Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External...
Transcript of Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External...
![Page 1: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/1.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical Activity
Peter Hertel
University of Osnabruck, Germany
Lecture presented at APS, Nankai University, China
http://www.home.uni-osnabrueck.de/phertel
October/November 2011
![Page 2: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/2.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Roadmap
• Permittivity
• No external fields
• External electric field
• External magnetic field
• Optical activity
![Page 3: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/3.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Roadmap
• Permittivity
• No external fields
• External electric field
• External magnetic field
• Optical activity
![Page 4: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/4.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Roadmap
• Permittivity
• No external fields
• External electric field
• External magnetic field
• Optical activity
![Page 5: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/5.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Roadmap
• Permittivity
• No external fields
• External electric field
• External magnetic field
• Optical activity
![Page 6: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/6.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Roadmap
• Permittivity
• No external fields
• External electric field
• External magnetic field
• Optical activity
![Page 7: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/7.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Roadmap
• Permittivity
• No external fields
• External electric field
• External magnetic field
• Optical activity
![Page 8: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/8.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
The electromagnetic field
• action on charged particles
p = q E + v ×B• Fourier transform fields
F (t,x) =
∫dω
2π
d3q
(2π)3F (ω, q) e
−iωte
iq · x
• Maxwell’s equations with % = 0, j = 0, µ = 1
q × H = −ωε0εEq × E = ωµ0H
• note that E, H and permittivity ε are Fourier transformsand depend on (ω, q).
![Page 9: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/9.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
The electromagnetic field
• action on charged particles
p = q E + v ×B
• Fourier transform fields
F (t,x) =
∫dω
2π
d3q
(2π)3F (ω, q) e
−iωte
iq · x
• Maxwell’s equations with % = 0, j = 0, µ = 1
q × H = −ωε0εEq × E = ωµ0H
• note that E, H and permittivity ε are Fourier transformsand depend on (ω, q).
![Page 10: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/10.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
The electromagnetic field
• action on charged particles
p = q E + v ×B• Fourier transform fields
F (t,x) =
∫dω
2π
d3q
(2π)3F (ω, q) e
−iωte
iq · x
• Maxwell’s equations with % = 0, j = 0, µ = 1
q × H = −ωε0εEq × E = ωµ0H
• note that E, H and permittivity ε are Fourier transformsand depend on (ω, q).
![Page 11: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/11.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
The electromagnetic field
• action on charged particles
p = q E + v ×B• Fourier transform fields
F (t,x) =
∫dω
2π
d3q
(2π)3F (ω, q) e
−iωte
iq · x
• Maxwell’s equations with % = 0, j = 0, µ = 1
q × H = −ωε0εEq × E = ωµ0H
• note that E, H and permittivity ε are Fourier transformsand depend on (ω, q).
![Page 12: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/12.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
The electromagnetic field
• action on charged particles
p = q E + v ×B• Fourier transform fields
F (t,x) =
∫dω
2π
d3q
(2π)3F (ω, q) e
−iωte
iq · x
• Maxwell’s equations with % = 0, j = 0, µ = 1
q × H = −ωε0εEq × E = ωµ0H
• note that E, H and permittivity ε are Fourier transformsand depend on (ω, q).
