This work is the natural extension of the efforts in Inverse Design Analog Computing at RF Frequencies. The goal was to create optical meta-structures that perform complex vector-matrix multiplication using inverse design.
As an experimentalist in a theory group, I speak both languages fluently. I understand the complications of the theory, inverse-design, fabrication, and measurement. My role on this project was to coordinate the efforts of the graduate students and step in to do any work that was outside anyone else's skill set. As such, I’m grateful to the graduate students on the team: Vahid Nikkhah, Ali Pirmoradi, and Farshid Ashtiani.
RF and Silicon Photonics design both share Maxwell’s equations, and at first glance, they appear similar. Indeed, the same simulation tools can be used for both. However, in practice, they are often wrestling with very different problems. This stems from the lack of good conductors at optical frequencies. At RF frequencies, we can build PEC waveguides that will suppress all but the desired lowest order modes. However, in optics, low-loss waveguides are built from dielectric cores in a dielectric cladding. This cladding can support undesired radiating modes.
Previous efforts in Inverse Design have focused on simulating full 3D devices. There are some excellent examples of this from the group of Jelena Vuckovic. These simulations fully model radiation and thus can optimize the structure to avoid it. However, this comes at a significant computational expense, particularly at optical frequencies where the wavelength is very small, even compared to modest structures.
Necessity is the mother of invention. We needed to create structures with many ports in order to do vector-matrix multiplication. Simulated in 3D, these structures are going to be too large for inverse design. We needed to come up with a 2D approximation for silicon photonics that worked for inverse design.
The insight we brought to this work was that many commercial foundries provide various levels of etch. These are typically used for fabricating devices like grating couplers. However, a wave propagating in a slab of 220nm of silicon will have a higher mode index than a wave propagating in a slab of 150nm silicon. Likening it to the RF work, it as if the etched regions are a lower-index material. That metaphor can only be carried so far though. If the thickness difference is too large, there will be scattering into lost radiated modes. Regardless, assuming that the step height is sufficiently small that we can ignore these losses, then the entire system can be designed in 2D using an effective-index approximation, and very large structures can be simulated and designed in a manner not unlike our RF work.