2nd semiconductor electronicsamano/h30/semi/semi-2.pdfoctober 22, 2018 8:45 ~10:15 ib015 2 nd...
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![Page 1: 2nd Semiconductor Electronicsamano/H30/SEMI/SEMI-2.pdfOctober 22, 2018 8:45 ~10:15 IB015 2 nd Semiconductor Electronics 1/33 Professor Hiroshi AMANO IMaSS, CIRFE amano@nuee.nagoya-u.ac.jp](https://reader034.vdocuments.site/reader034/viewer/2022042217/5ec0ffbaf8271e7b336e671a/html5/thumbnails/1.jpg)
October 22, 2018 8:45~10:15 IB015
2nd Semiconductor Electronics
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Professor Hiroshi AMANOIMaSS, CIRFE
[email protected]://www.echo.nuee.nagoya-u.ac.jp/~amano/H30/SEMI/index.html
Chapter Dates Contents2 October 22 Dielectric waveguide and optical fibers
![Page 2: 2nd Semiconductor Electronicsamano/H30/SEMI/SEMI-2.pdfOctober 22, 2018 8:45 ~10:15 IB015 2 nd Semiconductor Electronics 1/33 Professor Hiroshi AMANO IMaSS, CIRFE amano@nuee.nagoya-u.ac.jp](https://reader034.vdocuments.site/reader034/viewer/2022042217/5ec0ffbaf8271e7b336e671a/html5/thumbnails/2.jpg)
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Waveguide structure of edge emitting laser
Slab waveguide
n1>n2
Light
Light
Edge emitting laser diode has theslab waveguide structure.
http://slideplayer.com/slide/4678841/15/images/20/%EF%82%B7+AlGaAs+Materials+system:.jpg
GaAs
AlAs
Bandgap
GaAs AlAs
CoreClad
Clad
Small bandgap materials have alarge refractive index.
![Page 3: 2nd Semiconductor Electronicsamano/H30/SEMI/SEMI-2.pdfOctober 22, 2018 8:45 ~10:15 IB015 2 nd Semiconductor Electronics 1/33 Professor Hiroshi AMANO IMaSS, CIRFE amano@nuee.nagoya-u.ac.jp](https://reader034.vdocuments.site/reader034/viewer/2022042217/5ec0ffbaf8271e7b336e671a/html5/thumbnails/3.jpg)
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2.1Symmetric planar dielectric slab waveguide A. Waveguide Condition
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
Example of speckle noise Copyright © ファイバーラボ株式会社 All Rights Reserved
There are several waveguide mode.
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2.1Symmetric planar dielectric slab waveguide A. Waveguide Condition
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
k:free space wavenumber (propagation constant)𝜆𝜆: 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑓𝑓 𝑤𝑤𝑠𝑠𝑤𝑤𝑓𝑓𝑤𝑤𝑓𝑓𝑤𝑤𝑤𝑤𝑤𝑤𝑤
Phase change at B and C Phase at A and C should be the same.
Total internal reflection (TIR)
Total internal reflection (TIR)
![Page 5: 2nd Semiconductor Electronicsamano/H30/SEMI/SEMI-2.pdfOctober 22, 2018 8:45 ~10:15 IB015 2 nd Semiconductor Electronics 1/33 Professor Hiroshi AMANO IMaSS, CIRFE amano@nuee.nagoya-u.ac.jp](https://reader034.vdocuments.site/reader034/viewer/2022042217/5ec0ffbaf8271e7b336e671a/html5/thumbnails/5.jpg)
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2.1Symmetric planar dielectric slab waveguide A. Waveguide Condition
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
Propagation constant
Waveguide condition
Total internal reflection (TIR)
Total internal reflection (TIR)
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2.1Symmetric planar dielectric slab waveguide A. Waveguide Condition
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
𝐸𝐸1 𝑦𝑦, 𝑧𝑧, 𝑤𝑤 = 𝐸𝐸0 cos 𝜔𝜔𝑤𝑤 − κ𝑚𝑚𝑦𝑦 − 𝛽𝛽𝑚𝑚𝑧𝑧 + 𝛿𝛿At point P,
𝐸𝐸2 𝑦𝑦, 𝑧𝑧, 𝑤𝑤 = 𝐸𝐸0 cos 𝜔𝜔𝑤𝑤 + κ𝑚𝑚𝑦𝑦 − 𝛽𝛽𝑚𝑚𝑧𝑧Q: Confirm the following equation.
𝐸𝐸 𝑦𝑦, 𝑧𝑧, 𝑤𝑤 = 𝐸𝐸1 𝑦𝑦, 𝑧𝑧, 𝑤𝑤 + 𝐸𝐸2 𝑦𝑦, 𝑧𝑧, 𝑤𝑤 = 2𝐸𝐸0 cos 𝜔𝜔𝑤𝑤 − 𝛽𝛽𝑚𝑚𝑧𝑧 +𝛿𝛿2
cos κ𝑚𝑚𝑦𝑦 −𝛿𝛿2
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2.1Symmetric planar dielectric slab waveguide A. Waveguide Condition
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
δ is either 0, π, 2π.
