How to plot contour ?

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GULZAR
GULZAR 2024-4-29
编辑： Manikanta Aditya 2024-4-29
Ran in:
clc
clear
close all
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Define material properties and simulation parameters
n0 = 1; % Refractive index of air
ns = 1.46; % Refractive index of subtrate
% Parameters
lambda0=5e-6; % Wavelength of light in micrometers
frequency = linspace(58,67,1000);
c=3e8;
transmission=zeros(1,1000);
n01 = 1.578; % Refractive index of PS
n02 = 1.484; % Refractive index of PMMA
n=25;
nA = n01;
dA = lambda0/(4*nA); %% Thickness of First Layer in meters
nB = n02;
dB = lambda0/(4*nB); %% Thickness of Second Layer in meters
for i = 1:length(frequency)
f = frequency(i);
w=2*pi*f*1e12; %%% Angular frequency by frequency
DAA=dA * nA * (w/c);
DBB=dB * nB * (w/c);
%%% Transfer Matrix elements of first layer
ma11=cos(DAA); ma12=-1i*sin(DAA)/nA; ma21=-1i*nA*sin(DAA); ma22=cos(DAA);
MA=[ma11 ma12; ma21 ma22];
%%% Transfer MAtrix elements of Second layer
lb11=cos(DBB); lb12=-1i*sin(DBB)/nB; lb21=-1i*nB*sin(DBB); lb22=cos(DBB);
MB=[lb11 lb12; lb21 lb22];
M_total_P = (MB*MA)^n*(MA*MB)^n;
T1 = (2*ns/(ns*M_total_P(1,1)+ns*n0*M_total_P(1,2)+M_total_P(2,1)+n0*M_total_P(2,2)));
T=(n0 / ns) * abs(T1)^2;
transmission(i) = T;
end
plot(frequency,transmission)
this code is transmission spectra
I need a contour plot of this by varying the n01 and n02 with respect to Q factor
I did a program but is not working
can anyone help me
clc
clear
close all
tic
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Define material properties and simulation parameters
P = 0; %%% Hydrostatic pressure in MPa
n0 = 1; % Refractive index of air
ns = 1.46; % Refractive index of subtrate
% Parameters
lambda0=5e-6; % Wavelength of light in micrometers
%%% frequency Range
% f = 61.25; %% frequency in THz
frequency = linspace(58,67,1000);
c=3e8;
transmission=zeros(1,1000);
n01_ = linspace(1.3,4,25); % Refractive index of PS
n02_ = linspace(1.3,4,25); % Refractive index of PMMA
n=25;
% Q factor array
Q_factor_ = zeros(length(n01_), length(n02_));
for ii = 1:length(n01_)
n01 = n01_(ii);
nA = n01;
dA = lambda0/(4*nA); %% Thickness of First Layer in meters (varying with respect to n01)
for jj = 1:length(n02_)
n02 = n02_(jj);
nB = n02;
dB = lambda0/(4*nB); %% Thickness of Second Layer in meters (varying with respect to n02)
for i = 1:length(frequency)
f = frequency(i);
w=2*pi*f*1e12; %%% Angular frequency by frequency
DAA=dA * nA * (w/c); %%% (varying with respect to n01)
DBB=dB * nB * (w/c); %%% (varying with respect to n02)
%%% Transfer Matrix elements of first layer
ma11=cos(DAA); ma12=-1i*sin(DAA)/nA; ma21=-1i*nA*sin(DAA); ma22=cos(DAA);
MA=[ma11 ma12; ma21 ma22];
%%% Transfer MAtrix elements of Second layer
lb11=cos(DBB); lb12=-1i*sin(DBB)/nB; lb21=-1i*nB*sin(DBB); lb22=cos(DBB);
MB=[lb11 lb12; lb21 lb22];
M_total_P = (MB*MA)^n*(MA*MB)^n;
T1 = (2*ns/(ns*M_total_P(1,1)+ns*n0*M_total_P(1,2)+M_total_P(2,1)+n0*M_total_P(2,2)));
T=(n0 / ns) * abs(T1)^2;
transmission(i) = T;
desired_freq = 60;
peak_idx = find((frequency) == (desired_freq));
