MATLAB: Plot with two related x-axes

axesplot

This question may seem like it has been answered in the forums but I believe there is a subtlety that has not been directly answered. I want to plot the optical absorption coefficient of a material as a function of both photon wavelength (bottom x-axis) and energy (top x-axis) similar to this figure shown below. There are two problems with this task that I have not found sufficiently addressed. The first is to ensure that all of the points in the bottom axis line up with the points in the top axis (we need to some how link the two x-axes). Second, because of how energy and wavelength are related, one axis will be ascending while the other will be descending (Matlab doesn't like descending x-axes). How can you make the referenced plot? Can someone recreate the reference plot using the following data taken from the reference plot?
clear
close all
data = [0.35737704918032787, 92649850.48039015
0.3819672131147541, 72475211.53588514
0.41147540983606556, 55967196.301264346
0.4229508196721312, 51126728.207795605
0.4557377049180328, 47937263.23846833
0.5016393442622952, 43803474.996365294
0.539344262295082, 40544606.59504045
0.5688524590163934, 34277014.89316264
0.5950819672131147, 25461360.619704828
0.6229508196721312, 16618285.037019765
0.6655737704918033, 10037712.197086804
0.7213114754098361, 6724703.556947659
0.7950819672131147, 4169337.0144349397
0.8836065573770491, 2722604.5977291227
0.9557377049180328, 1997130.2156342946
1.0344262295081967, 1523018.3932672704
1.1049180327868853, 1255113.4937515096
1.1852459016393442, 1034416.372625131
1.2737704918032788, 886319.8712540427
1.359016393442623, 779309.6059234422
1.4540983606557378, 609961.3425615291
1.4918032786885247, 502533.5248888627
1.5098360655737708, 398203.214420678
1.5196721311475412, 299601.3683763488
1.5213114754098362, 195504.2893801002
1.5262295081967214, 119588.7737216253
1.5360655737704918, 65114.84416472715
1.5475409836065577, 38316.26954492593
1.5508196721311474, 25329.082065449114
1.559016393442623, 18331.533361062826
1.5688524590163935, 14713.897024069562
1.5934426229508198, 11361.99263934681
1.6196721311475408, 8773.786275376307
1.6508196721311474, 6433.761487810411
1.6754098360655738, 5032.800618487584
1.7049180327868854, 3787.196421050415
1.7327868852459019, 2886.942647505133
1.7557377049180327, 2287.679320744783
1.777049180327869, 1933.9100405245356];
%planks constant
h = 4.135e-15; %eV s
%speed of light
c = 3e8; %m/s
%Ge absorption coef
alpha = data(:,2); %1/m
%wavelength
lambda = data(:,1); %microns
%energy
E = h*c./(lambda*1e-6); %eV
figure(1)
plot(lambda,alpha,'r')
xlabel('Wavelength (\mum)')
ylabel('\alpha (m^{-1})')
set(gca,'Yscale','log')
figure(2)
plot(E,alpha,'r')
xlabel('Energy (eV)')
ylabel('\alpha (m^{-1})')
set(gca,'Yscale','log')

Best Answer

data = [0.35737704918032787, 92649850.48039015
0.3819672131147541, 72475211.53588514
0.41147540983606556, 55967196.301264346
0.4229508196721312, 51126728.207795605
0.4557377049180328, 47937263.23846833
0.5016393442622952, 43803474.996365294
0.539344262295082, 40544606.59504045
0.5688524590163934, 34277014.89316264
0.5950819672131147, 25461360.619704828
0.6229508196721312, 16618285.037019765
0.6655737704918033, 10037712.197086804
0.7213114754098361, 6724703.556947659
0.7950819672131147, 4169337.0144349397
0.8836065573770491, 2722604.5977291227
0.9557377049180328, 1997130.2156342946
1.0344262295081967, 1523018.3932672704
1.1049180327868853, 1255113.4937515096
1.1852459016393442, 1034416.372625131
1.2737704918032788, 886319.8712540427
1.359016393442623, 779309.6059234422
1.4540983606557378, 609961.3425615291
1.4918032786885247, 502533.5248888627
1.5098360655737708, 398203.214420678
1.5196721311475412, 299601.3683763488
1.5213114754098362, 195504.2893801002
1.5262295081967214, 119588.7737216253
1.5360655737704918, 65114.84416472715
1.5475409836065577, 38316.26954492593
1.5508196721311474, 25329.082065449114
1.559016393442623, 18331.533361062826
1.5688524590163935, 14713.897024069562
1.5934426229508198, 11361.99263934681
1.6196721311475408, 8773.786275376307
1.6508196721311474, 6433.761487810411
1.6754098360655738, 5032.800618487584
1.7049180327868854, 3787.196421050415
1.7327868852459019, 2886.942647505133
1.7557377049180327, 2287.679320744783
1.777049180327869, 1933.9100405245356];
fig = figure();
% setup bottom axis
ax = axes();
hold(ax);
ax.YAxis.Scale = 'log';
xlabel(ax, 'Wavelength ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 14);
ylabel(ax, '$\alpha$ ($m^{-1}$)', 'Interpreter', 'latex', 'FontSize', 14);
% setup top axis
ax_top = axes(); % axis to appear at top
hold(ax_top);
ax_top.XAxisLocation = 'top';
ax_top.YAxisLocation = "right";
ax_top.YTick = [];
% ax_top.XDir = 'reverse';
ax_top.Color = 'none';
xlabel(ax_top, 'Energy($e$V)', 'Interpreter', 'latex', 'FontSize', 14);
% linking axis
linkprop([ax, ax_top],{'Units','Position','ActivePositionProperty'});
ax.Position(4) = ax.Position(4) * .96;
h = 4.135e-15; %eV s
c = 3e8; %m/s
lambda = linspace(0.2,1.8,9); %m
E = h*c./lambda*10^6; % 10^6 because lambda is in microns
% configure limits of bottom axis
ax.XLim = [lambda(1) lambda(end)];
ax.XTick = lambda;
ax.XAxis.TickLength = [0.015, 0.00];
ax.YAxis.TickLength = [0.02, 0.00];
ax.XAxis.MinorTick = 'on';
ax.XAxis.MinorTickValues = linspace(0.2,1.8,17);
% configure limits and labels of top axis
y_ticks = [0.7 0.8 0.9 1 2 3 4 5];
lambda_y_tick = h*c./y_ticks*10^6;
ax_top.XLim = [lambda(1) lambda(end)];
ax_top.XTick = fliplr(lambda_y_tick);
ax_top.XTickLabel = compose('%1.1f', fliplr(y_ticks));
ax_top.XAxis.TickLength = [0.02, 0.00];
ax_top.XAxis.MinorTick = 'off';
plot(ax, data(:,1), data(:,2), 'r-', 'LineWidth', 3);
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