![Page 13: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/13.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Permittivity
• most general causal linear relationship between electricalfield and polarization field
Pi(t,x) = ε0
∫ ∞0
dτ
∫d3ξ Gij(τ, ξ)Ej(t− τ,x− ξ)
• Fourier transform
Pi(ω, q) = ε0 χij(ω, q) Ej(ω, q)
• Di = ε0 Ei + Pi
• Di = ε0 εijEi
• εij(ω, q) = δij + χij(ω, q)
• in general, permittivity εij depends on angular frequency ωand wave vector q
![Page 14: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/14.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Permittivity
• most general causal linear relationship between electricalfield and polarization field
Pi(t,x) = ε0
∫ ∞0
dτ
∫d3ξ Gij(τ, ξ)Ej(t− τ,x− ξ)
• Fourier transform
Pi(ω, q) = ε0 χij(ω, q) Ej(ω, q)
• Di = ε0 Ei + Pi
• Di = ε0 εijEi
• εij(ω, q) = δij + χij(ω, q)
• in general, permittivity εij depends on angular frequency ωand wave vector q
![Page 15: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/15.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Permittivity
• most general causal linear relationship between electricalfield and polarization field
Pi(t,x) = ε0
∫ ∞0
dτ
∫d3ξ Gij(τ, ξ)Ej(t− τ,x− ξ)
• Fourier transform
Pi(ω, q) = ε0 χij(ω, q) Ej(ω, q)
• Di = ε0 Ei + Pi
• Di = ε0 εijEi
• εij(ω, q) = δij + χij(ω, q)
• in general, permittivity εij depends on angular frequency ωand wave vector q
![Page 16: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/16.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Permittivity
• most general causal linear relationship between electricalfield and polarization field
Pi(t,x) = ε0
∫ ∞0
dτ
∫d3ξ Gij(τ, ξ)Ej(t− τ,x− ξ)
• Fourier transform
Pi(ω, q) = ε0 χij(ω, q) Ej(ω, q)
• Di = ε0 Ei + Pi
• Di = ε0 εijEi
• εij(ω, q) = δij + χij(ω, q)
• in general, permittivity εij depends on angular frequency ωand wave vector q
![Page 17: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/17.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Permittivity
• most general causal linear relationship between electricalfield and polarization field
Pi(t,x) = ε0
∫ ∞0
dτ
∫d3ξ Gij(τ, ξ)Ej(t− τ,x− ξ)
• Fourier transform
Pi(ω, q) = ε0 χij(ω, q) Ej(ω, q)
• Di = ε0 Ei + Pi
• Di = ε0 εijEi
• εij(ω, q) = δij + χij(ω, q)
• in general, permittivity εij depends on angular frequency ωand wave vector q
![Page 18: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/18.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Permittivity
• most general causal linear relationship between electricalfield and polarization field
Pi(t,x) = ε0
∫ ∞0
dτ
∫d3ξ Gij(τ, ξ)Ej(t− τ,x− ξ)
• Fourier transform
Pi(ω, q) = ε0 χij(ω, q) Ej(ω, q)
• Di = ε0 Ei + Pi
• Di = ε0 εijEi
• εij(ω, q) = δij + χij(ω, q)
• in general, permittivity εij depends on angular frequency ωand wave vector q
![Page 19: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/19.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Permittivity
• most general causal linear relationship between electricalfield and polarization field
Pi(t,x) = ε0
∫ ∞0
dτ
∫d3ξ Gij(τ, ξ)Ej(t− τ,x− ξ)
• Fourier transform
Pi(ω, q) = ε0 χij(ω, q) Ej(ω, q)
• Di = ε0 Ei + Pi
• Di = ε0 εijEi
• εij(ω, q) = δij + χij(ω, q)
• in general, permittivity εij depends on angular frequency ωand wave vector q
![Page 20: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/20.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 21: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/21.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 22: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/22.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 23: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/23.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 24: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/24.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 25: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/25.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 26: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/26.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 27: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/27.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 28: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/28.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 29: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/29.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Local interaction
• dispersion relation of photons is ω = cq/n
• dispersion relation of phonons is ω = vq
• where v is speed of sound
• acoustical and optical phonons
• photon and phonon dispersion relations intersect foroptical phonons
• v/c ≈ 0.01, q is small
• εij(ω, q) ≈ εij(ω, 0)
• normally, the permittivity depends on ω only
• Gij(τ, ξ) ≈ Gij(τ) δ3(ξ)
![Page 30: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/30.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 31: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/31.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 32: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/32.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 33: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/33.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 34: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/34.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 35: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/35.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 36: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/36.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 37: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/37.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 38: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/38.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 39: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/39.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Drude model
