2nd Semiconductor Electronicsamano/H30/SEMI/SEMI-2.pdfOctober 22, 2018 8:45 ～10:15 IB015 2 nd...

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

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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.

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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.

https://www.fiberlabs.co.jp/

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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)


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Propagation constant

Waveguide condition



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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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δ is either 0, π, 2π.

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C. TE and TM mode


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B. single and multi mode waveguides


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


http://www.fiberopticshare.com/single-mode-fiber-vs-multimode-fiber-choose-2.html

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Appendix: Total Internal Reflection


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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


B// =nc

E⊥, B⊥ =nc

E//

c: velocity of light

s-polarized TEsenkrecht

p-polarizedTM parallel

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

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

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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Snell’s equation

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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)


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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Brewstar angle

p-polarized TM

s-polarized TE

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How many modes?


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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V=2𝜋𝜋aλ

（𝑤𝑤12 − 𝑤𝑤22）１２

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Chapter Dates Contents3 October 29 Quantum Mechanics, Crystals, Band structure

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