Principle of sensitization of cursor effect
Since the FP cavity can produce a periodic cosine spectrum, it will be realigned after passing through several levels. Therefore, the spectrum of the cascade FP cavity is also periodic, and the free spectral range of the cascade FP cavity spectrum is related to the free spectral range of the two FP cavities. When the spectrum of one of the FP cavities shifts slightly but the spectrum of the other FP cavity does not change, by detecting the positions of the peaks (or troughs) of the original alignment and the peaks (or troughs) of the current alignment, the small changes can be If amplified, the output spectrum of the cascade FP cavity will change more than that of a single FP cavity.
Cursor effect implementation method
Two FP-type interferometers with similar cavity lengths are cascaded or connected in parallel, one of which is a sensing cavity used to measure the pressure to be measured. The other cavity is a reference cavity with a cavity length similar to the sensing cavity length and is used as a reference spectrum.
Formula expression
Let the incident electric field intensity be 1, the total reflection intensity can be expressed as the sum of the electric field intensity reflected from the two reflecting surfaces, the expression is:
Among them, a1 is the transmission loss of the first reflective surface;
1 is the reflectivity of the first reflecting surface;
2 is the reflectivity of the second surface;
θ=2/ is the phase shift of the beam propagation in the cavity.
Because the reflected light intensity is the square of the electric field intensity amplitude, the corresponding reflected light intensity is expressed according to the formula:
In order to facilitate matlab code writing, the reflected light intensity of the reference cavity is expressed as:
The reflected light intensity of the sensing cavity is expressed as:
The total reflected light intensity is:
Interference Spectrum
Set the sensing cavity length to 300um and the auxiliary cavity length to 280um. The interference superposition spectrum obtained through matlab simulation is as shown in Figure 1. The envelope composed of the maximum value in the spectrum is fitted. The obtained envelope curve is as shown in Figure 2. By recording the drift of the envelope curve, the sensing quantity can be analyzed Variety.
Cursor Effect Sensitization Analysis
Vernier effect sensitization effect is verified by comparing the changes in the interference spectrum before and after the cavity length of a single sensor changes. When the sensing cavity length changes from 300um to 301um, the interference spectrum of the single cavity before and after the cavity length changes (top) and dual cavity simulation interference spectrum (bottom).
Among them, after the length of the sensing cavity is increased by 1um, the simulated interference spectrum of the single cavity is red-shifted by 2nm, and the simulated interference spectrum of the dual-cavity is red-shifted by about 20nm.
Conclusion
This F-P pressure sensor uses the vernier effect to increase sensitivity, which can amplify the theoretical value of the sensor sensitivity by about 10 times. (The specific value of amplification can be changed according to the adjustment of the sensing cavity length and reference cavity length)
Matlab code for cursor effect
Single cavity sensing matlab code
liamud = linspace(1450,1460,10000); %wavelength
R1=0.04; % reflectance of the first reflective surface
R2=0.08; % reflectivity of the second reflective surface
a1 = 0.01; % projection loss of the first reflective surface
n1 = 1; % refractive index
L1 = 300000; % cavity length default unit nm
h1 = (2.*pi.*n1.*L1)./liamud;
I1 = R1 + (1-R1)^2.*(1-a1)^2.*R2 + 2.*(1-a1).*(1-R1).*(R1.*R2)^0.5. *cos(2.*h1);
%After the sensing cavity is deformed
L3 = 301000;
h3 = (2.*pi.*n1.*L3)./liamud;
I3 = R1 + (1-R1)^2.*(1-a1)^2.*R2 + 2.*(1-a1).*(1-R1).*(R1.*R2)^0.5. *cos(2.*h3);
figure;
plot(liamud, I1); %Vernier effect interference spectrum
hold on;
plot(liamud, I3); %Changes in the interference spectrum after the sensing cavity is deformed
% title('Interference Spectrum');
xlabel('Wavelength'); % You can modify the x-axis label according to the actual situation
ylabel('Reflected light intensity');
Double cavity cursor matlab code
liamud = linspace(1350,1550,10000); %wavelength
R1=0.04; %Reference cavity: reflectivity of the first reflective surface
R2=0.08; % reflectivity of the second reflective surface
R3=0.04; % sensing cavity: reflectivity of the first reflective surface
R4=0.08; % reflectivity of the second reflective surface
a1 = 0.01; %Reference cavity: Projection loss of the first reflective surface
a2 = 0.01; % sensing cavity: projection loss of the first reflective surface
n1 = 1; %reference cavity refractive index
n2 = 1; % sensing cavity refractive index
L1 = 280000; % reference cavity length default unit nm
L2 = 300000; % sensing cavity length, default unit nm
%Reflected light intensity of auxiliary cavity
h1 = (2.*pi.*n1.*L1)./liamud;
I1 = R1 + (1-R1)^2.*(1-a1)^2.*R2 + 2.*(1-a1).*(1-R1).*(R1.*R2)^0.5. *cos(2.*h1);
%Reflected light intensity of the sensing cavity
h2 = (2.*pi.*n2.*L2)./liamud;
I2 = R3 + (1-R3)^2.*(1-a2)^2.*R4 + 2.*(1-a2).*(1-R3).*(R3.*R4)^0.5. *cos(2.*h2);
% total reflected light intensity
IR = I1 + I2;
%After the sensing cavity is deformed
L3 = 301000;
h3 = (2.*pi.*n2.*L3)./liamud;
I3 = R3 + (1-R3)^2.*(1-a2)^2.*R4 + 2.*(1-a2).*(1-R3).*(R3.*R4)^0.5. *cos(2.*h3);
IR2 = I1 + I3;
% Find the maximum value point of IR
[peaks,locs] = findpeaks(IR);
% Generate function image
figure;
plot(liamud, IR, liamud(locs) ,peaks ,'linewidth',1); %interference spectrum envelope function
% plot(liamud, IR); %Vernier effect interference spectrum
hold on;
% plot(liamud, IR2); %Changes in the interference spectrum after the sensing cavity is deformed
% title('Interference Spectrum');
xlabel('Wavelength'); % You can modify the x-axis label according to the actual situation
ylabel('Reflected light intensity');