• Locality is built into the Drude model
• We investigate matter at location x = 0
• deviation of a charged particle from this position isx = x(t)
• equation of motion
m x(t) + Γx(t) + Ω2x(t) = q E(t,x(t))
• right hand side approximated by E(t, 0)
• electromagnetic waves are long
• involved wave vectors are small
• good so , because otherwise solving equation of motionby Fourier transforming it would be impossible
• at least difficult
![Page 40: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/40.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 41: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/41.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 42: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/42.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 43: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/43.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji
• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 44: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/44.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 45: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/45.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 46: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/46.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 47: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/47.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 48: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/48.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 49: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/49.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Isotropic and birefringent media
• no external electric or magnetic field
• Onsager: εij = εji
• negligible absorption: εij = ε∗ji• permittivity is a real symmetric tensor
• can be orthogonally diagonalzed
• optically isotropic : εij = n2δij
• optically uniaxial
εij =
n2o 0 00 n2o 00 0 n2e
• ordinary beam : e = cosαx+ sinαy and k = z
• extraordinary : k = cosαx+ sinαy and e = z
![Page 50: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/50.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Double refraction (birefringence) by calcite
![Page 51: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/51.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Pockels effect
• εij = n2ij +RijkEk• Rijk = Rjik
• such a tensor with three indexes not allowed for crystalswith inversion symmetry
• but for instance in lithium niobate (3m symmetry)
• Pockels effect causes additional birefringence . . .
• . . . which is proportional to the external field strength E• effect is fast (GHz), but requires large field strength
• therefore µm-optics (Integrated Optics)
![Page 52: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/52.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Pockels effect
• εij = n2ij +RijkEk
• Rijk = Rjik
• such a tensor with three indexes not allowed for crystalswith inversion symmetry
• but for instance in lithium niobate (3m symmetry)
• Pockels effect causes additional birefringence . . .
• . . . which is proportional to the external field strength E• effect is fast (GHz), but requires large field strength
• therefore µm-optics (Integrated Optics)
![Page 53: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/53.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Pockels effect
• εij = n2ij +RijkEk• Rijk = Rjik
• such a tensor with three indexes not allowed for crystalswith inversion symmetry
• but for instance in lithium niobate (3m symmetry)
• Pockels effect causes additional birefringence . . .
• . . . which is proportional to the external field strength E• effect is fast (GHz), but requires large field strength
• therefore µm-optics (Integrated Optics)
![Page 54: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/54.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Pockels effect
• εij = n2ij +RijkEk• Rijk = Rjik
• such a tensor with three indexes not allowed for crystalswith inversion symmetry
• but for instance in lithium niobate (3m symmetry)
• Pockels effect causes additional birefringence . . .
• . . . which is proportional to the external field strength E• effect is fast (GHz), but requires large field strength
• therefore µm-optics (Integrated Optics)
![Page 55: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/55.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Pockels effect
• εij = n2ij +RijkEk• Rijk = Rjik
• such a tensor with three indexes not allowed for crystalswith inversion symmetry
• but for instance in lithium niobate (3m symmetry)
• Pockels effect causes additional birefringence . . .
• . . . which is proportional to the external field strength E• effect is fast (GHz), but requires large field strength
• therefore µm-optics (Integrated Optics)
![Page 56: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/56.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Pockels effect
• εij = n2ij +RijkEk• Rijk = Rjik
• such a tensor with three indexes not allowed for crystalswith inversion symmetry
• but for instance in lithium niobate (3m symmetry)
• Pockels effect causes additional birefringence . . .
• . . . which is proportional to the external field strength E• effect is fast (GHz), but requires large field strength
• therefore µm-optics (Integrated Optics)
![Page 57: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/57.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Pockels effect
• εij = n2ij +RijkEk• Rijk = Rjik
• such a tensor with three indexes not allowed for crystalswith inversion symmetry
• but for instance in lithium niobate (3m symmetry)
• Pockels effect causes additional birefringence . . .
