For mmmmmooooorrrrreeeee information, check our development notebook (page 40 - 135).
An unstable laser intensity could have negative impact on experiments, one example being the Rabi Flopping. Rabi Flopping occurs when an electromagnetic field, in many cases is the laser, interacts with a two level system causing an oscillation between the two quantum states. The frequency of this oscillation is directly related to the amplitude of the pertubring EM field.
When the laser intensity varies, the excitation and de-excitation rates in the two level system can deviate from their expected values. This leads to shifts in the Rabi frequency, causing a mismatch between the observed transitions and the actual energy differences between the quantum states. As a result, the spectroscopic measurements may yield imprecise values for the system's energy levels. Therefore, maintaining a stable laser intensity is essential for precise spectroscopic analyses, ensuring accurate determination of the system's energy levels.
Another example is laser cooling, where we often want a specifict laser intensity to achieve the best cooling effect or to avoid heating up an trapped ion. Therefore, we expect the laser intensity to be what we set in a control computer. However, in practice, many factors could affect laser intensity: thermal fluctuation, mechanical vibration, etc.
Our goal for this project is to build a reliable laser intensity stabilizing device, exploiting PID feedback control, to stabilize a PULSED laser. We aim to suppress power flunctuation down to 1% for a pulse width of 5 μs.
- Laser: PL202 Thorlab Compact Laser
- Acousto-Optics Modulator: ATM-2001A2.12
- Voltage Variable Attenuator: ZX73-2500+
- Microcontroller: Arduino DUE
- RF Amplifier: ZHL-1-2W+
- Photodiode: PDA10A2
- Function Generator, DC Power Supply, Oscilloscope, Electronics, Optics
It is also worth noting that if the VVA tune goes beyond this saturation voltage level, the feedback usually fails. After the VVA tune voltage crosses the peak, if the received power is still below the setpoint, the Arduino will attempt to increase its DAC output to increase the diffraction efficiency of the AOM, so more power can be delivered to the 1st order light, which is our output. However, we are already in the region on the right off the peak, so the higher the voltage, actually the less diffraction efficiency. The Arduino then detects an even lower optical power and increases more DAC power, resulting in even smaller diffraction efficiency. This ends up into a loop stuck and maximum arduino DAC output with zero stabilization ability and potentially damages the AOM. We confirmed this prediction by observing spontaneous dropping of received laser power. By using a differential op-amp, we were able to linearly map the arduino DAC output (0.5~2.7 V) to (0~6 V) that perfectly terminates at the saturation point. However due to some external considerations we switched to an op-amp with much higher gain which again causes this problem (DAC automatically slides to 2.7V once it reaches around 1.1V）. Thus one major next step is to add it back and also implement an algorithm for double protection.
Arduino DUE is the fastest among the Arduino family, in terms of sampling rate and processing speed. However, it turned out that for our purpose of stabilzing a 5μs pulse, the speed of the Arduino DUE is still insufficient. Below is a summary of the time taken by different Arduino commands:
digitalRead(): 1.2μs
read_adc(): 1.8μs
micros(): 1.3μs
analogWrite(): 3.8μs
Serial.println(“ “): 1.3ms
loop(): 25μs [nothing is in the loop()]
read_adc() and analogWrite() take time on the order of the pulse length. So when the pulse length approaches these commands' runtimes, it happens frequently that a read_adc() which we expect to be executed when the pulse is high, actually returns a value (typically 0) when the pulse is low. This greatly compromises our stability because a reading of 0 misleads the Arduino to think that the intensity of the laser has dropped significantly so it needs to increase the power giving to the AOM. The result is a sudden jump on the laser intensity. This has been observed and is mitigated by our Peak Averaging algorithm.
P.S.: When working with Arduino code (.ino), be mindful that many C++ standard libraries (e.g., std::arr, vector) are not perfectly compatible with Arduino, and the error message may not point this out.
We also added a non-inverting op-amp with gain 7x between the photodiode and the Arduino ADC. In practice, our device should disturb with the experiments minimally, that implies only taking a small portion of laser power to feed into our stabilization loop. Hence, the signal given by the detecting photodiode will be weak and we want to amplify it so the Arduino can resolve the signal better.
