phy 452/562 lasers and modern opticsqit.physics.sunysb.edu/wp-content/uploads/2013/06/ph452... ·...
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Prof. Eden Figueroa
Lecture 5: Fabry-Perot resonators
PHY 452/562 Lasers and Modern Optics
Sept 10th 2013
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Experimental Intermezzo. Optical resonators. Fabry‐Perot theory. Resonator’s stability. Applications.
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Experimental Intermezzo
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This is one of the experiments to be performed in the lab:
Assume a beam propagating in the z‐direction with a Gaussian intensity profile:
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The total power in the beam is:
Consider the knife edge being translated in the x‐direction
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Making the substitutions:
Here we use the definition of the error function:
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To fit the data, we have to use a fitting function of the form:
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Fabry‐Perot resonators
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The first interferometer was constructed by Fabry and his colleague, Alfred Perot, in 1897.
It consisted of two perfectly flat glass plates coated on their parallel facing surfaces with thin silver films.
Alfred PerotCharles Fabry
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Jamin’s interferometer ‐ 1856 Mach‐Zehnder interferometer ‐ 1892
Michelson interferometer ‐ 1882 The multi‐beam interferometer by A. Fabryand Ch. Perot, 1897
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Fabry‐Perot Interferometers
• A cavity with highly reflective mirrors parallel to each other Acts like a resonator • Also called etalon
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Fabry‐Perot interferometers
reflected
incident
transmitted
Resonance condition: reflected wave = 0
⇔ all reflected waves interfere destructively
wavelength in free space
refractive index
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Relation between r, r’and t, t’ (Stokes relations)
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Calculation of the reflected wave
air glass air
incoming
reflected
transmitted
transmitted
reflected
reflected
reflected
reflected
transmitted transmitted
transmitted
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Calculation of the reflected wave
Use Stokes relationships
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Transmission & reflection coefficients
reflectioncoefficient
transmissioncoefficient