Optical systems are becoming increasingly important by resolving many bottlenecks in today's communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical system models using traditional paperand-pencil and computer simulation approaches sets limits especially in safety-critical applications. In order to overcome these limitations, we propose to employ higher-order-logic theorem proving as a complement to computational and numerical approaches to improve optical model analysis in a comprehensive framework. The proposed framework allows formal analysis of optical systems at four abstraction levels, i.e., ray, wave, electromagnetic, and quantum.Mathematics Subject Classification (2010). Primary (68T15,68Q60); Secondary (78A05,78A25, 81V80).

Abstract. In this paper, we report our first experiments in using learningassisted automated reasoning for the formal analysis of physical systems. In particular, we investigate the performance of automated proofs as compared to interactive ones done in HOL for the verification of ray and electromagnetic optics. Apart from automation, we also provide brief initial exploration of more general issues in formalization of physics, such as its presentation and foundations.

Optical systems are increasingly being used in safety-critical applications. Due to the complexity and sensitivity of optical systems, their verification raises many challenges for engineers. Traditionally, the analysis of such systems has been carried out by paper-and-pencil based proofs and numerical computations. However, these techniques cannot provide accurate results due to the risk of human error and inherent approximations of numerical algorithms. In order to overcome these limitations, we propose to use theorem proving (i.e., a computer-based technique that allows to express mathematical expressions and reason about their correctness by taking into account all the details of mathematical reasoning) as a complementary approach to improve optical system analysis. This paper provides a higher-order logic (a language used to express mathematical theories) formalization of electromagnetic optics in the HOL Light theorem prover. In order to demonstrate the practical effectiveness of our approach, we present the analysis of resonant cavity enhanced photonic devices.

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