Formal Analysis of Optical Waveguides in HOL

Hasan, Osman; Afshar, Sanaz Khan; Tahar, Sofiène

doi:10.1007/978-3-642-03359-9_17

Cited by 13 publications

(6 citation statements)

References 11 publications

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“…Here, we describe the most relevant works for analyzing optical systems using theorem proving. The pioneering work about the formal analysis of optical waveguides has been reported in [13]. However, this work is primarily based on real analysis in HOL4 which is insufficient to capture the dynamics of the real photonic systems which involve complex-valued electric and magnetic fields.…”

Section: Related Workmentioning

confidence: 99%

On the Formal Analysis of Photonic Signal Processing Systems

Siddique¹,

Tahar²

2015

Formal Methods for Industrial Critical Systems

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Abstract. Photonic signal processing is an emerging area of research, which provides unique prospects to build high-speed communication systems. Recent advancements in fabrication technology allow on-chip manufacturing of signal processing devices. This fact has lead to the widespread use of photonics in industrial critical applications such as telecommunication, biophotonics and aerospace. One the most challenging aspects in the photonics industry is the accurate modeling and analysis of photonic devices due to the complex nature of light and optical components. In this paper, we propose to use higher-order-logic theorem proving to improve the analysis accuracy by overcoming the known limitations of incompleteness and soundness of existing approaches (e.g., paper-and-pencil based proofs and simulation). In particular, we formalize the notion of transfer function using the signal-flow-graph theory which is the most fundamental step to model photonic circuits. Consequently, we formalize and verify the important properties of the stability and the resonance of photonic systems. In order to demonstrate the effectiveness of the proposed infrastructure, we present the formal analysis of a widely used double-coupler double-ring (DCDR) photonic processor.

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Section: Related Workmentioning

confidence: 99%

On the Formal Analysis of Photonic Signal Processing Systems

Siddique¹,

Tahar²

2015

Formal Methods for Industrial Critical Systems

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“…In [37], we presented the formal analysis of optical waveguide using the HOL4 theorem prover [25]. This work was rather a feasibility study of applying theorem proving in the domain of optics with the specific example of rectangular waveguides.…”

Section: Proposed Approachmentioning

confidence: 99%

“…Moreover, it was primarily based on the real analysis which is insufficient to capture the dynamics of most optical and photonic systems. After [37], we realized that the recent developments of multivariate analysis formalization in the HOL Light [35] theorem prover is a far better choice for optical system analysis. Currently available multivariate analysis theories can be built upon to develop all the mathematical requirements, given in Figure 1.…”

Section: Proposed Approachmentioning

confidence: 99%

Formal Analysis of Optical Systems

et al. 2014

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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).

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“…For the first time, in 2009, Hasan et al 8 presented the idea of formalizing optics using theorem proving by formal analysis of a planar waveguide. However, the authors considered the electromagnetic field equations of the planar waveguide as real functions, which make the formal definition of electromagnetic fields not general enough to address many applications.…”

Section: Introductionmentioning

confidence: 99%

“…The formal analysis of optical systems has gained some interest from the community recently (e.g., [8][9][10] ). For the first time, in 2009, Hasan et al 8 presented the idea of formalizing optics using theorem proving by formal analysis of a planar waveguide.…”

Section: Introductionmentioning

confidence: 99%

Formal analysis of electromagnetic optics

Khan-Afshar¹,

Hasan²,

Tahar³

2014

SPIE Proceedings

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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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Formal Analysis of Optical Waveguides in HOL

Cited by 13 publications

References 11 publications

On the Formal Analysis of Photonic Signal Processing Systems

On the Formal Analysis of Photonic Signal Processing Systems

Formal Analysis of Optical Systems

Formal analysis of electromagnetic optics

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