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The source angle localization problem is studied based on scattering of elastic waves in two dimensions by a phononic array and the exceptional points of its band structure. Exceptional points are complex singularities of a parameterized eigen-spectrum, where two modes coalesce with identical mode shapes. These special points mark the qualitative transitions in the system behavior and have been proposed for sensing applications. The equi-frequency band structures are analyzed with focus on the angle-dependent modal behaviors. At the exceptional points and critical angles, the eigen-modes switch their energy characteristics and symmetry, leading to enhanced sensitivity as the scattering response of the medium is inherently angle-dependent. An artificial neural network is trained with randomly weighted and superposed eigen-modes to achieve deep learning of the angle-dependent dynamics. The trained algorithm can accurately classify the incident angle of an unknown scattering signal, with minimal sidelobe levels and suppressed main lobewidth. The neural network approach shows superior localization performance compared with standard delay-and-sum technique. The proposed application of the phononic array highlights the physical relevance of band topology and eigen-modes to a technological application, adds extra strength to the existing localization methods, and can be easily enhanced with the fast-growing data-driven techniques.
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Differentiable scattering matrix for optimization of photonic structures
The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the structure’s optical performance changes with respect to design parameters, that is, the scattering matrix’s derivatives (or gradient). Here we address this need. We present a new algorithm for computing scattering matrix derivatives accurately and robustly. In particular, we focus on the computation in semi-analytical methods (such as rigorous coupled-wave analysis). To compute the scattering matrix of a structure, these methods must solve an eigen-decomposition problem. However, when it comes to computing scattering matrix derivatives, differentiating the eigen-decomposition poses significant numerical difficulties. We show that the differentiation of the eigen-decomposition problem can be completely sidestepped, and thereby propose a robust algorithm. To demonstrate its efficacy, we use our algorithm to optimize metasurface structures and reach various optical design goals.
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- PAR ID:
- 10203945
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Express
- Volume:
- 28
- Issue:
- 25
- ISSN:
- 1094-4087; OPEXFF
- Format(s):
- Medium: X Size: Article No. 37773
- Size(s):
- Article No. 37773
- Sponsoring Org:
- National Science Foundation
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