• . . . which is proportional to the external field strength E
• effect is fast (GHz), but requires large field strength
• therefore µm-optics (Integrated Optics)
![Page 58: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/58.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Pockels effect
• εij = n2ij +RijkEk• Rijk = Rjik
• such a tensor with three indexes not allowed for crystalswith inversion symmetry
• but for instance in lithium niobate (3m symmetry)
• Pockels effect causes additional birefringence . . .
• . . . which is proportional to the external field strength E• effect is fast (GHz), but requires large field strength
• therefore µm-optics (Integrated Optics)
![Page 59: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/59.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Pockels effect
• εij = n2ij +RijkEk• Rijk = Rjik
• such a tensor with three indexes not allowed for crystalswith inversion symmetry
• but for instance in lithium niobate (3m symmetry)
• Pockels effect causes additional birefringence . . .
• . . . which is proportional to the external field strength E• effect is fast (GHz), but requires large field strength
• therefore µm-optics (Integrated Optics)
![Page 60: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/60.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
A commercial Pockels cell for modulating light
![Page 61: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/61.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Faraday effect
• εij = n2ij + iKεijkBk• rotation of polarization proportional to the magnetic
induction
• effect is non-reciprocal
• optical isolator for protecting lasers from their own light
• best with ferro- or ferri-magnetic media, likeyttrium iron garnet etc.
• goal: realize the optical isolator in µm-optics
![Page 62: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/62.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Faraday effect
• εij = n2ij + iKεijkBk
• rotation of polarization proportional to the magneticinduction
• effect is non-reciprocal
• optical isolator for protecting lasers from their own light
• best with ferro- or ferri-magnetic media, likeyttrium iron garnet etc.
• goal: realize the optical isolator in µm-optics
![Page 63: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/63.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Faraday effect
• εij = n2ij + iKεijkBk• rotation of polarization proportional to the magnetic
induction
• effect is non-reciprocal
• optical isolator for protecting lasers from their own light
• best with ferro- or ferri-magnetic media, likeyttrium iron garnet etc.
• goal: realize the optical isolator in µm-optics
![Page 64: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/64.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Faraday effect
• εij = n2ij + iKεijkBk• rotation of polarization proportional to the magnetic
induction
• effect is non-reciprocal
• optical isolator for protecting lasers from their own light
• best with ferro- or ferri-magnetic media, likeyttrium iron garnet etc.
• goal: realize the optical isolator in µm-optics
![Page 65: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/65.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Faraday effect
• εij = n2ij + iKεijkBk• rotation of polarization proportional to the magnetic
induction
• effect is non-reciprocal
• optical isolator for protecting lasers from their own light
• best with ferro- or ferri-magnetic media, likeyttrium iron garnet etc.
• goal: realize the optical isolator in µm-optics
![Page 66: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/66.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Faraday effect
• εij = n2ij + iKεijkBk• rotation of polarization proportional to the magnetic
induction
• effect is non-reciprocal
• optical isolator for protecting lasers from their own light
• best with ferro- or ferri-magnetic media, likeyttrium iron garnet etc.
• goal: realize the optical isolator in µm-optics
![Page 67: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/67.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Faraday effect
• εij = n2ij + iKεijkBk• rotation of polarization proportional to the magnetic
induction
• effect is non-reciprocal
• optical isolator for protecting lasers from their own light
• best with ferro- or ferri-magnetic media, likeyttrium iron garnet etc.
• goal: realize the optical isolator in µm-optics
![Page 68: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/68.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
A commercial optical isolator
![Page 69: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/69.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
![Page 70: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/70.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
![Page 71: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/71.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
I found this in the internet when looking for optical activity.
