Analysis of optical waveguides using Mathematica (R)

Costa, João Crisóstomo Weyl Albuquerque; Pereira, Deidre; Giarola, A.J.

doi:10.1109/sbmomo.1997.646832

Cited by 2 publications

(1 citation statement)

References 3 publications

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“…In this context, the analysis is mostly done using computer simulation 3 and Computer Algebra Systems ("CASs"). 4 Although these techniques make the analysis less cumbersome -and thus less error-prone, due to the nature of numerical algorithms and large set of unverified simplification algorithms, 5 one should not rely solely on these traditional techniques, especially when used in safety-critical areas (e.g., laser surgery), where system flaws may result in the loss of human lives.…”

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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Section: Introductionmentioning

confidence: 99%