The region of the electromagnetic spectrum around 193THz (corresponding to the better-known 1550nm telecom wavelength) is the world's largest photonics playground. Thanks to the wide availability of cost-effective, performant and easy-to-use optical components operating at this particular frequency, advanced experimentation, learning and prototyping in photonics becomes possible without a small team, a massive pile of cash to burn through, and the patience of a saint. In fact, it becomes a fun and rewarding activity.
Still, high-quality and practical information about this domain remains rare and difficult to find. This website documents my own explorations and experiments in this area. It will sometimes cover atomic and quantum physics topics - my interest in laser technology comes from my experience as the lead developer of the ARTIQ control system (used mostly in trapped-ion and ultracold atom experiments), trying to reproduce some experiments myself (as one does), and being constantly put off by problems related to lasers which are a central component of those experiments: poor performance, proprietary unserviceable designs, unobtainium parts, unreliability, user-hostile design, and stratospheric prices which in combination with the other issues always make you feel like you are being ripped off. Even Germany's Federal Ministry of Education and Research generally appears to agree (in German). Certainly, there must be a better way of doing these things!
This website is by no means limited to experiments around the 193THz optical frequency, the name is simply a tribute to this great enabler.
The content assumes that you are already familiar with the general theory and practice of lasers, as well as related fields such as electronics and signal processing. If you are not, the excellent Sam's Laser FAQ is a good place to start. The RP Photonics Encyclopedia is another great resource with concise and accurate articles that include more advanced concepts, though they are written from a more formal and theoretical standpoint. For the practical aspects of working with fiber optics, the FOA has comprehensive tutorials intended for telecom technicians, which are very useful.
I can be contacted regarding these articles at root@193THz.com. I can't be bothered to submit anything to academic journals as some people have suggested, but in lieu of peer review, I will publish any intelligent technical comments.
Experiments on this website involve, among other hazards, high voltage at dangerous levels, and visible or invisible laser beams that can cause permanent eye damage and start fires. Splicing optical fibers produces glass shards that can cause injury. Make yourself familiar with the hazards and take appropriate control measures. Use the information provided here entirely at your own risk.
September 2023
Following the conclusions of the previous experiment, the pump diode was connected, with a series resistor, to a LT3042-based low-noise voltage regulator module from Aliexpress. The pump/output heterodyne signal looked a lot better than with the Rigol unit, but there were sidebands every few MHz, which seem to be coming from a small high-frequency oscillation produced by the module. The corresponding sidebands were not present in the SBS laser output, so it looks like the phase modulation of the DFB output that it produced simply distorted the Brillouin gain curve without too much impact on the SBS laser. Adding small ceramic capacitors at the output of the regulator made the sidebands mostly disappear. This module, however, has substantial low-frequency noise which is due at least in part to its temperature sensitivity (blowing hot air on it causes a lot of mode sweeping in the SBS laser) and mode hops still occur every couple hundred milliseconds without a control loop.
A simple control loop was put in place by detecting the peak frequency in the pump/output heterodyne signal, subtracting a frequency setpoint, and implementing a proportional controller that modulates the TEC current produced by a precision Sinara 8451 thermostat. This was an opportunity to try out some of the upcoming C++23 features, in particular the Networking TS, which are looking quite good. This simple system was able to keep the laser stable for several minutes in the absence of substantial external disturbances. The software was also improved to plot the lineshape (coming from a delayed self-heterodyne measurement) in synchrony with the pump/heterodyne signal, so that the correlation between the two can be easily seen.
The LT3042-based regulator was replaced with part of a Kirdy laser driver prototype. This is a much more sophisticated design based on the LTC6655 precision voltage reference, MAX5719 20-bit low-noise DAC, and ADA4898 high-speed low-noise op-amps driving a power MOSFET as a constant-current source. The performance of this device is excellent, with the SBS laser remaining stable for several seconds with the control loop disabled and no visible effect from hot air being blown on the laser driver. Engaging the proportional controller after the pump laser warmed up resulted in an easy lock that appears to remain stable indefinitely (as long as the fiber cavity isn't disturbed).
Even when the laser is running stable, a side mode is still weakly present about 30dB-40dB below the main line (note that the display saturates on the screenshots, so it looks worse than it actually is). To put this number into perspective, blocking one polarization of a two-mode stabilized HeNe laser with a commonly available polarizer results in a SMSR of 20dB-30dB, a typical telecom DFB has a SMSR of 35dB-40dB, and IPS laser diodes can reach 70dB with a passive optical filter (in the case of this SBS laser, since the side mode is so close, a more complicated filter based on an actively stabilized cavity would probably have to be used).
The control loop does not need to involve fancy hardware, i.e. a X-band downconverter, SDR, and PC are not required. In normal operation, the pump/heterodyne signal consists in a strong single frequency component. This 10.6GHz signal could be sampled in a high-order Nyquist zone using a high-speed flip-flop such as the NB7V52M, whose output could then be easily processed by a low-end CPLD or even the timer unit of a microcontroller. We are not interested in the exact value of the Nyquist order since we only want to measure the frequency variations within a bandwidth of a few MHz. We simply need to know whether the Nyquist order is odd or even, so that the correct sign for the error signal can be determined. This can be done entirely in firmware by looking at the direction of the measured frequency change as the pump laser is being cooled. We also want to stay clear of the boundaries of the Nyquist zone to avoid flip-flop metastability and other difficulties with the frequency measurement. This can be done by adjusting the sample rate using a precision programmable oscillator (for example Skyworks Si549) to drive the flip-flop clock. This all could be integrated on a small add-on module for Kirdy, which would make for a simple and compact SBS laser controller.
September 2023
The previous experiment demonstrated a low-cost laser with an impressively narrow instantaneous linewidth. Yet, it isn't very stable: it is affected by significant amplitude noise, mode hops, and low-intensity side modes that would appear briefly and randomly.