peak_val = transmission(peak_idx);
half_max = peak_val / 2;
peak_left_edge = find(transmission(1:peak_idx) < half_max, 1, 'last');
peak_right_edge = find(transmission(peak_idx:end) < half_max, 1, 'first') + peak_idx - 1;
fwhm = frequency(peak_right_edge) - frequency(peak_left_edge); %%% full width at half maximum
% Calculate Q factor
Q = desired_freq ./ fwhm;
% Store Q factor in array
Q_factor_(:,:,i) = Q;
end
end
end
contourf(n01_,n02_,Q_factor_)

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Manikanta Aditya
Manikanta Aditya 2024-4-29
Ran in:
Hi @GULZAR,
The issue with your contour plot attempt lies in the incorrect handling of the Q_factor_ array. You're attempting to store the Q factor in a 3D array (Q_factor_(:,:,i) = Q;) inside a loop that iterates over frequency, but your intention seems to be to create a 2D matrix where each element corresponds to a combination of n01 and n02 indices. The Q factor calculation should be based on the transmission spectrum characteristics for each combination of n01 and n02, not for each frequency.
Check this code with plot of contour:
clc;
clear;
close all;
tic;
% Define material properties and simulation parameters
n0 = 1; % Refractive index of air
ns = 1.46; % Refractive index of substrate
lambda0 = 5e-6; % Wavelength of light in micrometers
frequency = linspace(58,67,1000); % Frequency range
c = 3e8; % Speed of light
n01_ = linspace(1.3,4,25); % Refractive index of PS range
n02_ = linspace(1.3,4,25); % Refractive index of PMMA range
n = 25; % Number of layers
Q_factor_ = zeros(length(n01_), length(n02_)); % Initialize Q factor matrix
for ii = 1:length(n01_)
for jj = 1:length(n02_)
transmission = zeros(1,length(frequency)); % Reset transmission for each n01, n02 combination
n01 = n01_(ii);
n02 = n02_(jj);
dA = lambda0 / (4 * n01); % Thickness of First Layer in meters
dB = lambda0 / (4 * n02); % Thickness of Second Layer in meters
for i = 1:length(frequency)
f = frequency(i);
w = 2 * pi * f * 1e12; % Angular frequency
DAA = dA * n01 * (w / c);
DBB = dB * n02 * (w / c);
% Transfer Matrix for first layer
ma11 = cos(DAA); ma12 = -1i * sin(DAA) / n01;
ma21 = -1i * n01 * sin(DAA); ma22 = cos(DAA);
MA = [ma11 ma12; ma21 ma22];
% Transfer Matrix for second layer
lb11 = cos(DBB); lb12 = -1i * sin(DBB) / n02;
lb21 = -1i * n02 * sin(DBB); lb22 = cos(DBB);
MB = [lb11 lb12; lb21 lb22];
% Total Transfer Matrix
M_total_P = (MB * MA)^n * (MA * MB)^n;
T1 = (2 * ns / (ns * M_total_P(1,1) + ns * n0 * M_total_P(1,2) + M_total_P(2,1) + n0 * M_total_P(2,2)));
T = (n0 / ns) * abs(T1)^2;
transmission(i) = T;
end
% Simplified Q factor calculation (for demonstration)
% Ideally, you should find the peak and its FWHM more accurately
[maxT, idx] = max(transmission);
desired_freq = frequency(idx);
fwhm = 1; % Placeholder for FWHM calculation
Q = desired_freq / fwhm;
Q_factor_(ii, jj) = Q; % Store Q factor
end
end
% Plotting the contour
figure;
contourf(n01_, n02_, Q_factor_', 20); % Transpose Q_factor_ for correct orientation
colorbar;
xlabel('n01');
ylabel('n02');
title('Q Factor Contour');
toc;
Elapsed time is 10.374777 seconds.