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C. TE and TM mode
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
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B. single and multi mode waveguides
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
Total internal reflection (TIR) condition sinθm>sinθc =𝑛𝑛2𝑛𝑛1
Waveguide condition
𝑚𝑚 ≤2𝑉𝑉 − 𝜙𝜙
𝜋𝜋Q: Confirm this equation.
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B. single and multi mode waveguides
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
http://www.fiberopticshare.com/single-mode-fiber-vs-multimode-fiber-choose-2.html
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Appendix: Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
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Fresnel’s equations for Reflection and Transmission
https://pdfs.semanticscholar.org/presentation/f8c8/c79a742942ff7439b42418cd690b9dbfbd0b.pdf
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
B// =nc
E⊥, B⊥ =nc
E//
c: velocity of light
s-polarized TEsenkrecht
p-polarizedTM parallel
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p-polarized wave (Transverse Magnetic)
Ei// =(0, Ei0//sin𝜃𝜃i, -Ei0//cos𝜃𝜃i)
Q: Confirm that magnetic field iswritten as follows.
H = H⟂ = (n1c𝜇𝜇
Ei0//, 0,0)c: velocity of lightµ:permeability of core material =µ0
From Maxwell’s equation ∇ × E=−∂B𝜕𝜕t
∇ × E=−j𝜔𝜔𝜇𝜇H
∇ × E=−jk × E = −j𝜔𝜔𝜇𝜇H
H=k×E𝜔𝜔𝜔𝜔
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p-polarized wave (Transverse Magnetic)
Boundary condition
At the interface, both the tangentialcomponent of electric field and magneticfield is continuous.
Hi0⟂ − Hr0⟂ = Ht0⟂Ei0// cos 𝜃𝜃i + Er0// cos 𝜃𝜃i = Et0// cos 𝜃𝜃t
𝜇𝜇1=𝜇𝜇2=𝜇𝜇0
Q: Confirm that reflection and transmission of TM wave is written as follows.
r// = Er0//
Ei0//= n1 cos 𝜃𝜃t-n2 cos 𝜃𝜃in1 cos 𝜃𝜃t+n2 cos 𝜃𝜃i
t// = Et0//
Ei0//= 2n1 cos 𝜃𝜃in1 cos 𝜃𝜃t+n2 cos 𝜃𝜃i
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s-polarized wave (Transverse Electric)
Ei⟂ =(Ei0⟂,0,0)
Hi// =(0, n1c𝜔𝜔
Ei0⟂sin𝜃𝜃i, −n1c𝜔𝜔
Ei0⟂cos𝜃𝜃i)
r⟂ = Er0//
Ei0//= n1 cos 𝜃𝜃i-n2 cos 𝜃𝜃tn1 cos 𝜃𝜃i+n2 cos 𝜃𝜃t
t⟂ = Et0//
Ei0//= 2n1 cos 𝜃𝜃in1 cos 𝜃𝜃i+n2 cos 𝜃𝜃t
HW: Confirm that reflection and transmission of TE wave is written as follows.
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Fresnel’s equations for Reflection and Transmission
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
Snell’s equation
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Fresnel’s equations for Reflection and Transmission
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
n=n2n1
s-polarized
p-polarized
Q: Confirm the following equations.
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Brewstar angle
s-polarized
p-polarized
Q: Confirm the following equations.
R⟂ = r⟂2 =sin2(𝜃𝜃i−𝜃𝜃t)
sin2(𝜃𝜃i+𝜃𝜃t)
R// = r//2 =tan
2(𝜃𝜃i−𝜃𝜃t)tan2(𝜃𝜃i+𝜃𝜃t)
If n1>n2, θi<θt R⟂ ≠0, but if θi+θt=𝜋𝜋2
, then R// =0
tan𝜃𝜃p = n2n1
𝜃𝜃p :Brewstar’s angle
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Examples of Brewstar angle
https://www.researchgate.net/publication/316732445_Blue_sun_glints_on_water_viewed_through_a_polarizer/figures?lo=1
Without polarizer With polarizer
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Examples of Brewstar angle
http://lipas.uwasa.fi/~TAU/AUTO3160/slides.php?Mode=NoFrame&Page=105&MicroExam=On&Images=On&Menu=Off&Brother=Big
Ellipsometry
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Phase change upon total internal reflection (TIR)
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
When θi>θc (sinθc=n2n1
) in the presence of TIR, the reflection coefficients becomecomplex quantities of the type,
n=n2n1
r⟂ =1× exp(-jϕ⟂)r// =1× exp(-jϕ//)
sinθi>n2n1
=n, then
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
Brewstar angle
p-polarized TM
s-polarized TE
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How many modes?
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
For TIR, θi>θc , sin𝜃𝜃i > n2n1
Waveguide condition
Q: Consider a planer dielectric guide with a core thickness 20 µm, n1=1.455,n2=1.440, light wavelength of 900 nm. Find the number of TE modes.
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
V=2𝜋𝜋aλ
(𝑤𝑤12 − 𝑤𝑤22)12
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
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Total Internal Reflection
Optoelectronics and Photonics: Principles & Practices, Second Edition, S. O. Kasap, Pearson Education, ISBN-10: 0273774174, ISBN-13: 9780273774174. © 2013 Pearson Education
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Chapter Dates Contents3 October 29 Quantum Mechanics, Crystals, Band structure
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