We can try to understand what is going on if we consider that the pump laser is not stabilized at all and its output is therefore affected by optical frequency noise on the order of hundreds of MHz (on top of its 5-10MHz instantaneous linewidth, which is narrower than the Brillouin gain bandwidth and unlikely to be the issue here). One can expect those noisy fluctuations to be transferred to the Brillouin gain curve. Those fluctuations are at least one order of magnitude greater than the FSR of the fiber cavity. Therefore, the gain experienced by the lasing mode is fluctuating, the mode that gets selected for lasing is constantly changing, and the laser may randomly cross into multi-mode regions. This is illustrated by the following diagram:
If we assume that the Brillouin shift is constant, this gives us a way to measure the position of the lasing mode with respect to the Brillouin gain peak, and correct the frequency of the pump laser to keep the lasing mode at the same position within the gain curve (preferably near the peak). Indeed, we can heterodyne the pump laser with the output of the SBS laser, and obtain a RF signal at the Brillouin shift frequency (around 10GHz) detuned by the difference between the lasing cavity mode and the Brillouin gain peak (neglecting any frequency-pulling effects).
Photodetectors for laboratory purposes with over 10GHz of bandwidth are, as usual, ridiculously priced and yet another opportunity for pen-pushers to waste your time with end user certificates and other Kafkian procedures. It is also difficult to build one with inexpensive equipment, since the capacitance at the TIA input needs to be minimized to a level that typically requires wire-bonding between the bare dies of the photodiode and TIA chip. The trick is to butcher a 25-gigabit Ethernet optical SFP (available inexpensively from FS.com, Gigalight, and others) and make use of its internal high-speed optical receiver. Simply using the standard SFP data output does not sound like a good option. We want to look at the raw analog signal before the limiting amplifier which would destroy information, particularly in the case of 25G devices which also contain a CDR and equalizer.
The supply chain for those SFPs appears to be a bit of a insiders' club, since it is basically impossible to buy separately the photodiode/TIA module (called "ROSA" in manufacturer jargon) and in most cases obtain any documentation about it. Both SFPs I disassembled from FS and Gigalight were built around two different ICs from MACOM with part numbers that are not listed on the MACOM website (and those that are listed do not have public datasheets). Emails were of course ignored after I told them that I just wanted to experiment with a SFP. The SFP laser modules ("TOSA") are similarly undocumented and impossible to buy separately.
Fortunately, it is not very difficult to figure out how to use an undocumented ROSA (or a TOSA, but this will be for another article). It will typically connect to the SFP's main PCB using a small flexible printed circuit with several solder pins. Several of these pins are ground and can be identified by looking at the printed circuit layouts and/or checking for a low-impedance path with the ground pins at the (standard) SFP connector using a DC multimeter. The main output can be clearly identified by the differential transmission line pattern on the SFP's main PCB. This usually leaves only two pins, which are RSSI and the power input. They can be identified, and the correct ROSA supply voltage determined, by measuring the voltage at those pins with the SFP operating with and without an optical input signal. Tracing the PCB can be difficult due to the frequent use of via-in-pad and blind vias in those miniaturized devices. For reference, here is the appearance and pinout of the FS.com 25G ROSA (with a MTX2-183+ glued on the flex PCB, not part of the original SFP). The normal current draw is around 25mA.
The output pins of the ROSA were connected to a MTX2-183+ balun transformer to adapt the differential signal to a 50-ohm coaxial connection compatible with standard RF equipment. You may be able to use baluns that are easier to obtain and cheaper than the MTX2-183+ - I chose it because of its particularly broad bandwidth, as the literature about the exact value of the Brillouin shift in fibers is somewhat contradictory and I wanted to be able to search for the Brillouin heterodyne signal in as much RF spectrum as practically possible. It is important to AC-couple the MTX2-183+ using two capacitors, as both pins of the ROSA have a DC bias that the MTX2-183+ would short-circuit to ground, potentially resulting in permanent damage. Take note that the center point of the secondary of the MTX2-183+ is grounded. This had escaped me during the first attempt at building this circuit, and I immediately noticed that something was wrong as the ROSA was drawing an unreasonable current. Luckily, I switched it off and investigated before any damage was done. Since I didn't have any capacitors on hand that I knew would work over 10GHz, I desoldered the original coupling capacitors from the SFP and used that. Those were 0201 SMD capacitors, which made for a tedious and cosmetically questionable soldering job, with the capacitors hanging in mid-air with one pin soldered to the MTX2-183+ and the other connected to the flex printed circuit with a fine copper wire. You may want to plan things better, try to use bigger capacitors, and perhaps even spin a small custom PCB. The primary of the MTX2-183+, on the other hand, is internally AC-coupled as per the "Marchand balun" design commonly used as such high frequencies. So you will not be able to check the coax connection with a DC multimeter. One last thing to be careful about is that some pins marked "NC" in the MTX2-183+ datasheet are in reality connected to ground.
The original cover of the SFP was cut in half with a dremel to leave space for the balun/coax hack-job and the 3.3V power cables, and the part that holds the ROSA and fiber connector screwed back in place. The end result is not particularly beautiful, and that SFP's warranty was definitely voided, but it is functional.
The 50-ohm output of the ROSA was downconverted using a HMC412-based mixer module (Aliexpress) with the IF output feeding a bladeRF software-defined radio. The LO input of the mixer was driven using the doubled output of a low-cost ADF5355-based RF generator from Aliexpress, with an amplifier ("2-18G Broadband LNA" from TGCHR Store) to meet the LO power requirements of the HMC412.
With the RF generator set to 9000MHz, and the bladeRF set to 1650MHz in Gqrx, a strong signal was visible near the middle of the waterfall display, corresponding to a Brillouin shift around 10.6GHz. It was quite satisfying to be able to measure this, when every other setup in the literature appears to cost as much as a sports car :)
The signal also appeared to show some evidence of the mode-sweeping/mode-hopping behavior theorized above, though at the speed at which it would be happening, it was difficult to draw any conclusions due to Gqrx's cap at 60 frames per second even when small Fourier transform sizes are selected. Therefore, a basic alternative program with no arbitrary FPS limit was developed using libbladeRF, PocketFFT for C++, GLFW and dear imgui. This produced a much clearer picture and stronger support for the theory. Indeed, it became apparent that the SBS laser would mode-hop when and only when the heterodyne frequency was near its minimum or maximum value.
