File:Phonon polaritons.svg
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Summary[edit]
This image presents the dispersion relation of phonon polaritons according to a simple theory[1], giving the two following dispersion relations for the coupled optical phonon/electromagnetic field system :
- longitudinal optical phonons (LO phonons)
- polaritons (transverse em field + TO phonons)
The dashed red curves correspond to the uncoupled modes (photons and phonons: Ω = 0), and the black curves represent solutions of the above equations with parameters chosen to fit the dispersion relation of polaritons in GaP[2], giving
- Uncoupled optical phonon frequency
- ω0 = 45.4 meV
- Coupling parameter
- Ω = 61 meV
- Electric susceptibility
- χ∞ = 7.5
Note that k is very small compared to π/a.
- ↑ Max Born, Kun Huang, Dynamical Theory of Crystal Lattices, Oxford University Press, 1954 (ISBN 9780198503699), « Chapter 8 : Infrared Dispersion and the Retardation Effect on Lattice Vibrations »
- ↑ C. H. Henry and J. J. Hopfield, Raman Scattering by Polaritons, Phys. Rev. Lett. 15, 964 - 966 (1965).
(further minor editing and conversion to svg done with inkscape)
Summary[edit]
DescriptionPhonon polaritons.svg |
English: Dispersion relation of phonon polaritons with parameters corresponding to GaP.
Français : Relation de dispersion des polaritons avec des paramètres correspondant au GaP. |
Date | |
Source | Own work |
Author | Mathieu Perrin |
SVG development InfoField | |
Source code InfoField | MATLAB codee=1.602e-19;
hbar = 1.05457168e-34;
c=2.9978e8;
ang=1e-10;
omega0=45.4e-3*e/hbar; %conversion meV->rd/s
Om=61e-3*e/hbar;
chi=7.5;
k=linspace(0,0.0004/ang)';
y1=omega0*ones(size(k)); %uncoupled phonon dispersion
y2=c*k/sqrt(1+chi); %uncoupled photon dispersion
y3=sqrt(y1.^2+Om^2/(1+chi));%longitudinal phonons
%solve for omega in
%k^2*c^2=omega^2*(1+chi+Om^2/(omega0^2-omega^2))
a1 = (1+chi)*ones(size(k));
a2 = -((1+chi)*omega0^2+k.^2*c^2+Om^2);
a3 = k.^2*c^2*omega0^2;
D = sqrt(a2.^2-4*a1.*a3);
y4=sqrt((-a2+D)./(2*a1));%upper polaritons
y5=sqrt((-a2-D)./(2*a1));%lower polaritons
plot(k*ang, [y1 y2]*1000*hbar/e,'r--','Linewidth',1.8);
hold on
plot(k*ang, [y3 y4 y5]*1000*hbar/e,'k','Linewidth',1.8);
hold off
axis([0 0.0004 35 60]);
set(gca,'FontSize',18,'TickLength',[.02 .02],'LineWidth',1.5);
xlabel('k (A^{-1})'); %A to be replaced
ylabel('h\omega (meV)'); %h to be replaced
|
Licensing[edit]
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 11:20, 13 February 2010 | 436 × 450 (14 KB) | Cepheiden (talk | contribs) | fiex rendering error of one exponent | |
11:15, 13 February 2010 | 436 × 450 (15 KB) | Cepheiden (talk | contribs) | fixed font scaling | ||
23:19, 15 November 2008 | 450 × 436 (21 KB) | Mathieu Perrin (talk | contribs) | |||
22:55, 15 November 2008 | 450 × 436 (21 KB) | Mathieu Perrin (talk | contribs) | |||
22:53, 15 November 2008 | 450 × 436 (21 KB) | Mathieu Perrin (talk | contribs) | |||
22:42, 15 November 2008 | 450 × 436 (22 KB) | Mathieu Perrin (talk | contribs) | |||
22:33, 15 November 2008 | 450 × 436 (20 KB) | Mathieu Perrin (talk | contribs) | {{Information |Description={{en|1=Dispersion relation of phonon polaritons with parameters corresponding to GaP.}} {{fr|1=Relation de dispersion des polaritons avec des paramètres correspondant au GaP.}} |Source=travail personnel (own work) |Author=[[Use |
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Height | 450.11px |