Hope this helps you!
  2 个评论
GULZAR
GULZAR 2024-4-29
I need the Q factor according to full width at half maximum
Manikanta Aditya
Manikanta Aditya 2024-4-29
编辑：Manikanta Aditya 2024-4-29
Ran in:
Check this script for Q factor according to full width at half maximum, if it helps you can accept the answer:
The Q factor based on the full width at half maximum (FWHM) of the transmission peak for each combination of n01 and n02, and then plots a contour map of these Q factors.
clc;
clear;
close all;
tic;
% Define material properties and simulation parameters
n0 = 1; % Refractive index of air
ns = 1.46; % Refractive index of substrate
lambda0 = 5e-6; % Wavelength of light in micrometers
frequency = linspace(58,67,1000); % Frequency range
c = 3e8; % Speed of light
n01_ = linspace(1.3,4,25); % Refractive index of PS range
n02_ = linspace(1.3,4,25); % Refractive index of PMMA range
n = 25; % Number of layers
Q_factor_ = zeros(length(n01_), length(n02_)); % Initialize Q factor matrix
for ii = 1:length(n01_)
for jj = 1:length(n02_)
transmission = zeros(1,length(frequency)); % Reset transmission for each n01, n02 combination
n01 = n01_(ii);
n02 = n02_(jj);
dA = lambda0 / (4 * n01); % Thickness of First Layer in meters
dB = lambda0 / (4 * n02); % Thickness of Second Layer in meters
for i = 1:length(frequency)
f = frequency(i);
w = 2 * pi * f * 1e12; % Angular frequency
DAA = dA * n01 * (w / c);
DBB = dB * n02 * (w / c);
% Transfer Matrix for first layer
ma11 = cos(DAA); ma12 = -1i * sin(DAA) / n01;
ma21 = -1i * n01 * sin(DAA); ma22 = cos(DAA);
MA = [ma11 ma12; ma21 ma22];
% Transfer Matrix for second layer
lb11 = cos(DBB); lb12 = -1i * sin(DBB) / n02;
lb21 = -1i * n02 * sin(DBB); lb22 = cos(DBB);
MB = [lb11 lb12; lb21 lb22];
% Total Transfer Matrix
M_total_P = (MB * MA)^n * (MA * MB)^n;
T1 = (2 * ns / (ns * M_total_P(1,1) + ns * n0 * M_total_P(1,2) + M_total_P(2,1) + n0 * M_total_P(2,2)));
T = (n0 / ns) * abs(T1)^2;
transmission(i) = T;
end
% Find peak and FWHM
[peakT, peakIdx] = max(transmission);
peakFreq = frequency(peakIdx);
% Find left and right half max points
halfMax = peakT / 2;
leftIdx = find(transmission(1:peakIdx) <= halfMax, 1, 'last');
rightIdx = find(transmission(peakIdx:end) <= halfMax, 1, 'first') + peakIdx - 1;
% Ensure fwhmFreq is defined before use
if isempty(leftIdx) || isempty(rightIdx)
fwhmFreq = NaN; % Assign NaN or another placeholder if FWHM can't be computed
else
fwhmFreq = frequency(rightIdx) - frequency(leftIdx);
end
% Calculate Q factor only if fwhmFreq is not NaN
if ~isnan(fwhmFreq) && fwhmFreq > 0
Q = peakFreq / fwhmFreq;
Q_factor_(ii, jj) = Q; % Store Q factor
else
Q_factor_(ii, jj) = NaN; % Assign NaN or a placeholder value indicating calculation was not possible
end
end
end
% Plotting the contour
figure;
contourf(n01_, n02_, Q_factor_', 20); % Transpose Q_factor_ for correct orientation
colorbar;
xlabel('n01');
ylabel('n02');
title('Q Factor Contour');
toc;
Elapsed time is 9.891317 seconds.

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