Microphonics were reduced by potting the fiber cavity in epoxy resin, making a kind of a "fiber cake". You may want to use clear resin (unlike what I did) so that any major problems inside the potted volume can be found with a VFL. Stabilizing the pump laser's temperature to the millikelvin level using a Sinara 8451 thermostat connected to the butterfly package's TEC and thermistor produced a minor improvement in stability. The last source of technical noise to investigate was the laser diode's power supply, which was simply a Rigol DP832 in constant voltage mode with a series resistor. The Rigol unit was replaced with two 3000F 2.7V ultracapacitors connected in series to increase the maximum permissible voltage. I was rewarded with this fantastic plot of the SBS laser mode-sweeping as the capacitors discharged (virtually noiselessly) and the pump laser's optical frequency varied accordingly, confirming the theory above and pinpointing the origin of the noise that was causing the instabilities we had seen.
A small amount of frequency pulling is also apparent as the lines are not completely straight and slightly bend in the middle (try this).
This mode-sweep plot also tells us what current noise level is acceptable for driving the pump laser diode. We can see that one cycle of mode-sweeping takes 450ms. This is with a laser current of 150mA, a series resistor of 11 ohm and 1500F of capacitance. Assuming constant voltage across the laser diode, this corresponds to an estimated current drop of 4 microamperes per mode-sweep cycle. The conclusions of this experiment are: A proper driver for SBS pump laser diodes should exhibit noise significantly below that, and the laser control system would be able to detect instability regions and operate the SBS laser away from them by looking at the pump/output heterodyne signal and servoing on the pump laser current or temperature.
July 2023
With the exception of the venerable 633nm HeNe laser (equipped with simple stabilization electronics and polarizing filter), single-frequency lasers with linewidths below ~100kHz are uncommon and often very expensive. For example, the grossly overpriced proprietary ECDL found in modern atomic physics labs can exhibit a free-running linewidth over a hundred kHz, and often requires external reduction of its linewidth using a complicated electronic servo, an expensive reference cavity, and a small army of postdocs to keep it aligned.
Surprisingly, ordinary optical fiber that costs less per meter than toilet paper can be optically pumped, exhibit narrow-band and homogeneously broadened gain, and serve as the medium for the realization of a very narrow (few kHz) linewidth laser, thanks to a phenomenon known as stimulated Brillouin scattering. The best study of this type of laser that I have found is Alain Küng's excellent PhD thesis (in French), which provides a clear and detailed quantitative analysis with practical examples and realizations. The main difficulty with this type of laser is that the pump light must already have a pretty narrow (~MHz) bandwidth, so pumping with FP diodes (without external cavities) to reach interesting spectroscopic wavelengths sounds challenging. Nevertheless, Brillouin gain remains easy to observe and experiment with using single-frequency telecom DFB diodes, and a stimulated Brillouin scattering (SBS) laser is easy to construct.
According to the literature, the SBS process can amplify a signal about 10GHz red-detuned from the pump. To obtain the required pump and signal frequencies, two identical Eudyna FLD5F15CX-H DFB diodes are wired in series so they experience the same current, and then the pump's TEC is turned on with the polarity for cooling (in DFB datasheets, this usually corresponds to the polarity indicated by the plus and minus signs on the laser pinout) to increase the pump's frequency, or, alternatively, the signal's TEC is turned on with the polarity for heating.
The two lasers are sent in opposite directions into a 75m coil of single-mode telecom fiber using two circulators, as shown on the figure below:
The first circulator injects the pump light and separates the signal light to send it into a photodiode. The EDFA in the pump path is optional, but the SBS effect is more dramatic at high pump intensities. The second circulator is used as an isolator to prevent the pump laser from destabilizing or damaging the signal laser. The built-in isolator of DFB packages is not enough and only prevents laser instability up to injected powers of some dozen microwatts! Since we want more pump power than signal power, a manual variable optical attenuator (VOA) is inserted after the signal DFB to reduce the laser power sent into the fiber coil.
Cost-effective 1550nm fiber-coupled circulators can be obtained from Shenzhen Box Optronics and many other telecom suppliers. Despite their claims of decades of experience and their brandishing of patents (some of them expired), the 1550nm fiber-coupled circulators manufactured by a famous U.S. scientific supplier are literally 10x more expensive and do not have better optical specs.
When the laser pump frequency is ramped up by cooling it (or, alternatively, the signal frequency is ramped down), a peak of amplification can be seen at the photodiode output! From subjective experience with fiber ring resonators connected to thermally frequency-sweeped DFBs, the width of the gain peak appears consistent with a bandwidth of some dozen MHz, as reported in Alain Küng's thesis.
Unexplained features of the plot include a high background noise that increases with the intensity of the pump and is present even without the signal laser (Brillouin ASE noise?), a peak of absorption (the system working in reverse - signal laser causing SBS amplification of the pump? the two DFBs are not strictly identical and could easily start with >10GHz of detuning from manufacturing tolerances), and some disturbance somewhat in the middle (the two lasers having the same frequency?). But, in any case, plenty of gain is clearly observable!
Replacing the signal laser with the SBS output from the first circulator and tapping into the cavity light with a 99:1 FBT splitter (as shown on the figure below) produced an output power of 2.6mW with 150mW of pump light. Clearly, the fiber was lasing, since the 2.6mW at the output of the splitter meant that 260mW was circulating into the ring, and the power output was relatively stable despite DFB frequency fluctuations that could be induced by passing current into the TEC. Only a laser resonance could result in this!
The linewidth of the emitted laser light was determined using a conventional self-heterodyne measurement technique with an all-fiber setup using a pair of PLC splitters from FS.com, a 10km spool of fiber, and a fiber-coupled AOM.
The photodiode is connected directly to a bladeRF software defined radio, with the integrated bias-tee turned on (the trick is to create a file ~/bladerf.conf containing the line "biastee_rx on") and biased in reverse from the bladeRF's DC output voltage. Incorrect polarity will likely destroy the photodiode. To make it foolproof, you can add a series current-limiting resistor with an AC bypass capacitor in parallel with the resistor, which should remove this risk. The Gqrx program can then be used to display the spectrum. Make sure to use the libbladeRF frontend directly without the SoapySDR layer, which has some bugs and missing features.
