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High resolution spectroscopy Fabry-Perot Interferometer Student: Victor-Cristian Palea Coordinator: Ș. L. Liliana Preda
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Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Oct 31, 2019

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Page 1: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

High resolution spectroscopy Fabry-Perot Interferometer

Student: Victor-Cristian Palea Coordinator: Ș. L. Liliana Preda

Page 2: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 3: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸1𝑑 𝐸2𝑑

𝐸3𝑑

𝐸4𝑑

…

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 4: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸1𝑑 𝐸2𝑑

𝐸3𝑑

𝐸4𝑑

…

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 5: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸1𝑑 𝐸2𝑑

𝐸3𝑑

𝐸4𝑑

…

𝐸1π‘Ÿ 𝐸2π‘Ÿ

𝐸3π‘Ÿ

𝐸4π‘Ÿ

𝐸5π‘Ÿ

…

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 6: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Source: https://physi.wordpress.com/tag/reflection/

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 7: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸1𝑑 𝐸2𝑑

𝐸3𝑑

𝐸4𝑑

…

𝐸1π‘Ÿ 𝐸2π‘Ÿ

𝐸3π‘Ÿ

𝐸4π‘Ÿ

𝐸5π‘Ÿ

…

t – transmission coefficient

t’ – transmission coefficient

r’ – reflection coefficient

r – reflection coefficient

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 8: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Source: References [1]

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 9: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸1𝑑 𝐸2𝑑

𝐸3𝑑

𝐸4𝑑

…

𝐸1π‘Ÿ 𝐸2π‘Ÿ

𝐸3π‘Ÿ

𝐸4π‘Ÿ

𝐸5π‘Ÿ

…

𝛿 =2πœ‹

πœ†02𝑛𝑑 βˆ™ cos πœƒ

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 10: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸1𝑑 𝐸2𝑑

𝐸3𝑑

𝐸4𝑑

…

𝐸1π‘Ÿ 𝐸2π‘Ÿ

𝐸3π‘Ÿ

𝐸4π‘Ÿ

𝐸5π‘Ÿ

…

πΈπ‘—π‘Ÿ = 𝐸0𝑑 π‘Ÿ 𝑑′ 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝐸𝑗𝑑 = 𝐸0𝑑 π‘Ÿ 𝑑′𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝐸1π‘Ÿ = 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘

𝛿 =2πœ‹

πœ†02𝑛𝑑 βˆ™ cos πœƒ

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 11: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸1𝑑 𝐸2𝑑

𝐸3𝑑

𝐸4𝑑

…

𝐸1π‘Ÿ 𝐸2π‘Ÿ

𝐸3π‘Ÿ

𝐸4π‘Ÿ

𝐸5π‘Ÿ

…

πΈπ‘—π‘Ÿ = 𝐸0𝑑 π‘Ÿ 𝑑′ 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝐸𝑗𝑑 = 𝐸0𝑑 π‘Ÿ 𝑑′𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝐸1π‘Ÿ = 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 12: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΈπ‘Ÿ = πΈπ‘—π‘Ÿ

𝑁

𝑗

= 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘ + 𝐸0𝑑 π‘Ÿ 𝑑

β€² 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)𝑁

𝑗=2

πΈπ‘Ÿ = 𝐸0π‘’π‘–πœ”π‘‘ π‘Ÿ +

π‘Ÿβ€²π‘‘π‘‘β€²π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘π‘Ÿ 1 βˆ’ π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

2π‘Ÿ2(1 βˆ’ cos 𝛿)

1 + π‘Ÿ4 βˆ’ 2π‘Ÿ2 cos 𝛿

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 13: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΈπ‘Ÿ = πΈπ‘—π‘Ÿ

𝑁

𝑗

= 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘ + 𝐸0𝑑 π‘Ÿ 𝑑

β€² 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)𝑁

𝑗=2

πΈπ‘Ÿ = 𝐸0π‘’π‘–πœ”π‘‘ π‘Ÿ +

π‘Ÿβ€²π‘‘π‘‘β€²π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘π‘Ÿ 1 βˆ’ π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

