(G. Gaullier et al., Univ. Grenoble Alpes – CEA LETI, Grenoble, France)
Shape optimization techniques were quite recently applied to photonic components [1] but to the best of our knowledge, no application to optical computing has been reported yet. Here, the issue of performing a matrix-vector product by shape optimized components is addressed. Driven by the circuit designs available for modelling a unitary or orthogonal matrix by conventional Mach Zehnder Interferometers (MZI) [2], a gain less real matrix is considered through its singular value decomposition.
The shape optimized circuit (see Figure) is made from a reduced set of building blocks, namely 50/50 couplers, phase shifters, S-bends and pure attenuators. For each unitary component, the piecewise constant optical index of materials representing a shape is recovered by looking for the best (in the sense of the local optimization criteria) position of the interface [3]. The criteria used are based on the real and imaginary parts of the scattering parameters.
Schematic view of a circuit relative to a 4 × 5 matrix comprising MZI (blue hexagons), pure phase shifters (blue squares), attenuation (in magenta).
During the NUSOD-20 Conference, I will detail the methodology and present the unconventional shapes obtained by optimization that leads to very compact components and to an expected footprint reduction by a factor of ~ 2000 in comparison with a conventional MZI based circuit.
[1] J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics”, Laser Photonics Rev., vol. 5, no. 2, pp. 308–321, (2011). [2] W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, et I. A. Walmsley, “An Optimal Design for Universal Multiport Interferometers”, Optica, vol. 3, n° 12, pp. 1460-1465 (2016) [3] N. Lebbe, C. Dapogny, E. Oudet, K. Hassan, et A. Gliere, “Robust shape and topology optimization of nanophotonic devices using the level set method”, J. Comput. Phys., vol. 395, pp. 710-746, (2019).
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