AOMs are not cheap components, and the lower-priced ones seem to be available from CASTECH and CSRayzer. They will set you back around 1000 USD. Unfortunately it is difficult to make a reliable measurement of a single laser without one, due to the high levels of noise near DC. If you want to avoid the AOM without sacrificing measurement quality, you may be able to offset-lock two DFBs using the other bladeRF RX channel, a computer-controlled TEC driver (Rigol DP832 might be enough its noise is too high and its firmware will eventually crash as you hammer it with frequent current change commands) and some Python/Numpy scripting. You would then use those two offset beams to pump independent SBS lasers and measure their beat note. I have not attempted this offset lock scheme with DFB lasers, only HeNe with a small homemade induction heater on the tube's metallic mirror mount, but I'm pretty sure that it would still work. From a quick experiment the frequency of DFB modules without external stabilization seem to be stable enough at 100ms timescales so a simple software-based control loop in Python may be enough despite its low update rate and high latency.
The AOM is driven directly with a RF generator that puts out just 40mW at 80MHz. The AOM's diffraction efficiency is of course very low at such drive levels, but this avoids the complications associated with dealing with several watts of RF, in particular the risk of damaging the expensive AOM if its maximum RF power level is exceeded. Since we have plenty of laser power to work with, and heterodyne gain from the other, unattenuated arm of the interferometer, this works well enough. By inserting the AOM before the fiber delay line, the attenuation provided by the AOM also has the advantage of suppressing Brillouin scattering from the long fiber spool which, when sent back into the laser, could destabilize it (this problem was actually my first encounter with Brillouin scattering, while attempting to measure the linewidth of a DFB diode).
The linewidth measurement of the first laser revealed strong multimode operation with many narrow peaks. This laser was thus improved in several ways:
With those modifications, the laser is mostly single-frequency and narrow-linewidth, as shown on this Gqrx screenshot. The two lobes of noise on the sides are an artifact of the bladeRF's transceiver chip, and the solid lines at frequencies other than 80MHz are some RF pickup that remains present with the laser off. There are still some low-intensity spurious modes that appear intermittently, and may be related to mode sweeping - the pump DFB was not stabilized at all and its frequency on a ~1s timescale was fluctuating well above the FSR of the SBS laser resonator. Locking the DFB's wavelength to a HCN spectroscopic cell or just stabilizing its temperature may help, but this will be for another day. Still, this is to be contrasted with the same measurement made on the direct DFB diode's output.
With a fiber delay line of "only" 10km, it is not possible to give an accurate measurement of such a narrow linewidth, though building a recirculating fiber loop with the cheap EDFA sounds feasible. Still, the results appear consistent with the linewidths of a few kHz reported in the literature. Some papers will claim a linewidth of a few dozen Hz for this type of laser, but upon reading the details this is only valid for the linewidth of the beat note of two resonances occuring in the same laser cavity and therefore subject to the same external disturbances. At this level of precision, vibrations and other environmental disturbances have a major effect on the optical frequency fluctuations, as demonstrated in the video: Laser linewidth vs. Queen. To reach dozens Hertz of linewidth without an external servo mechanism, the laser cavity needs to have a level of mechanical stability that a mere coil of fiber simply cannot provide. Nevertheless, even with acoustic vibration levels normally not found in a physics lab, the SBS laser keeps its linewidth below that of a pricy and finicky ECDL.
July 2023
Light at 1550nm is normally invisible to silicon sensors such as the camera inside a mobile phone. However, due to two-photon absorption, the sensitivity of the sensor grows with the intensity, and at high enough intensities, it becomes visible.
This effect is exploited to build simple autocorrelators for NIR pulsed lasers by splitting the beam in two and recombining them onto a silicon photodiode. Due to this nonlinear process, the photodiode only responds when the beams (pulses) temporally overlap. Scanning the path difference between the beams gives a measurement of the laser pulse duration. Such autocorrelators are essentially Michelson interferometers with a photodiode and voice coil mounted mirror. They are of course expensive, because anything that an ultrafast laser beam touches instantaneously becomes solid gold.
It is possible to observe this effect with a powerful laser beam generated with low-cost telecom components and a mobile phone camera. In this video, you can see that the laser light that otherwise produces no visible scatter or dot on the lens generates bright flashes when it goes straight into the sensor. The beam is produced with a Eudyna FLD5F15CX-H DFB emitting 1550nm at about 30mW, which is then amplified to almost 200mW by a low-cost Chinese EDFA (check Aliexpress or Taobao) and then collimated with a small lens from Shenzhen Box Optronics.
Quantitative measurements can be taken by directing the beam into a silicon photodiode (for example TEFD4300 glued into a SC/PC adapter with the zirconia guide removed) and ramping up the laser power (for example with a fiber-coupled manual VOA inserted into the output of the EDFA, and a 99:1 FBT splitter to measure the current power). The nonlinear response becomes evident.
Note that such a beam is capable of burning things like black paper or plastic, and this experiment may damage your camera! Do this only with a camera that you do not care about, for example from an old discarded phone. Obviously, suitable laser safety goggles are a must every time the EDFA is on. Collimating the beam makes it more dangerous than it normally is.
June 2023
Hydrogen cyanide has many absorption lines that can serve as wavelength references for lasers around 1550nm, and easy-to-use cells are specified in NIST SRM 2519a and available commercially at reasonable prices from Wavelength References Inc. While hydrogen cyanide may sound scary at first, the minuscule amount contained in those cells make them completely safe to handle, even if the glass envelope is broken.
Using those cells, it is possible to exploit the dependency of laser frequency on the diode current (often called "chirp" and unwanted in telecom systems) to make a very simple and inexpensive demonstrator of the basic technique of FM spectroscopy. A Eudyna FLD5F15CX-H DFB was connected to a function generator with a series resistor, programmed to output a small sine wave with a large DC offset. The output fiber is connected to the HCN cell, followed by a photodiode going into an oscilloscope channel. Another oscilloscope channel monitors the voltage at the output of the function generator. The TEC of the Eudyna laser was connected to a lab power supply and allows larger changes of the laser wavelength in order to scan over the HCN absorption lines.
