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Gires–Tournois etalon

Gires–Tournois etalon is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Gires–Tournois etalon rather than just read about it. In short: In optics, a Gires–Tournois etalon (also known as Gires–Tournois interferometer) is a transparent plate with two reflecting surfaces, one of which has very high reflectivity, ideally unity. Due to multiple-beam interference, light incident on a Gires–Tournois etalon is (almost) completely reflected, but has an effective phase shift that depends strongly on the wavelength of the light.

Gires–Tournois etalon — main illustration
Gires–Tournois etalon — illustration

Key takeaways

  • Gires–Tournois etalon belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Gires–Tournois etalon to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Gires–Tournois etalon from memory before moving on to harder problems.

Reference excerpt

In optics, a Gires–Tournois etalon (also known as Gires–Tournois interferometer) is a transparent plate with two reflecting surfaces, one of which has very high reflectivity, ideally unity. Due to multiple-beam interference, light incident on a Gires–Tournois etalon is (almost) completely reflected, but has an effective phase shift that depends strongly on the wavelength of the light. The complex amplitude reflectivity of a Gires–Tournois etalon is given by

r = − r 1 − e − i δ 1 − r 1 e − i δ {\displaystyle r=-{\frac {r_{1}-e^{-i\delta }}{1-r_{1}e^{-i\delta }}}}

where:

r1 is the complex amplitude reflectivity of the first surface,

δ = 4 π λ n t cos ⁡ θ t {\displaystyle \delta ={\frac {4\pi }{\lambda }}nt\cos \theta _{t}} , n is the index of refraction of the plate, t is the thickness of the plate, θt is the angle of refraction the light makes within the plate, and λ is the wavelength of the light in vacuum.

Nonlinear effective phase shift

Suppose that r 1 {\displaystyle r_{1}} is real. Then | r | = 1 {\displaystyle |r|=1} , independent of δ {\displaystyle \delta } . This indicates that all the incident energy is reflected and intensity is uniform. However, the multiple reflection causes a nonlinear phase shift Φ {\displaystyle \Phi } . To show this effect, we assume r 1 {\displaystyle r_{1}} is real and r 1 = R {\textstyle r_{1}={\sqrt {R}}} , where R {\displaystyle R} is the intensity reflectivity of the first surface. Define the effective phase shift Φ {\displaystyle \Phi } through

r = e i Φ . {\displaystyle r=e^{i\Phi }.}

One obtains

tan ⁡ ( Φ 2 ) = − 1 + R 1 − R tan ⁡ ( δ 2 ) {\displaystyle \tan \left({\frac {\Phi }{2}}\right)=-{\frac {1+{\sqrt {R}}}{1-{\sqrt {R}}}}\tan \left({\frac {\delta }{2}}\right)}

For R = 0, no reflection from the first surface and the resultant nonlinear phase shift is equal to the round-trip phase change ( Φ = δ {\displaystyle \Phi =\delta } ) – linear response. However, as can be seen, when R is increased, the nonlinear phase shift Φ {\displaystyle \Phi } gives the nonlinear response to δ {\displaystyle \delta } and shows step-like behavior. Gires–Tournois etalon has applications for laser pulse compression and nonlinear Michelson interferometer. Gires–Tournois etalons are closely related to Fabry–Pérot etalons. This can be seen by examining the total reflectivity of a Gires–Tournois etalon when the reflectivity of its second surface becomes smaller than 1. In these conditions the property | r | = 1 {\displaystyle |r|=1} is not observed anymore: the reflectivity starts exhibiting a resonant behavior which is characteristic of Fabry-Pérot etalons.

References F. Gires, and P. Tournois (1964). "Interferometre utilisable pour la compression d'impulsions lumineuses modulees en frequence". C. R. Acad. Sci. Paris. 258: 6112–6115. (An interferometer useful for pulse compression of a frequency modulated light pulse.) Gires–Tournois Interferometer in RP Photonics Encyclopedia of Laser Physics and Technology

Illustrations

Gires–Tournois etalon: Schematic of a Gires-Tournois etalon when light impinges at normal incidence on the first reflecting plate.
Schematic of a Gires-Tournois etalon when light impinges at normal incidence on the first reflecting plate.
Gires–Tournois etalon: Nonlinear phase shift Φ as a function of δ for R = 0, 0.1, 0.5, and 0.9
Nonlinear phase shift Φ as a function of δ for R = 0, 0.1, 0.5, and 0.9
Gires–Tournois etalon: Amplitude reflectivity and group delay induced by a Gires-Tournois interferometer with the intensity reflectivity of the first surface being R = 0.3 {\textstyle R=0.3} and that of the second surface being R 2 = 1 {\textstyle R_{2}=1} , i.e. as for a perfect reflector (blue line). In this case the amplitude reflectivity is unity for all frequencies and the resonant behavior of the interferometer is observed only in the imparted group delay. As R 2 {\displaystyle R_{2}} becomes smaller than 1 (red and green lines), for instance due to losses at the reflector, the Gires-Tournois interferometer starts behaving as a Fabry-Pérot etalon. Other parameters of the calculation are t = 30   μm {\textstyle t=30\ {\text{μm}}} , n = 1 {\textstyle n=1} and θ t = 0 {\textstyle \theta _{t}=0} .
Amplitude reflectivity and group delay induced by a Gires-Tournois interferometer with the intensity reflectivity of the first surface being R = 0.3 {\textstyle R=0.3} and that of the second surface being R 2 = 1 {\textstyle R_{2}=1} , i.e. as for a perfect reflector (blue line). In this case the amplitude reflectivity is unity for all frequencies and the resonant behavior of the interferometer is observed only in the imparted group delay. As R 2 {\displaystyle R_{2}} becomes smaller than 1 (red and green lines), for instance due to losses at the reflector, the Gires-Tournois interferometer starts behaving as a Fabry-Pérot etalon. Other parameters of the calculation are t = 30   μm {\textstyle t=30\ {\text{μm}}} , n = 1 {\textstyle n=1} and θ t = 0 {\textstyle \theta _{t}=0} .

Worked examples

Example 1 — a first encounter with Gires–Tournois etalon

Start with the simplest possible case. Write down what Gires–Tournois etalon claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Gires–Tournois etalon before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Gires–Tournois etalon ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Gires–Tournois etalon

In research
Gires–Tournois etalon appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Gires–Tournois etalon in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Gires–Tournois etalon is common in secondary-school and first-year university syllabi. It links to neighbouring topics Interferometers, Optical components, so understanding it makes those chapters shorter.
In everyday life
Look for Gires–Tournois etalon outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Gires–Tournois etalon in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Gires–Tournois etalon means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Gires–Tournois etalon out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Gires–Tournois etalon in simple terms?

In optics, a Gires–Tournois etalon (also known as Gires–Tournois interferometer) is a transparent plate with two reflecting surfaces, one of which has very high reflectivity, ideally unity. Due to multiple-beam interference, light incident on a Gires–Tournois etalon is (almost) completely reflected…

Why does Gires–Tournois etalon matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Gires–Tournois etalon?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Gires–Tournois etalon.

Tags

  • Interferometers
  • Optical components

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