2π‘Ÿ2(1 βˆ’ cos 𝛿)

1 + π‘Ÿ4 βˆ’ 2π‘Ÿ2 cos 𝛿

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 14: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΈπ‘Ÿ = πΈπ‘—π‘Ÿ

𝑁

𝑗

= 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘ + 𝐸0𝑑 π‘Ÿ 𝑑

β€² 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)𝑁

𝑗=2

πΈπ‘Ÿ = 𝐸0π‘’π‘–πœ”π‘‘ π‘Ÿ +

π‘Ÿβ€²π‘‘π‘‘β€²π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ 𝐸0π‘’π‘–πœ”π‘‘π‘Ÿ 1 βˆ’ π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

2π‘Ÿ2(1 βˆ’ cos 𝛿)

1 + π‘Ÿ4 βˆ’ 2π‘Ÿ2 cos 𝛿

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 15: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΈπ‘Ÿ = πΈπ‘—π‘Ÿ

𝑁

𝑗

= 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘ + 𝐸0𝑑 π‘Ÿ 𝑑

β€² 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)𝑁

𝑗=2

πΈπ‘Ÿ = 𝐸0π‘’π‘–πœ”π‘‘ π‘Ÿ +

π‘Ÿβ€²π‘‘π‘‘β€²π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘π‘Ÿ 1 βˆ’ π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

2π‘Ÿ2(1 βˆ’ cos 𝛿)

1 + π‘Ÿ4 βˆ’ 2π‘Ÿ2 cos 𝛿

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 16: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΈπ‘Ÿ = πΈπ‘—π‘Ÿ

𝑁

𝑗

= 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘ + 𝐸0𝑑 π‘Ÿ 𝑑

β€² 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)𝑁

𝑗=2

πΈπ‘Ÿ = 𝐸0π‘’π‘–πœ”π‘‘ π‘Ÿ +

π‘Ÿβ€²π‘‘π‘‘β€²π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘π‘Ÿ 1 βˆ’ π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿ2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

2π‘Ÿ2(1 βˆ’ cos 𝛿)

1 + π‘Ÿ4 βˆ’ 2π‘Ÿ2 cos 𝛿

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 17: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΈπ‘Ÿ = πΈπ‘—π‘Ÿ

𝑁

𝑗

= 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘ + 𝐸0𝑑 π‘Ÿ 𝑑

β€² 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)𝑁

𝑗=2

πΈπ‘Ÿ = 𝐸0π‘’π‘–πœ”π‘‘ π‘Ÿ +

π‘Ÿβ€²π‘‘π‘‘β€²π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘π‘Ÿ 1 βˆ’ π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿ2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

2π‘Ÿ2(1 βˆ’ cos 𝛿)

1 + π‘Ÿ4 βˆ’ 2π‘Ÿ2 cos 𝛿

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 18: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΈπ‘Ÿ = πΈπ‘—π‘Ÿ

𝑁

𝑗

= 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘ + 𝐸0𝑑 π‘Ÿ 𝑑

β€² 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)𝑁

𝑗=2

πΈπ‘Ÿ = 𝐸0π‘’π‘–πœ”π‘‘ π‘Ÿ +

π‘Ÿβ€²π‘‘π‘‘β€²π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘π‘Ÿ 1 βˆ’ π‘’βˆ’π‘–π›Ώ

1 βˆ’ π‘Ÿ2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 19: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸1𝑑 𝐸2𝑑

𝐸3𝑑

𝐸4𝑑

…

𝐸1π‘Ÿ 𝐸2π‘Ÿ

𝐸3π‘Ÿ

𝐸4π‘Ÿ

𝐸5π‘Ÿ

…

πΈπ‘—π‘Ÿ = 𝐸0𝑑 π‘Ÿ 𝑑′ 𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝐸𝑗𝑑 = 𝐸0𝑑 π‘Ÿ 𝑑′𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝐸1π‘Ÿ = 𝐸0π‘Ÿπ‘’π‘–πœ”π‘‘

