# Formal Stability Analysis of Optical Resonators

@inproceedings{Siddique2013FormalSA, title={Formal Stability Analysis of Optical Resonators}, author={Umair Siddique and Vincent Aravantinos and Sofi{\`e}ne Tahar}, booktitle={NASA Formal Methods}, year={2013} }

An optical resonator usually consists of mirrors or lenses which are configured in such a way that the beam of light is confined in a closed path. Resonators are fundamental components used in many safety-critical optical and laser applications such as laser surgery, aerospace industry and nuclear reactors. Due to the complexity and sensitivity of optical resonators, their verification poses many challenges to optical engineers. Traditionally, the stability analysis of such resonators, which is…

## 24 Citations

Formal Analysis of Geometrical Optics using Theorem Proving

- Physics
- 2015

Geometrical optics is a classical theory of Physics which describes the light propagation in the form of rays and beams.
One of its main advantages is efficient and scalable formalism for the…

Towards the formal analysis of microresonators based photonic systems

- Physics2014 Design, Automation & Test in Europe Conference & Exhibition (DATE)
- 2014

This paper provides a higher-order logic formalization of optical microresonators which are the most fundamental building blocks of many photonic devices and presents the formal analysis of 2-D microres onator lattice optical filters.

Stability Verification of Optical and Laser Resonators in HOL Light

- Physics
- 2014

Optical and laser resonators are widely used in optical communication, bio-sensors and aerospace systems. Ray optics provides an efficient formalism to analyze the stability properties of such…

Formal verification of stability and chaos in periodic optical systems

- Physics, Computer ScienceJ. Comput. Syst. Sci.
- 2017

A new approach for the verification of optical systems

- Computer Science, PhysicsOptics & Photonics - Optical Engineering + Applications
- 2013

This paper provides a higher-order logic (a language used to express mathematical theories) formalization of ray optics in the HOL Light theorem prover, and formalizes the notion of light ray and optical system mathematically in the software.

Towards ray optics formalization of optical imaging systems

- PhysicsProceedings of the 2014 IEEE 15th International Conference on Information Reuse and Integration (IEEE IRI 2014)
- 2014

This paper presents the ray optics formalization of cardinal points which are the most fundamental requirement to model imaging properties of optical systems and presents the verification of Cardinal points for a general system consisting of any number of optical components.

On the Formalization of Cardinal Points of Optical Systems

- Physics, Computer ScienceFormalisms for Reuse and Systems Integration
- 2015

The formalization of cardinal points which are the most fundamental requirement to model imaging properties are presented and the formal verification of the cardinal points for an arbitrary optical system consisting of any number of optical components is presented.

Formal modeling and verification of integrated photonic systems

- Physics, Computer Science2015 Annual IEEE Systems Conference (SysCon) Proceedings
- 2015

This work proposes a framework to formally specify and verify the critical properties of complex photonic systems within the sound core of a higher-order-logic theorem prover and presents the formal specification of a microring resonator based photonic filter.

On the formal analysis of Gaussian optical systems in HOL

- Physics, Computer ScienceFormal Aspects of Computing
- 2016

This paper presents the formalization of Gaussian beams and verify the corresponding properties such as beam transformation, beam waist radius and location, and builds formal reasoning support for the analysis of quasi-optical systems.

On the Formal Analysis of Photonic Signal Processing Systems

- Computer ScienceFMICS
- 2015

Higher-order-logic theorem proving is proposed to be used 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).

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