The result of the laser scanning over a spectroscopic line is shown on this oscilloscope picture. The purple trace is the laser offset voltage and the yellow trace is the photodiode voltage. It can be clearly seen that the phase between the signals reverses as the spectroscopic line is crossed, which is the key feature of FM spectroscopy. The amplitude also changes as the spectroscopy signal interferes constructively or destructively with the large amounts of laser amplitude modulation present.
There are certainly better ways to perform FM spectroscopy, in particular with a view to reducing the large amounts of laser amplitude modulation, but this is probably the simplest setup that would possibly work. It is interesting to note that a DWDM SFP basically contains all the required components to do this (except the HCN cell of course). Those SFPs contain a microcontroller, often with a publically available datasheet, which is normally used to perform laser temperature stabilization and housekeeping functions such as diagnostics over the I2C bus. It could in theory be reprogrammed to run the show, with simple hardware modifications to the SFP to reduce the modulation depth of its laser driver and to reroute the TX and RX signals to the microcontroller. This could make for a very compact and low-cost laser with high absolute wavelength accuracy. If you attempt this, do let me know :)
April 2023
The Pound-Drever-Hall method is a common and powerful technique to lock cavities to lasers and lasers to cavities. For example, a "transfer cavity" can be locked to a reference laser using one PDH control loop that tunes the cavity, and then another laser can be locked to the same cavity using a second PDH control loop that tunes the laser. This results in the optical frequency of the second laser being stabilized to the optical frequency of the reference laser, plus or minus an integer multiple of the cavity's FSR.
Another example which is conceptually simpler (but rather painful in practice due to phase-matching problems, cavity mirror alignment issues, and expensive optical coatings) is to build up optical power from a laser into a resonant cavity that contains a nonlinear crystal, which takes advantage of the facts that nonlinear crystals are more efficient at high power levels and that most of the light which isn't converted simply goes through the crystal unchanged. This dramatically increases the efficiency of the nonlinear process, at the expense of a very substantial increase in complexity and cost.
Lastly, in optical clocks an ultra-stable cavity is often used as a "flywheel", through application of the PDH process, to keep the frequency of the clock laser extremely stable between the interrogations of the atomic reference, which can be spaced by several seconds.
A detailed description of the PDH technique can be found in the very good paper "An introduction to Pound-Drever-Hall laser frequency stabilization", by Eric D. Black of the LIGO collaboration.
The PDH technique can also be used with a very inexpensive fiber ring resonator. While it obviously won't detect gravitational waves, it is more than a cute demonstration. It could in theory be used to reduce the linewidth of a DFB semiconductor laser via electronic feedback, or perform resonant pumping of a stimulated Brillouin scattering laser and dramatically increase its efficiency (up to 50% is theoretically possible). The transfer cavity application mentioned above is also possible, with the caveat that dispersion in the fiber has to be taken into account if the absolute optical frequency of the locked laser is to be known precisely. The shape of the error signal is not exactly the same as with conventional two-mirror resonators, but it is very similar and possesses the key property of odd parity about the cavity's resonance peak, which is what makes feedback loops possible.
The fiber resonator is formed, just like in the previous article, by splicing two ports of a 2X2 FBT splitter and using a polarization controller to align the incoming light with the birefringence axes of the resonant fiber loop. While the PDH technique could be demonstrated by tuning the laser alone using its TEC, this experiment is a good opportunity to also demonstrate a simple trick for tuning fiber ring resonators. Before the resonator is spliced, take a dozen centimeters of multi-strand silicone electrical wire, and strip both ends over 1-2 cm. Then remove all copper strands except one which will be used as a resistive heater, and pass the bare optical fiber that will form the resonator into the wire's insulation together with the remaining strand. Silicone insulation makes it easier to remove all the strands over a relatively long section of cable, and is also a better thermal insulator. An example of wire to use is RS 359-683. Splice the fibers, and slide the splice into the wire's insulation to provide some protection. Note that the splice point will remain fragile and bending the fiber should be avoided as much as possible in this area (which is why splice protection sleeves contain a rigid metal bar), though the moderate bending from the resonator loop will typically be OK. If you are building a long resonator with a small FSR, you can of course protect the splice with a traditional sleeve and place the heater somewhere else. Hold things in place using heat-shrink tubing, which of course had to be inserted prior to splicing. The result looks like this and passing a few amperes into the remaining copper strand heats the fiber and causes the resonator to sweep over many FSRs.
The sidebands for PDH can be produced by injecting RF into the drive current of the DFB laser diode, which avoids using an expensive EOM (but it is very difficult to get rid of the sidebands afterwards, which can be a problem in some applications). Only a very small amount of RF power is required, but one must be careful that electrical noise from the RF generator does not reach the laser. Coupling both ground and signal using capacitors of a small value is a simple solution that helps cut low-frequency noise and eliminate ground loops; alternatively, one can build a simple RF isolation transformer with a few turns of enameled wire on a piece of plastic. Efficiency may be terrible with those solutions, but the power is so low that it does not really matter. Tune the RF power while scanning the cavity (repeatedly turn the heater on and off) so that small sidebands appear on each side of the resonance peaks.
Once this is done, the PDH error signal can be easily observed. The curve shows some irregularities which are related to polarization issues (orthogonally polarized mode resonating at the same time with a slighly different FSR from the birefringence); they can be reduced with (tedious) adjustment of the polarization controller and probably by using PM fiber and the associated expensive splicers. Those irregularities are far more visible on the PDH error signal than on the intensity plot. This signal was demodulated with a somewhat pricy Sinara 4459 Pounder, but it sounds definitely possible to do it on a shoestring using RF modules from Aliexpress/Taobao instead.
February 2023
A few months ago I came across the paper Optogalvanic spectroscopy of the hyperfine structure of the 5p65d2D3/2,5/2 and 5p64f2Fo5/2,7/2 levels of La III. Like almost every experimental atomic physics paper, it involves wanton use of expensive and annoying laser equipment such as a ECDL, FPI and BOA. However, it occured to me that superior optical telecommunication components are available at the wavelengths involved, which could make for an interesting replication. This article broadly describes the procedure as well as practical tips to sucessfully complete it.