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 20: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸𝑑 = 𝐸𝑗𝑑

𝑁

𝑗

= 𝐸0𝑑 π‘‘β€²π‘Ÿβ€²(2π‘—βˆ’1)𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝑁

𝑗

𝐸𝑑 = 𝐸0π‘’π‘–πœ”π‘‘

𝑑𝑑′

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘1 βˆ’ π‘Ÿ2

1 βˆ’ π‘Ÿ2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 21: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸𝑑 = 𝐸𝑗𝑑

𝑁

𝑗

= 𝐸0𝑑 π‘‘β€²π‘Ÿβ€²(2π‘—βˆ’1)𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝑁

𝑗

𝐸𝑑 = 𝐸0π‘’π‘–πœ”π‘‘

𝑑𝑑′

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘1 βˆ’ π‘Ÿ2

1 βˆ’ π‘Ÿ2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 22: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸𝑑 = 𝐸𝑗𝑑

𝑁

𝑗

= 𝐸0𝑑 π‘‘β€²π‘Ÿβ€²(2π‘—βˆ’1)𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝑁

𝑗

𝐸𝑑 = 𝐸0π‘’π‘–πœ”π‘‘

𝑑𝑑′

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘1 βˆ’ π‘Ÿ2

1 βˆ’ π‘Ÿ2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 23: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸𝑑 = 𝐸𝑗𝑑

𝑁

𝑗

= 𝐸0𝑑 π‘‘β€²π‘Ÿβ€²(2π‘—βˆ’1)𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝑁

𝑗

𝐸𝑑 = 𝐸0π‘’π‘–πœ”π‘‘

𝑑𝑑′

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘1 βˆ’ π‘Ÿ2

1 βˆ’ π‘Ÿ2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 24: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐸𝑑 = 𝐸𝑗𝑑

𝑁

𝑗

= 𝐸0𝑑 π‘‘β€²π‘Ÿβ€²(2π‘—βˆ’1)𝑒𝑖(πœ”π‘‘βˆ’(π‘—βˆ’1)𝛿)

𝑁

𝑗

𝐸𝑑 = 𝐸0π‘’π‘–πœ”π‘‘

𝑑𝑑′

1 βˆ’ π‘Ÿβ€²2π‘’βˆ’π‘–π›Ώ= 𝐸0𝑒

π‘–πœ”π‘‘1 βˆ’ π‘Ÿ2

1 βˆ’ π‘Ÿ2π‘’βˆ’π‘–π›Ώ

πΌπ‘Ÿ =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 25: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

𝐼𝑑 =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

𝐼𝑖 = πΌπ‘Ÿ + 𝐼𝑑

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 26: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

πΌπ‘Ÿ =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 +2π‘Ÿ1 βˆ’ π‘Ÿ2

2

sin2𝛿2

𝐼𝑖 = πΌπ‘Ÿ + 𝐼𝑑

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 27: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

𝐹 sin2𝛿2

1 + 𝐹 sin2𝛿2

πΌπ‘Ÿ =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 + 𝐹 sin2𝛿2

𝐼𝑖 = πΌπ‘Ÿ + 𝐼𝑑

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 28: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

πΌπ‘Ÿ =πΈπ‘ŸπΈπ‘Ÿ

βˆ—

2= 𝐼𝑖

𝐹 sin2𝛿2

1 + 𝐹 sin2𝛿2

𝐼𝑑 =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 + 𝐹 sin2𝛿2

𝐼𝑖 = πΌπ‘Ÿ + 𝐼𝑑 β‡’ 1 =πΌπ‘ŸπΌπ‘–+𝐼𝑑𝐼𝑖≑ 𝑅 + 𝑇

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 29: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝛿

