Optique non-linéaire from Coursera

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Syllabus

De l'optique lineaire à l'optique non-lineaire

Après une brève description de l’origine microscopique de la réponse linéaire d’un matériau, ce chapitre introduira l’origine physique de l’absorption et de l’indice de réfraction. On montrera ensuite comment un régime d’excitation plus élevé impose de sortir du cadre d’une réponse strictement linéaire. Enfin, une introduction au langage Scilab permettra de disposer d’un outil de calcul numérique qui sera utilisé dans toute la suite du cours.

Transformation de Fourier

On introduira successivement les séries et les transformées de Fourier. L’analyse de Fourier d’un signal sonore nous permettra d’illustrer un certain nombre de propriétés utiles comme par exemple la relation entre largeur temporelle et largeur spectrale, qui sera approfondie en TD. On introduira également des notions importantes comme le retard de groupe et la dérive de fréquence. Enfin, la transformée de Fourier discrète permettra d’illustrer ces notions de manière numérique.

Propagation en régime linéaire (domaine temporel)

On établira l’équation de propagation en régime linéaire à partir des équations de Maxwell, puis on discutera plus en détail le cas particulier d’une onde plane. On étudiera ainsi la propagation d’une impulsion brève, dominée par la dispersion chromatique de l’indice de réfraction. Le rôle central joué par la phase spectrale sera illustrée en TD et par des expériences d’interférométrie.

Propagation en régime linéaire (domaine spatial)

Ce chapitre est consacré au cas particulier d’un faisceau monochromatique, ce qui permet d’étudier en détail l’évolution du profil spatial au cours de la propagation dans le cadre de l’approximation paraxiale. On développera notamment l’analogie spatio-temporelle, qui permettra de faire le parallèle entre la diffraction d’un faisceau lumineux et la dispersion d’une impulsion brève.

Propagation en régime non-linéaire

On aborde ici le régime non-linéaire, qui sera traité tout d’abord dans le cas d’une superposition d’ondes monochromatiques. On obtient alors un système d’équations différentielles non-linéaires couplées. Puis, dans le cas d’une impulsion brève, on établira l’équation de propagation non-linéaire dans le cadre de l’approximation de l’onde lentement variable. On discutera enfin de l’influence de la symétrie du matériau sur la nature de sa réponse optique non-linéaire.

Doublage de fréquence

L’optique non-linéaire du deuxième ordre donne lieu à des processus comme l’addition et la différence de fréquences. Ce chapitre porte sur le cas particulier du doublage de fréquence, ou génération de seconde harmonique. On introduira notamment la notion d’accord de phase, qui peut être obtenu par exemple à l’aide d’un matériau biréfringent. La méthode alternative dite du quasi accord de phase sera développée en TD.

Mélange à trois ondes

Toujours dans le cadre de l’optique non-linéaire du deuxième ordre, le mélange à trois ondes permet de comprendre l’origine physique du phénomène d’amplification paramétrique, qui permet notamment de concevoir des sources lumineuses accordables sur une très grande gamme spectrale. Les applications en optique quantique seront également brièvement évoquées. Le TD portera sur le doublage de fréquence en régime fort.

Effet Kerr optique

L’optique non-linéaire du troisième ordre donne lieu à une très grande variété de phénomènes physiques, dont l’effet Kerr optique constitue un exemple emblématique résultant de la variation de l’indice de réfraction avec l’intensité lumineuse. On étudiera ici les conséquences dans le domaine spatial (autofocalisation) et spectro-temporel (génération de continuum spectral). Le TD portera sur l’effet Kerr optique effectif résultant d’une cascade de deux effets du second ordre.

Autres effets non-linéaires du troisième ordre

Ce chapitre porte sur la saturation d’absorption, l’absorption à deux photons, la fluorescence par excitation à deux photons et la génération de troisième harmonique. Les applications de certains de ces phénomènes à la microscopie non-linéaire d’objets biologiques seront illustrées par des résultats expérimentaux obtenus au Laboratoire d’Optique et Biosciences.

Lasers femtosecondes

Ce dernier chapitre introduit le phénomène à l’origine du fonctionnement stationnaire d’un laser femtoseconde, qui est un effet de type soliton permettant une compensation parfaite entre la dispersion de vitesse de groupe et l’effet Kerr optique. Les applications en métrologie à l’aide de peignes de fréquences seront également évoquées, de même que l’amplification à dérive de fréquence.

Examen final

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Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Exploitant les applications des lasers de femtosecondes, le cours offre un excellent aperçu pour ceux qui souhaitent comprendre les interactions laser-matière

Ce cours fournit une base solide pour les étudiants souhaitant poursuivre des recherches en optique non linéaire

Le cours comprend des exercices de travaux dirigés pour illustrer les concepts théoriques, ce qui facilite la compréhension des étudiants

Le cours nécessite une compréhension préalable de l'optique linéaire, ce qui peut être un obstacle pour les étudiants sans formation préalable dans ce domaine

Reviews summary

Highly rated nonlinear optics course

This course on nonlinear optics has received exceptional reviews from students, with all six reviews giving it a perfect score of 5 out of 5. Students have praised the course for its detailed content, clear explanations, and relevance to their research. Overall, this course is highly recommended for anyone interested in learning about nonlinear optics.

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Optique non-linéaire with these activities:

Review Fourier analysis

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Review Fourier analysis to refresh your knowledge and better prepare you to understand the material in this course.

Browse courses on Fourier Analysis

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Read your notes or textbook on Fourier analysis.
Go online and find some practice problems on Fourier analysis.
Take a practice quiz on Fourier analysis.

Follow a tutorial on using a nonlinear optics software package

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Follow a tutorial on using a nonlinear optics software package to gain hands-on experience with the material in this course.

