%Fig_5_4.m %optical Lorentz dielectric constant and optical reflectivity; clear all; clf; %plotting parameters + fontsizes FS = 18; %label fontsize 18 FSN = 16; %number fontsize 16 LW = 2; %linewidth % Change default axes fonts. set(0,'DefaultAxesFontName', 'Times New Roman'); set(0,'DefaultAxesFontSize', FSN); % Change default text fonts. set(0,'DefaultTextFontname', 'Times New Roman'); set(0,'DefaultTextFontSize', FSN); eye=complex(0,1); %square root of minus one m0=9.1095e-31; %bare electron mass [kg] hbar=1.05459e-34; %Plank constant hbar [J s] echarge=1.60219e-19; %electron charge [C] clight=2.997924e8; %speed of light [m s^-1] epsilon0=8.854187e-12; %permittivity of free space [F m^-1] n0=12.75e28; %electron density [m^-3] 1e25 is 1e19cm^-3 wp2=n0*echarge^2/(epsilon0*m0); wp=sqrt(wp2); %plasma frequency [rad s^-1] w0=1.00*wp/3.317; %resonant frequency in terms of wp, %set to zero for no atom restoring force 0.80 w02=w0^2; Ep=hbar*wp/echarge; %plasma energy [eV] Ep2=Ep^2; E0=hbar*w0/echarge; E02=E0^2; gamma=E0/8; %broadening [eV] E0/8 Ep*8e-2 1.81 meV npoints=1000; %number of points in plot y1min=0.001*Ep; %minimum energy in plot y1max=1.5094*Ep; %maximum energy in plot y1=linspace(y1min,y1max,npoints); %energy [eV] y2=y1+(eye*gamma); %************************************************************************* % epsilon is complex permittivity of dielectric %************************************************************************* eps=1-(Ep2./((y1.*y1-E02)+(eye*y1*gamma))); %************************************************************************* ttl=['\it{n}\rm_0 = ',num2str(n0/1e28,'%5.1f'),... ' \times 10^{28} m^{-3}, \it{E}\rm_{0} = ',... num2str(E0,'%5.2f'),' eV, \it{E}\rm_{p} = ',... num2str(Ep,'%5.2f'),' eV, \gamma = ',num2str(gamma,'%5.2f'),' eV']; %************************************************************************* omega=y1*echarge/hbar; %omega [rad s^-1] n_index=(eps).^0.5; %complex refractive index %************************************************************************* figure(1) % reflectivity at normal incidence is a ratio of complex index squared reflect=(abs((n_index-1)./(n_index+1))).^2; plot(y1,reflect,'r','LineWidth',LW); hold on; %grid on; plot(E0,0,'*'); plot(Ep,0,'o'); title(ttl); xlabel('Photon energy, \it{E}\rm (eV)'); ylabel('\it{R}\rm'); hold off; axis([y1min y1max 0 1]); %************************************************************************* figure(2) ttl4=['\it{n}\rm_{index}']; plot(y1,real(n_index),'b','LineWidth',LW); hold on; plot(y1,imag(n_index),'r','LineWidth',LW); %grid on; plot(E0,0,'*'); plot(Ep,0,'o'); title(ttl); xlabel('Photon energy, \it{E}\rm (eV)'); ylabel(ttl4); hold off; axis([y1min y1max 0 1.1*max(real(n_index))]);