![Page 72: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/72.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 73: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/73.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 74: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/74.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 75: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/75.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 76: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/76.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 77: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/77.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji
• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 78: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/78.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 79: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/79.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 80: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/80.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 81: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/81.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 82: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/82.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 83: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/83.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity
• recall εij = εij(ω, q)
• Invariance with respect to time reversal:Gij(τ, ξ) = Gji(τ,−ξ)
• which implies εij(ω, q) = εji(ω,−q)
• if present, a magnetic field must be inverted as well
• recall that εij is also hermitian: εij = ε∗ji• up to first order in q:
• εij = n2ij + χoaijkqk
• χoaijk is purely imaginary and antisymmetric in the first two
indexes
• ∆εoaij = iεijkgk with gk = Gklql
• gyration vector gk depends linearly on the wave vector ql
• Gkl is a rank 2 pseudo-tensor
![Page 84: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/84.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 85: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/85.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 86: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/86.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 87: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/87.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 88: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/88.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 89: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/89.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 90: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/90.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 91: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/91.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 92: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/92.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 93: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/93.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 94: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/94.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Genuine and pseudo tensors
• Coordinate transformation x→ x ′ such thatds2 = dx21 + dx22 + dx23 does not change
• x ′i = Rijxj where RR† = R†R = I
• detRR† = (detR)2 = 1
• detR = +1 : proper rotation
• detR = −1 : space inverions and proper rotation
• tensors Tij... transform as T ′ij... = RimRjn . . . Tmn...
• they are called genuine tensors
• pseudo tensors Pij... transform asP ′ij... = (detR)RimRjn . . . Pmn...
• δij is a genuine tensor of rank 2
• εijk is a pseudo tensor of rank 3
![Page 95: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/95.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 96: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/96.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 97: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/97.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 98: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/98.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 99: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/99.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 100: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/100.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 101: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/101.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 102: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/102.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 103: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/103.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 104: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/104.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 105: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/105.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 106: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/106.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Optical activity (ctd.)
• ∆χoaij = iεijkgk with gk = Gklql
• Ei and Pi are genuine vectors
• hence susceptibility χij is a genuine tensor of rank 2
• g must be a pseudo vector
• qi is a genuine vector
• Gkl therefore is a rank 2 pseudo tensor
• Only materials which have no mirror symmetry showoptical activity
• Material must distinguish between left and right handed
• dextrose, quartz, . . .
• Optically active materials cause a rotation of thepolarization proportional to the sample thickness
• The effect is reversible, as contrasted with the Faradayeffect
![Page 107: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/107.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Right vs. left handed quartz crystals.
![Page 108: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/108.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 109: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/109.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 110: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/110.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 111: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/111.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 112: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/112.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 113: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/113.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 114: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/114.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 115: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/115.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 116: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/116.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 117: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/117.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Dextrose
• optical activity of sugar discovered by Seebeck in 1811
• this explains the name optical activity
• dextrose is naturally produced sugar
• glucose (sugar) from Greek γλυκυς=glycys=sweet
• dextrose from Latin dexter=right
• artificially produced sugar does not showleft/right-handedness
• biologically produces sugar (dextrose) is optically effective
• Nature has no tendency to prefer left to right handedness
• Question: Are all sugar producing plants copies of the firstplant, which randomly decided between left and right?
![Page 118: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/118.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Thomas Seebeck, German physicist, 1770-1831
![Page 119: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/119.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 120: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/120.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 121: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/121.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 122: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/122.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 123: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/123.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 124: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/124.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 125: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/125.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 126: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/126.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 127: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/127.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 128: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/128.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 129: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/129.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 130: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/130.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Quartz
• Quartz is silicon dioxide, SiO2
• the most common mineral on earth
• just think of sand
• single crystals are either left or right optically active
• however, twins are also found
• world wide distribution is very close to 1:1 for left:rightcrystals
• there seems to be no preference of nature for left or right
• although parity is not a symmetry of nature. . .
• TCP is
• P alone not
• but only in weak interactions
![Page 131: Optical Activity Peter Hertel Roadmap Permittivity …Roadmap Permittivity No external elds External electric eld External magnetic eld Optical activity Drude model Locality is built](https://reader034.fdocuments.in/reader034/viewer/2022042622/5f85f06c905a027e8c12a489/html5/thumbnails/131.jpg)
OpticalActivity
Peter Hertel
Roadmap
Permittivity
No externalfields
Externalelectric field
Externalmagnetic field
Opticalactivity
Natural quartz