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Find a tutorial on using a nonlinear optics software package.
Follow the steps in the tutorial.
Use the software package to solve a problem.

Join a study group and discuss nonlinear optics concepts

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Join a study group and discuss nonlinear optics concepts to reinforce your understanding of the material in this course.

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Find a study group or form your own.
Meet with your study group regularly to discuss nonlinear optics concepts.
Work together to solve problems and answer questions.

Five other activities

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Organize and review your notes and assignments

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Organize and review your notes and assignments to better prepare for this course.

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Gather all of your notes and assignments for this course.
Organize them into a logical order.
Review them regularly.

Solve practice problems on nonlinear optics

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Solve practice problems on nonlinear optics to reinforce your understanding of the material in this course.

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Find a textbook or online resource with practice problems on nonlinear optics.
Work through the problems on your own.
Check your answers against the solutions provided in the textbook or online resource.

Write a summary of a research paper on nonlinear optics

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Write a summary of a research paper on nonlinear optics to deepen your understanding of the material in this course and improve your writing skills.

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Find a research paper on nonlinear optics that you find interesting.
Read the paper carefully and take notes.
Write a summary of the paper, including the main findings and conclusions.

Volunteer at a research lab that works on nonlinear optics

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Volunteer at a research lab that works on nonlinear optics to gain hands-on experience with the material in this course.

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Find a research lab that works on nonlinear optics.
Contact the lab and inquire about volunteer opportunities.
Attend the volunteer training program.
Work with the lab staff on nonlinear optics projects.

Contribute to an open-source nonlinear optics project

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Contribute to an open-source nonlinear optics project to gain hands-on experience with the material in this course and improve your programming skills.

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Find an open-source nonlinear optics project to contribute to.
Fork the project on GitHub.
Make changes to the project.
Submit a pull request to the project.
Work with the project maintainers to get your changes merged.

Career center

Learners who complete Optique non-linéaire will develop knowledge and skills that may be useful to these careers:

Nonlinear Optics Researcher

Nonlinear Optics Researchers study the behavior of light in nonlinear materials, which are materials that exhibit a nonlinear relationship between the electric field and the polarization. This course can help lay the foundation for a career in this field by providing a thorough understanding of the fundamental principles of nonlinear optics.

See salaries and explore the career path for Nonlinear Optics Researcher

Nonlinear Optics Device Engineer

Nonlinear Optics Device Engineers design and develop devices that use nonlinear optics to perform various functions, such as frequency conversion, optical switching, and optical amplification. This course can help lay the foundation for a career in this field by providing a thorough understanding of the fundamental principles of nonlinear optics.

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Laser Engineer

Laser Engineers specialize in the design, development, implementation, and maintenance of laser systems and their components. This course can help lay the foundation for a career in this field by providing a thorough understanding of the fundamental principles of nonlinear optics. Knowledge of nonlinear optics is particularly important for Laser Engineers who work with high-intensity lasers.

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Laser Physicist

Laser Physicists study the physics of lasers, which are devices that emit coherent light. This course can help build a foundation for a career in this field by providing a good understanding of the fundamental principles of nonlinear optics, which is used in many types of lasers.

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Optical Engineer

Optical Engineers design and develop optical systems, which are used in a wide variety of applications, including imaging, spectroscopy, and telecommunications. This course can help prepare you for a career in this field by providing a solid understanding of the principles of nonlinear optics, which is used in many advanced optical systems.

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Photonics Engineer

Photonics Engineers design and develop devices and systems that use light to perform various functions, such as transmitting data, generating images, and detecting objects. This course can help build a foundation for a career in this field by providing a good understanding of the fundamental principles of nonlinear optics, which is used in many photonics devices.

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Ultrafast Optics Researcher

Ultrafast Optics Researchers study the behavior of light on ultrafast timescales, which are timescales on the order of femtoseconds or picoseconds. This course can help prepare you for a career in this field by providing a solid understanding of the principles of nonlinear optics, which is used in many ultrafast optics applications.

See salaries and explore the career path for Ultrafast Optics Researcher

Quantum Optics Engineer

Quantum Optics Engineers design and develop devices and systems that use the principles of quantum mechanics to manipulate light. This course can help prepare you for a career in this field by providing a solid understanding of the principles of nonlinear optics, which is used in many quantum optics applications.

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Biomedical Optics Engineer

Biomedical Optics Engineers design and develop optical devices and systems for use in medical applications, such as imaging, diagnostics, and therapy. This course may be useful for those interested in this field, as it provides a good understanding of the principles of nonlinear optics, which is used in some biomedical optics applications.

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Materials Scientist

Materials Scientists study the properties of materials and develop new materials with improved properties. This course may be useful for those interested in this field, as it provides a good understanding of the principles of nonlinear optics, which is used to study the optical properties of materials.

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Optical Communications Engineer

Optical Communications Engineers design and develop optical communication systems, which are used to transmit data over long distances. This course may be useful for those interested in this field, as it provides a good understanding of the principles of nonlinear optics, which is used in some optical communication systems.

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Scientist

Scientists conduct research to advance our understanding of the world around us. This course may be useful for those interested in this field, as it provides a good understanding of the principles of nonlinear optics, which is used in many areas of science.

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Engineer

Engineers design, develop, and maintain systems, machines, and structures. This course may be useful for those interested in this field, as it provides a good understanding of the principles of nonlinear optics, which is used in many engineering applications.

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Physicist

Physicists study the fundamental laws of nature and the behavior of matter and energy. This course may be useful for those interested in this field, as it provides a good understanding of the principles of nonlinear optics, which is used in many areas of physics.

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Professor

Professors teach and conduct research at universities and colleges. This course may be useful for those interested in this field, as it provides a good understanding of the principles of nonlinear optics, which is a topic that is often taught at the university level.

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