The manipulation of ion and neutral atom qubits, including laser cooling, requires lasers with excellent absolute wavelength accuracy and stability. Spectroscopy is a common way to tune and verify such lasers. In the case of optogalvanic spectroscopy, the target ion species itself is often used as the wavelength reference. While there are multiple difficulties with doubly-ionized lanthanum that are not present with conventional ions, it can in theory be used as a qubit directly.
The laser is a "butterfly" DFB module from Shenzhen Box Optronics intended for CWDM telecommunications with fiber coupled output. Center wavelengths of 1410nm and 1390nm at 25C are semi-standard and near the La III wavelengths of interest. Nominal output power is 10mW. Thanks to the DFB technology, the lasers have single-frequency output and the frequency can be tuned via the integrated TEC, over a large range and without any of the nasty behavior exhibited by FP diodes and ECDLs. The modules also integrate a monitor photodiode and thermistor. The linewidth is not specified, but I have measured it to be below 10MHz, which is more than good enough for this experiment. While this may come as a surprise to people who are used to paying ridiculous prices to certain laser companies, it appears that many semiconductor lasers have linewidths in the ballpark of MHz or dozens MHz, including the diode of a $5 laser pointer if you can operate it in a single-frequency region.
The laser is simply driven with a two-channel lab power supply connected to the diode with a current-limiting resistor, and to the TEC. It is important NOT to drive the laser directly from the lab power supply in constant-current mode without the resistor. Many lab power supplies contain a decoupling capacitor which could charge to the full voltage limit, and then discharge into the diode when it is connected and damage it. Laser diodes have much less tolerance for current spikes than LEDs. So the power supply must be operated in constant-voltage mode instead, and with a resistor in series with the laser to "smooth" the response and make the current easy to control.
It is also a good idea to use a high-quality power supply and, before connecting the laser, test it for output voltage spikes particularly when it is switched on and off and when the controls are changed (note that laser diodes do not like reverse polarity either). Or just invest in a proper laser driver ;)
If you are operating the laser near its maximum rated output power, it is important that said maximum power be never exceeded, not even for a short time. This is harder than it sounds for two reasons: (1) laser diodes are more efficient at lower temperatures, and (2) the diode heats up as current goes through it. This means that if you run the laser at a current level that is safe, then turn it off for a few seconds and allow it to cool down, then suddenly apply the same current again, the laser would briefly produce more power and can become damaged. Only using a temperature controller on the butterfly package may NOT be enough depending on the operating conditions of the laser and how close you are to the damage threshold, because of the thermal resistance and thermal lag between the different components of the butterfly package. This is why good laser drivers have an option to ramp up the diode current over a couple hundred milliseconds when they are turned on. Another thing to be aware of is that the laser power will increase as you use the TEC for cooling during wavelength sweeps. So you basically have three options: (1) operate the DFB at, say, 50% to 75% of its rated power to keep ample safety margins (this will increase its linewidth, but it is well below the Doppler broadening in the HCL) (2) keep an eye on the laser power (low-cost multimeter in ammeter mode on the monitor photodiode is enough) as you slowly change the operating conditions of the laser, or (3) use a good laser driver which automatically takes care of those problems.
The original paper uses a free-space Fabry-Perot interferometer that gives a pulse every time the optical frequency crosses a 500MHz boundary, which is very useful to monitor the variations in optical frequency, as well as verify the correct operation of the laser. Obviously we do not want to use such an annoying device, which is expensive, fragile (I have one which developed mirror rot due to the high air humidity in HK), and finicky to align. It is much better to take a 2X2 FBT splitter costing less than a dozen dollars and splice two ports together to make an all-fiber ring resonator. A ratio of 90:10 gives a suitable finesse for this experiment with sharp peaks not overly affected by the laser linewidth, and a fiber loop length of about 40cm gives a FSR of about 500MHz as in the original paper. Fusion splicing can be done with a low-cost kit from China - I used the JIC Fiber T-808S available at a fraction of the cost of a Thorlabs SFPI. A high-quality mechanical splice might perhaps work instead, but the higher splice loss would broaden the peaks.
The main difficulty comes from the birefringence induced by the fiber being bent in the loop, which can cause unwanted resonance peaks or no resonance at all. This can be solved by using an inexpensive three-loop polarization controller (available from Box Optronics as well as several shops on Aliexpress and Taobao) connected right before the fiber resonator, and fiddling with it while the laser wavelength is being swept until the peaks look clean on the oscilloscope display. All fibers leading to the resonator should be held in place using tape and a solid plate (I am using a small low-cost aluminum optical breadboard from China, which also holds the HCL and its fiber interface) in order to keep the polarization stable. It is much easier to find a suitable position for the polarization controller's loops than align a free-space FPI.
After the PC is adjusted, turning up the TEC and watching a long series of perfectly regular peaks scroll on the oscilloscope display is very satisfying, especially if you have spent some time attempting the same with a ECDL and free-space FPI.
Calibrating the FSR can be done with a technique similar to the one described in the original paper, however an expensive optical phase modulator is not necessary as you can instead inject RF into the DFB current and then similarly adjust the RF frequency to overlap the sidebands with the resonator peaks.
As in the original paper, the HCL is a Photron P827A. Compared to the standard P827 model, it is filled with argon instead of neon and slightly more expensive. The argon fill has two advantages: (1) according to the original paper, it gives better signal-to-noise ratio than neon (2) there is a strong well-documented neutral argon line at 1409.36nm. The Ar I line is easy to see and very useful to demonstrate that your setup is working at all - with the laser tuned on the line, you can wave a piece of paper in front of the HCL window and see the output vary, which gives clear evidence that what you are observing is indeed the optogalvanic effect. The La III signal is much weaker and can be more easily missed. The Ar I line can also be used as a wavelength reference; you can count the fiber resonator peaks from it and know when to expect the La III signal.
To couple the beam from the fiber into the HCL, it is first collimated and launched into free space with a small fiber-fused lens from Box Optronics. It is then reflected off two aluminum first-surface mirrors on kinematic mounts to provide adjustments in all four degrees of freedom. Depending on your mechanical skills, there may be a better way to do it. Those collimation lenses are not ideal - they produce a small beam diameter which diverges fairly rapidly, so you need to pack the HCL, mirrors and lens close together to minimize the distance that the beam travels and spreads. An alternative could be to use a collimation tube with a SMA905 connector (note that FS.com can provide SMA905 patch cables if you ask), which can either be purchased from Taobao or Aliexpress, or made yourself by gluing the shell of an electronic SMA connector to the collimation part of a disassembled laser pointer. Unlike the Box Optronics lenses, these options do not provide AR coating for NIR wavelengths, which may or may not be a problem.