πœ‹

𝛿

πœ‹ Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea

Proiect cercetare Θ™tiinΘ›ifica I

Page 30: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐹 =2π‘Ÿ

1 βˆ’ π‘Ÿ2

2

𝛿

πœ‹

𝛿

πœ‹ Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea

Proiect cercetare Θ™tiinΘ›ifica I

Page 31: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝛿 = 𝑓(πœ†, πœƒ, 𝑛, 𝑑) 𝐹 =2π‘Ÿ

1 βˆ’ π‘Ÿ2

2

𝛿

πœ‹

𝛿

πœ‹ Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea

Proiect cercetare Θ™tiinΘ›ifica I

Page 32: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 33: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

???

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 34: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 35: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Source: https://www.sao.ru/hq/lsfvo/devices/scorpio/ifp/cubes.html

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 36: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Source:https://nl.wikipedia.org/wiki/Fabry-P%C3%A9rot-interferometer#/media/File:Fabry-Perot_interferences_figure.jpg

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 37: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Source:https://nl.wikipedia.org/wiki/Fabry-P%C3%A9rot-interferometer#/media/File:Fabry-Perot_interferences_figure.jpg

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 38: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Source: http://newton.physics.metu.edu.tr/~mdogruel/ht0017a4.gif

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 39: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 40: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 41: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐼𝑑 =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 + 𝐹 sin2𝛿2

𝐼𝑑𝐼𝑖=

1

1 + 𝐹 sin2𝛿122

=1

2

𝛿12= 2 sinβˆ’1

1

𝐹

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 42: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐼𝑑 =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 + 𝐹 sin2𝛿2

𝐼𝑑𝐼𝑖=

1

1 + 𝐹 sin2𝛿122

=1

2

𝛿12= 2 sinβˆ’1

1

𝐹

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 43: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝐼𝑑 =πΈπ‘‘πΈπ‘‘βˆ—

2= 𝐼𝑖

1

1 + 𝐹 sin2𝛿2

𝐼𝑑𝐼𝑖=

1

1 + 𝐹 sin2𝛿122

=1

2

𝛿12= 2 sinβˆ’1

1

𝐹

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 44: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝛿12= 2 sinβˆ’1

1

𝐹

𝐹 =2π‘Ÿ

1 βˆ’ π‘Ÿ2

2

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 45: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

𝛿12= 2 sinβˆ’1

1

𝐹

𝐹 =2π‘Ÿ

1 βˆ’ π‘Ÿ2

2

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 46: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

Page 47: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

References

[1] Peucheret, C. Note on Fabry-PΓ©rot Interferometers

[2] Born, M., Wolf, E. (1999) Principles of Optics Cambridge, University Press

[3] Wyant, J. Multiple Beam Interference Retrieved from

http://wyant.optics.arizona.edu/MultipleBeamInterference/MultipleBeamInterference.pdf

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I

http://wyant.optics.arizona.edu/MultipleBeamInterference/MultipleBeamInterference.pdf
http://wyant.optics.arizona.edu/MultipleBeamInterference/MultipleBeamInterference.pdf
Page 48: Fabry-Perot InterferometerΒ Β· π‘Ÿ= π‘Ÿ 𝑁 = 0π‘Ÿ πœ”π‘‘+ 0𝑑 π‘Ÿ 𝑑′ (πœ”π‘‘βˆ’( βˆ’1)𝛿) 𝑁 =2 π‘Ÿ= 0 πœ”π‘‘π‘Ÿ+ π‘Ÿβ€²π‘‘π‘‘β€² βˆ’ 𝛿

Appendix Reversibility principle

1 = 𝑑𝑑′ + π‘Ÿ2 0 = π‘‘π‘Ÿβ€² + π‘Ÿπ‘‘

Universitatea Politehnica BucureΘ™ti – Ingineria Θ™i AplicaΘ›iile Laserilor Θ™i Acceleratorilor - Victor-Cristian Palea Proiect cercetare Θ™tiinΘ›ifica I


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