Source-linked AI summary
Nanophotonic Computational Design
Jesse Lu, Jelena Vuckovic
TL;DR
Nanophotonic components are difficult to design by hand when complex, robust devices require many parameters. The paper introduces a full-parameter-space, design-by-specification method that generates linear devices without manual tuning, demonstrating compact, efficient, manufacturable, and robust structures across varied functionalities.
Problem
Conventional nanophotonic design hand-tunes a small number of parameters, while increasingly complex and robust optical networks require many more.
Method
The method formulates user performance specifications as hard design objectives over a full three-dimensional parameter space, without manual tuning.
Results
The method produces fully three-dimensional, multi-modal, compact, efficient, novel, and manufacturable devices, including structures robust to wavelength, temperature, and fabrication shifts.
Takeaways & Limitations
Devices can be designed solely from specified functionality and performance, suggesting the method may apply broadly across linear nanophotonic devices.
Takeaways & Limitations
The demonstrated results use planar 250 nm etched silicon slabs surrounded by silica with fixed permittivity values.
Abstract
from arXiv · showhide
In contrast to designing nanophotonic devices by tuning a handful of device parameters, we have developed a computational method which utilizes the full parameter space to design linear nanophotonic devices. We show that our method may indeed be capable of designing any linear nanophotonic device by demonstrating designed structures which are fully three-dimensional and multi-modal, exhibit novel functionality, have very compact footprints, exhibit high efficiency, and are manufacturable. In addition, we also demonstrate the ability to produce structures which are strongly robust to wavelength and temperature shift, as well as fabrication error. Critically, we show that our method does not require the user to be a nanophotonic expert or to perform any manual tuning. Instead, we are able to design devices solely based on the users desired performance specification for the device.
1. Introduction
Nanophotonic design is shifting from hand-tuning a few parameters toward computational use of the full design space. The proposed design-by-specification method produces complex linear devices from user performance requirements without manual tuning.
- Increasingly complex, dense, and robust optical networks require nanophotonic components designed with more parameters than conventional hand-tuning uses.
- Larger parameter spaces can enable smaller and higher-performance devices, but their complexity prevents effective manual search.
- The method uses the full three-dimensional parameter space to design linear nanophotonic components without user intervention or manual tuning.
- The method produces devices that are extremely compact, highly efficient, functionally novel, and robust to wavelength, temperature, and fabrication shifts.
- Designs are generated solely from specified functionality and performance, suggesting applicability to linear nanophotonic devices broadly.
2. Problem formulation
The formulation prioritizes user-specified optical performance as a hard design constraint while allowing non-zero physics residuals. Performance is expressed through bounded field-overlap amplitudes for selected output patterns.
- The design problem is formulated to use the full parameter space and depend solely on the user’s performance specification.
- The objective-first formulation prioritizes the design objective over exact satisfaction of the electromagnetic physics equations.It therefore permits non-zero physics residuals and can even allow an unphysical field when the residual is not exactly zero.
- Field-overlap constraints encode device performance by forcing amplitudes at output ports to lie between user-defined bounds.The overlaps combine each mode’s electric field with user-chosen output fields, and multiple fields can be specified.
- The structure variable is relaxed from binary material values to bounded values during formulation, then serves as the design objective.
3. Method of solution
The method solves the formulation iteratively with ADMM, alternating updates of electromagnetic fields, structure variables, and a dual variable. Hardware-accelerated three-dimensional FDFD computation and later boundary tuning support scalable, manufacturable designs.
- ADMM solves the formulation by iteratively updating the mode fields, structure variable, and dual variable.
- Three-dimensional field updates involve millions of variables and ill-conditioned matrices, so the method uses a hardware-accelerated iterative FDFD solver.
- The cloud-based solver is designed to scale to arbitrarily many modes without significant penalty.
- Structure updates are simpler because the considered structures are planar and therefore use only thousands of variables.
- The continuous structure is converted to a boundary parameterization and tuned with steepest descent to obtain a discrete, manufacturable design.
4. Results
The demonstrated devices use three-dimensional planar silicon-silica structures and combine novel functionality, high efficiency, compact footprints, manufacturability, and tolerance to operating and fabrication variation.
- The demonstrations use three-dimensional planar structures made from a 250 nm etched silicon slab surrounded by silica.The simulations use εSi = 12.25 and εSiO2 = 2.25.
- The produced designs combine novel functionality, high efficiency, compact footprints of only a few square vacuum wavelengths, and manufacturability.
- Devices can be designed to exhibit different functionality for different input excitations and to tolerate wavelength, temperature, and fabrication errors.
4.1. Mode converters
The method designs fully three-dimensional TE and TM waveguide mode converters from performance specifications, achieving compact footprints and strong mode rejection. The demonstrated converters support high-efficiency conversion into second-order modes, although conversion efficiency falls below the ≥90% target in both examples.