The 1410nm and 1389nm wavelengths are completely invisible, which poses a bit of an alignment challenge. NIR viewers and cameras are always expensive and often poorly performing (you are basically paying five digits for a miserable 0.08 megapixel camera), so I do not recommend using those. Instead, you can simply couple a "visual fault locator" (VFL) red laser (FS.com, Aliexpress, Taobao, and also included with many fusion splicing kits) into the fiber and perform the alignment using that. You can verify with a beam card that the chromatic aberration is not excessive (note that most upconverting beam cards can do 1550nm but not 1410nm/1389nm, however some of the other "light charging" beam cards can work). For this, it helps to use the VFL in blinking mode, and combine both beams with a PLC splitter (unlike the FBT type, they can be used satisfactorily with visible light).
There are cheap HCLs available on Taobao and Aliexpress, however when trying one I could not get any optogalvanic signal out of it, and lanthanum lines were only faintly visible in its output with a grating spectrometer, whereas they were very clear with the Photron lamp. I do not know if this a one-off quality issue or if those lamps are generally bad - a similar low-cost calcium HCL from China gave me strong Ca lines on the grating spectrometer. More data points welcome :) They are also filled exclusively with neon in any case, and their construction does not look as nice as Photron.
One problem with the HCL is it may produce a strong oscillation at startup, of about a dozen volts (across the 10k anode resistor as in the original paper) and with a frequency of several hundred Hz to several kHz. This oscillation saturates the lock-in amplifier and renders it unusable. The oscillation appears to be accompanied with a plume of plasma over the lamp's anode, as shown on this picture. It appears the solution is to warm up the lamp at high current (25mA) for about 10 minutes, during which the oscillation diminishes in frequency, becomes intermittent, and finally disappears. It does not reappear after the lamp current is lowered. Using an oscilloscope, monitor the HCL's AC signal after the coupling capacitor to check for this problem.
The entire optical layout is as follows:
The implementation may look like this (oscilloscope showing the fiber resonator output and the lock-in amplifier output while going over the strong Ar I line).
Fiber splitters with various ratios can be obtained inexpensively from Box Optronics or from various sellers on Taobao. Testing them with an optical power meter (FS.com) showed that they work well enough at 1410/1390nm despite being designed for 1550/1310nm.
In place of the mechanical beam chopper from the original paper, a MEMS variable optical attenuator (VOA) from FS.com is used. This keeps the experiment free from large moving parts and keeps the laser beams in fibers and everything "plug and play" as much as possible. They are not intended for amplitude modulation but they can still be used up to several hundred Hz. Compared to a Mach-Zehnder modulator, the VOA has lower insertion loss and lower cost, but also much slower response time. A photodiode after a second fiber splitter can be used to adjust the VOA drive waveform for maximum contrast and to provide a reference to the lock-in amplifier (see below).
Components are connectorized with SC/APC. The main reason for this is adapters, patch cords, and other components are available with this connector from FS.com with high quality, point-and-click ordering, short lead time, and low price. Many suppliers for other components (photodiodes, laser, splitters, ...) offer SC/APC connectorization at no additional cost. FC/APC is a more common choice for laboratory laser equipment and only slightly more expensive - if you already have FC/APC gear around, you may want to choose that instead.
The lock-in amplifier is an inexpensive "Modem AD630" board from Lockzhiner Electronics. It consists in a AD620 amplifier, followed by the AD630 demodulator and a low-pass filter based on a NE5532. Several similar boards from other suppliers exist and can be found on Aliexpress and Taobao. While the performance of this gadget applied correctly can rival that of much pricier instruments, its use is not straightforward and there are several pitfalls that must be avoided - which is not difficult nor expensive when you are aware of them.
First of all, the "Modem AD630" is incapable of quadrature demodulation. This means that the reference and input signals must be in phase. This is an issue in our setup as the response time of the MEMS VOA is not negligible compared to the period of the modulating waveform, and the VOA introduces substantial phase shift. This is solved by using a second 99:1 splitter to sample the beam after the VOA and direct a small portion to a photodiode, which provides the required in-phase signal compensated for the VOA response time. The reference input of the "Modem AD630" expects an AC signal and is a bare floating IC input. To interface it correctly, the bare photodiode is loaded with a 10k resistor, followed by an AC coupling capacitor, and a 100k pull-down.
The second issue is the AD620 input stage can saturate. You'll want to power the board near its maximum rated voltage (e.g. +/-12V) to prevent this from occuring and extend the dynamic range of the amplifier. You'll also want to solder a test point at the output of the AD620 and monitor the signal with an oscilloscope to check for saturation as you adjust the gain pot. At high gain settings, the amplifier may also oscillate by itself. With the HCL powered on and warmed up, adjust the gain for maximum amplitude while staying away from saturation and oscillation. It is a bit of a mystery why the "Modem AD630" does not already include an easy way to probe the output of the AD620, as it is difficult to troubleshoot and properly adjust the gain pot without that.
The last difficulty is interfacing the HCL with the "Modem AD630" input. The original paper simply shows an AC coupling capacitor - doing this literally with the "Modem AD630" would not work and would almost certainly result in the board getting destroyed. Additional components required after the coupling capacitor are (1) a pull-down to ground as the input is again a bare floating IC input (2) protection clamping diodes to the power supply rails (3) zener diodes to prevent overvolting the supply rails (might be overkill, but better safe than sorry) (4) a series resistor, capable of taking high voltage, between the capacitor and protected input. When the lamp strikes, its impedance suddenly drops and the anode potential falls by several hundred volts. This causes the coupling capacitor to discharge through the lamp and the protection diodes. Without the series resistor, this discharge causes a large current spike which produces a visible flash inside the lamp, and which cannot be good for the protection diodes and the lamp's lifetime.
Oscilloscope picture showing the strong Ar I line at 1409.36nm.
