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ShalikaSingh - 09:04, Tuesday 18 February 2025 (3918)Get code to link to this report
Measuring modulation depth of EOM using Opamp based RF circuit

At first I checked the power of linear polarization (after HWP+QWP) which is incident on EOM. The measurement in oscilloscope of Moku showed 500Vp-p. This is the input power.

Then the photodiode measured the power after EOM in cross polarizer configuration. This was the output power.'

I apply voltage from 0-2Vp-p using Moku to the Opamp circuit. I then obtain the following plot (Fig 1) of Transmission % vs. Voltage. The data is saved in "Characteristics_20250217.txt".

The frequency of the RF circuit was identified by taking In1(from photodiode)/Out1(Input to the RF circuit). I measured the place of resonant frequency using laser.

Interpretation:

That result means the fitting routine found the parameters:

y = 112.8 sin(0.5x+0.5)**2 - 21.4 by using the fit function: A sin (Bx + C) **2 + D

which implies:

  • Amplitude: 112.8, so the sin^2 term varies by 112.8.

  • Frequency: 0.5, meaning the period is T = 2pi/0.5 = 12.57

  • Phase shift: 0.5, so the sine's argument is shifted.

  • Offset: -21.4, which makes the minimum value y_{min}=-21.4 (since  sin**2 goes from 0 to 1, the output ranges from 112.8-21.4=91.4).

Images attached to this report
3918_20250218064659_transmissioncharacteristics20250217.png
Comments related to this report
ShalikaSingh - 14:51, Tuesday 18 February 2025 (3922)

According to theory written in "Optical Electronics" by Yariv, for a amplitude modulation EOM

TransmissionOut/ Input  = sin^2(  pi/2   *    V/Vpi)

If I can properly, obtain my transfer function measurement then I can very well define my V. Hence, I can estimate the fit parameters better. Also, the quality of fit can then be better estimated by seeing if we have this pi/2 factor inside the sin square function or not.

Currently I am using the voltage input to RF circuit, and not the voltage across the EOM electrodes.

ShalikaSingh - 16:51, Tuesday 18 February 2025 (3923)

The maximum Transmisison factor achieved with this circuit was 0.86 or 86%. I can calculate what is roughly the maximum voltage I provided.

Vpi = 306.26V from elog 3750

Vpi * asin(sqrt(0.86)) / 1.5 = 284 V at resonant freq of 189.13 kHz.

Considering the length of transmission line I have as l = 35cm, of R0=50 ohm, I can compute the stray capacitance of the EOM due to the tranmission line as follows:

f = np.arange(1E5, 1E6, 1E4)
lam = 3E8/f #lambda
omega = 2 * np.pi * f
C_eom = 12E-12 #12pF, capacitance of eom from thorlabs datasheet
Z_eom = 1/(1j*omega*C_eom)
Beta = 2*np.pi/lam
l = 35E-2 #length of cable
R0 = 50 #ohm, impedance of cable
 
The resultant input impedance then becomes, 
Z_in_eom = R0 * (Z_eom * np.cos(Beta * l) + 1j*R0*np.sin(Beta*l)) / (R0*np.cos(Beta*l) + 1j*Z_eom*np.sin(Beta*l)) 
 
We can then evlauate roughly the stray capapcitance as:
 
C_reality_eom = np.real( 1/ ((1j*omega*Z_in_eom))) #F
 
This leads to the EOM becoming a 35pF capacitor. This is the reason of my reduction in gain of LC series circuit. This is also the reason of shift resonant frequency of the circuit. If the cable is longer, the stray capacitance will increase further more. In short, you should either take into account the length of your cable between your circuit and EOM or reduce the length of transmisison line as much as possible. If I take into account this 35pF into my simulation with Opamp, the maxmium voltage at my eom is 280V, and the reosnant freq is around 230Khz. 
 
It is quite interesting because the total capacitance looking from the input of the cable becomes a little bit larger depending on the length of the cable. In order to decrease the amount of the stay capacitance, one has to reduce the length of the transmission line.
f = np.arange(1E5, 1E6, 1E4)
# f_res = 189.128E3 #Khz
# omega_res = 2*np.pi*f_res
lam = 3E8/f
omega = 2 * np.pi * f
C_eom = 12E-12 #14pF
ind = 6.8*2*1E-3 #mH
Z_eom = 1/(1j*omega*C_eom)
Z_ind = 1j*omega*ind
Beta = 2*np.pi/lam
l = 90E-2 #length of cable
R0 = 50 #ohm
 
Z_in_eom = R0 * (Z_eom * np.cos(Beta * l) + 1j*R0*np.sin(Beta*l)) / (R0*np.cos(Beta*l) + 1j*Z_eom*np.sin(Beta*l))
Z_in_ind = R0 * (Z_ind * np.cos(Beta * l) + 1j*R0*np.sin(Beta*l)) / (R0*np.cos(Beta*l) + 1j*Z_ind*np.sin(Beta*l))
C_reality_eom = np.real( 1/ ((1j*omega*Z_in_eom))) #F
L_reality_ind = np.real(Z_in_ind/(1j*omega))