- Mode-converter functionality: The mode converters demonstrate high-efficiency conversion into second-order waveguide modes, supporting multi-mode on-chip optical networks.The TE and TM designs use fundamental-polarized inputs and second-order outputs, with rejection of the transmitted fundamental mode.
- TE mode converter: 1.6 × 2.4 microns at 1550 nm is the reported footprint and operating wavelength for the TE converter.
- TE mode converter: 86.4% conversion efficiency into the second-order mode was achieved for the TE converter, versus the ≥90% specification.Power remaining in the transmitted fundamental rejection mode was 0.7%, below the 1% allowance.
- Three-dimensional design: The TE and TM examples show that the method supports fully three-dimensional structures without approximations.The TM design required only changing the input and output mode polarization in the performance specification.
- TM mode converter: 76.9% conversion efficiency into the second-order mode was achieved for the TM converter, while fundamental-mode rejection was 1.0%.The lower TM efficiency may be attributed to lower confinement of TM modes in thin slabs.
4.2. Mode splitters
The method designs mode splitters that distinguish spatial profile, polarization, and wavelength, including a three-dimensional spatial splitter with a 2.8 × 2.8 micron footprint.
- Mode splitters can separate inputs by spatial profile, polarization, or wavelength.
- Spatial mode splitter: The spatial splitter targets over 90% desired-arm power and below 1% opposing-arm power.
- Spatial mode splitter: The demonstrated three-dimensional spatial splitter occupies a 2.8 × 2.8 micron footprint.
- TE/TM splitter: The TE/TM splitter separates fundamental TE- and TM-polarized modes into distinct output arms.
- Spatial mode splitter: 88.7% and 77.4% conversion efficiencies were achieved for the spatial splitter, with 0.27% and 0.20% rejection powers.
4.3. Hubs
The method designs multi-input, multioutput hubs that rearrange modes and route overlapping signals within a single layer, including wavelength-dependent switching.
- Hubs act as general cross-connect structures that rearrange modes between multiple input and output waveguides.
- 2×2×2 hub: A 2×2×2 hub switches between uncoupled and cross-coupled routing at 1550 nm and 1310 nm wavelengths.
4.4. Fiber couplers
The method designs compact and multifunctional fiber couplers that couple light into in-plane waveguides and combine coupling with spatial- or wavelength-mode splitting.
- Fiber couplers couple normally incident optical-fiber light into in-plane waveguides.
- Compact fiber coupler: A compact coupler overlaps in-plane coupling and focusing into a narrow waveguide within one footprint.
- Compact fiber coupler: 51.5% coupling efficiency was achieved for the compact fiber coupler, below its above-90% specification.
- Mode-splitting fiber coupler: The method combines fiber coupling with spatial mode splitting so different fiber modes enter different in-plane waveguides.
- Mode-splitting fiber coupler: The mode-splitting fiber coupler has lower efficiencies but demonstrates functionality not previously demonstrated.
- Wavelength-splitting fiber coupler: A wavelength-splitting fiber coupler couples different-wavelength fiber modes in-plane before splitting them into separate waveguides.
4.5. Broadband wavelength splitter
Broadband wavelength operation is achieved by specifying multiple target wavelengths, and the resulting splitter shows tolerance to temperature shifts and fabrication error.
- Performance of the original wavelength splitter quickly drops away from its target wavelengths.
- Broadband design: Adding multiple target wavelengths around the originals achieves broadband operation.
- Temperature robustness: Stable operating points persist over a temperature range of nearly 1000 K.
- Fabrication robustness: Up to 8 nm of over- or under-etching is sustained before performance falls below 70% at central operating wavelengths.
- Robustness: Broadband-device design appears to be a valid heuristic for seeking tolerance to temperature shifts and fabrication error.
5. Conclusion
The method designs fully three-dimensional, multimodal, compact, efficient, and manufacturable nanophotonic structures, including devices difficult or impossible to design by hand. It also produces broadband devices robust to temperature shifts and fabrication errors.
- The method designs fully three-dimensional and multi-modal structures with compact footprints, high efficiency, and manufacturability.
- Mode-splitting fiber couplers achieve 32.6% conversion efficiency for fundamental-mode input and 22.7% for third-order-mode input.
- The demonstrated devices include nanophotonic mode converters, splitters, hubs, and fiber couplers, many of which had not previously been demonstrated and cannot be designed by hand.
- The broadband device maintains stable operating wavelengths over temperature shifts up to 905 K and over-/under-etching errors up to 8 nm.
- The wavelength-splitting fiber coupler achieves 31.6% conversion efficiency at 1550 nm and 28.6% at 1310 nm.
- Broadband operation is enabled by adding multiple target wavelengths, while original central wavelengths retain greater than 70% efficiency despite up to 8 nm etch error.