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Nonlinear Fiber Optics

Lecture 1 : Maxwell’s Equations

Debanuj Chatterjee

Postdoctoral researcher, PhLAM, University of Lille, France

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Outline

  • Information on the course
    • IKAA
    • Short Summer Course pilot program
    • Registration
  • Student and Teacher introduction
  • What is fiber optics?
  • History of Maxwell’s equations
  • Helmholtz equation
  • Fizeau’s experiment

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What is an optical fiber?

Total internal reflection of light

There is a problem!

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From law to theory?

  • Total internal reflection of light
  • Taught as a special case of Snell’s law (incidence angle>critical angle)

But can we derive Snell’s law?

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Can you derive Snell’s law?

Willebrord Snellius (1621)

Christaan Huygens (1690)

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Can you derive Snell’s law?

Willebrord Snellius (1621)

Isaac Newton (1672)

Think about it!

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Gauss, Faraday, Ampere, etc.

Carl Friedrich Gauss(1835)

Andr Marie Ampere (1826)

Gauss’ law

Ampere’s law

Michael Faraday (1832)

Faraday’s law

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Maxwell’s Equations

James Clerk Maxwell (1873)

  • United the developments in electricity and magnetism into a single framework
  • Predicted electromagnetic waves can exist and propagate in vacuum
  • Calculated the speed of those waves

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Maxwell’s Equations

(Gauss)

(Ampere-Maxwell)

(Faraday-Maxwell)

(Gauss-Maxwell)

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Maxwell’s Equations

(Gauss)

(Ampere-Maxwell)

(Faraday-Maxwell)

(Gauss-Maxwell)

Olivier Heavyside (1880)

Olivier Heavyside concised 20 equations of Maxwell to 4 equations