We are currently implementing a peak average algorithm to capture the laser beam intensity and calculate error signal. Essentially we calculate the error signal based on past 100 ADC readings by sorting this array and averaging the leading 10 terms. These two numbers (100, 10) are very conservative choice for a 100kHz pulse with 50% duty cycle and we have tested them to perform good stabilization. Ideally we hope the sampling window and number of valid leading terms to be able to self-adjust to different frequency and duty cycle. We have attempted synchronizing arduino ADC sampling with the real laser pulse by either using a Transistor-Transistor Logic(TTL) or directly sending pulse signal synchronized with laser pulse to arduino's digital pin. However, due to constraints from arduino runtime, we observe severe phase mismatch between two pulses which makes the ADC sample plenty of unwanted random intermediate and off-pulse voltage levels. We also attempted just taking one single max over a smaller sampling window; however, we sometimes observed large jumps in voltage levels, which is dangerous to our equipments, because of sudden fluctuations in the raw signal. Below is a graph of typical arduino ADC readout:
By P correction alone, often the intensity cannot get back to the setpoint. This is because when the difference between the setpoint and the signal becomes smaller, the P correction also diminishes, resulting in weaker correcting power. Eventually, the geometric series converges to some fixed value, away from the setpoint. Thus, we introduce the integral (I) correction. The I correction sums all the previous errors (defined as signal - setpoint), and tries to minimize this cumulated error. It is therefore able to detect the aforementioned constant offset and bring the intensity to the wanted value.
The derivative (D) correction is used as a damping term to suppress overshoots and oscillations. When the P coefficient is too large, the controller tends to overcorrect for an error, which introduces extra noise and could sometimes damage the system. The D correction is proportional to the derivative of the signal, so when the signal is changing too fast, either because of overcorrecting or the signal is truly flunctuating suddenly, the D correction kicks in to slow down these abrupt changes. Below is a plot from the scope that shows how turning on the D term helps calming down the oscillation.
It is worth noting that an overnight trial contains tens of thousands of data with both on and off pulse and intermediate value which makes the graph really messy and hard to analyze. Thus we plot it as a histogram, calculate the percentage error of high peak, and compare it with the percentage error of short-term pulse.
We observe a drift in the raw signal's intensity for this 6-hour trial: the percentage error of the raw signal is 3.2%, 3 times the percentage error for a 300μs trial, which suggests a drift in the laser intensity in the long run. If there is no stabilization happening, we would expect the stabilized signal to have a 3 times larger percentage error as well, compared to the percentage error within one sampling window (4.3%).
The histogram presented above illustrates the stabilized intensity signals of a pulsed laser over a 6-hour overnight trial. The percentage error for this stabilized signal was 4.4%, no where near the 3x drift of the raw signal. While this value falls short of our goal of 1%, it aligns closely with the 4.3% error of the system's short-term fluctuation over 1 sampling window, which shows that our device is suppressing any detectable errors (longer than 1 sampling window).
Our testing laser does not drift significantly over long time, therefore, to show the effect of our stabilization, we placed a variable filter in front of the laser which blocked a portion of light depending on how much it is rotated. Below are two situations which could happen in practice.
At the right end, the stabilized signal is brought up by a larger fluctuation and the stabilization fails. This is because when the raw signal is higher than the setpoint, the Arduino tries to output a low voltage to increase the attenuation of the VVA, so the AOM gets less power and less optical power will be delivered; however, the Arduino output has got to the minimum and it cannot lower the intensity any more. So the stabilized signal is now swinging with the fluctuation. This is what happens when the error is out of the dynamic range.
The top priority is to find a microcontroller with faster sampling rate and shorter processing time. We made the Arduino DUE to work by designing sophisticated algorithm, which sacrifices short-term stability for long-term reliability. Currently, the Arduino is ignorant of fluctuations faster than 100ms, which makes our goal of suppressing the flunctuation down to 1% unreachable. However, if a new microcontroller can keep up with the short pulse length, a more straightforward algorithm can be employed which should make this blind time much shorter and therefore we can address those fast fluctuations.
Our current setup concerns most about fast iteration, so we used breadboards for circuit. However, breadboard is more susceptible to noise than a printed circuit board, so we should switch to PCB once we are confident with our final circuit design. We should also replace the two exterior DC power supplies with Acopian AC-DC supplies to make the PCB more compact and portable.
This project was made for UCSB's PHYS CS15C course by Zhuoru Li, Tommy Dan, and Vinay Baid.
This project was built upon the Continuous-Wave Intensity Stabilization by Chaoshen Zhang, Sam Gebretsadkan, Vivian Liao and Rei Landsberger.
We especially want to thank Luka Sever-Walter, Sam Gebretsadkan, Chaoshen Zhang, Professor Andrew Jayich, Eric Deck, and Robert Kwapisz for their continuous support over the course of this project.