Video where the TEC is turned on and off to repeatedly scan over the Ar I line.
Oscilloscope picture of my very first observation of the La III spectrum near 1409.6nm, showing hyperfine structure. The X axis is flipped compared to the figure in the original paper as the optical frequency was decreasing when this picture was taken. Note the oscilloscope's vertical scale: 5mV/div compared to 500mV/div in the pictures above for Ar I. The La III signal is two orders of magnitude weaker than the Ar I signal! The signal-to-noise ratio is not great but there are probably low-hanging fruits.
More to come later!
All amounts are in U.S. dollars and approximative. Not included are common electronic lab equipment (oscilloscope, DC power supplies, soldering iron, function generator), fusion splicing kit (can be as low as $600 for Chinese models), and laser safety glasses. If you are starting from zero, the MHS5200A function generator is very low-cost ($50) and definitely capable. If you want it really cheap, replacing the MEMS VOA with a homemade mechanical chopper built from scrap and sampling the beam with a Fresnel reflection from a microscope slide is likely feasible, and all mechanical mounts could be homemade from scrap as well (the alignment is not very critical). The polarization controller is also somewhat optional - manually bending and taping the fiber around also works, though it is time-consuming, fiddly and tedious.
| CWDM DFB laser | $200 (one wavelength) |
| Hollow cathode lamp | $350 |
| MEMS VOA | $170 |
| Polarization controller | $70 |
| Fiber splitters | 3*$10=$30 |
| Collimation lens | $10 |
| Photodiodes | 2*$5=$10 |
| Optical breadboard, mounts, mirrors | $250 (varies) |
| AD630 lock-in amplifier | $50 |
| VFL | $10 |
| Total | $1,150 |
Thanks to David Allcock and Steven Olmschenk for productive discussions about this experiment.
Thanks to Samuel Goldwasser, Rüdiger Paschotta, and Alexandra Elbakyan for making educational literature available.
July 2022
I picked up on eBay an Ando AQ6140 optical spectrum analyzer which, in what constitutes a rare demonstration of honesty from an eBay seller of this kind of product, was described as "powering up but unable to boot". After arrival and a quick investigation, the reason for the boot failure appeared to be a faulty system CF card inside. The embedded computer was working fine otherwise, as it could run OpenBSD from a new CF card.
Unfortunately, the original CF card was totally unresponsive and could not be read at all from another computer; its controller (a proprietary and unobtainium Sandisk chip) appears to be completely dead. The flash chip inside is also a proprietary and obscure Sandisk model and the position of ground and power pins did not match any common NAND pinout, so data extraction sounded difficult (pictures: 1 2). Contacting Yokogawa/Ando to obtain a replacement firmware image resulted in a pure stream of B.S. along the lines of "the internal reference laser is dead" (it wasn't), "the internal reference laser can no longer be manufactured because it needs helium" (orders of magnitude less than a party balloon), "why don't you buy our newest model?" (I'd rather buy a small yacht), etc.
Opening the top cover of the unit reveals the main two electronic boards. They can be easily removed to access the other components of the device: the main power supply, a high-voltage power supply, a Vexta/Oriental Motor stepper control board, and the optical block where the magic happens. The optical block is made of a cast iron machined block that holds all the other components with the optics in place. Inside is a traditional scanning Michelson interferometer with two corner cubes on a moving carriage and a HeNe laser as reference (which is working fine contrary to what Yokogawa/Ando claimed), which is very similar to Michelson wavemeter designs described in the literature. The most remarkable thing is that the moving carriage is directly connected to a stepper motor with a synchronous belt; there is apparently not much being done to isolate the carriage from vibrations or make its motion smooth, and they certainly did not take extreme measures such as the air bearings described in some wavemeter papers.
Overall, the unit appears to be exceptionally well-built and maintainable (unlike e.g. the Burleigh WA20 which is totally janky, ridiculously frustrating to align, and an electrocution and fire hazard), it is a shame that Yokogawa/Ando does not care at all about repairs and tells lies to try to sell their new products.
The two photodiodes for the reference and measurement interferograms are mounted on a small circuit board, part of the optical block, which also contains two transimpedance amplifiers. The outputs are carried over coax cables to the DSP board. There, the edges of the reference interferogram are used by an analog circuit to clock an ADC that digitizes the measurement inteferogram (synchronous sampling). This and Nyquist's theorem probably have to do with the shortest wavelength that the AQ6140 is advertised as being capable of measuring (1270nm, which is close to 2*633nm=1266nm). So far so good, but things go downhill quickly from there, which is why I eventually gave up trying to make use of the original electronics.
The ADC is interfaced through an Altera FLEX FPGA to a TMS320 DSP whose sole purposes appear to be filling a large bank of SRAM with the samples, and communicating with a second TMS320 DSP over a pair of dual-ported (and expensive-looking) SRAM chips. This second TMS320 DSP performs the Fourier transform and communicates with the embedded computer on the ISA bus using a second Altera FLEX FPGA and more of that pricy dual-port SRAM. Dealing with the TMS320 is very much a pain in the neck, with antiquated development tools and a proprietary equivalent of JTAG for which debug probes are only available from dodgy vendors at ridiculous prices (I didn't buy). The computer board, based on a CARD-586 module from Epson, is also a monstrosity with a third FPGA dedicated to making the CF card look like a floppy disk during boot so that the BIOS can access it, a full 6502/UVPROM/SRAM mini-computer whose sole purpose is to scan the front panel keys and emulate a PC keyboard, and an ASIC (!) to generate pulses for the stepper driver and for which they apparently ran out of signals on the ISA bus since some of the ASIC's control and address lines had to go through an ISA GPIO chip. I'm not certain if it would have been fully doable considering the lousy ISA DMA bandwidth available at the time and Conway's law considerations, but it looks like the entire digital part of this system (other than the CARD-586) could have been advantageously replaced with a single FPGA. Ironically the CARD-586 has more FPU power (and much nicer development tools) than the TMS320 and its FPU probably just sat unused. But one thing is for sure: manufacturing those boards must have cost a lot of money!
I eventually managed to obtain optical spectra by digitizing the two signals from the TIAs using an oscilloscope and sending the data to a computer for a bit of processing with Python/NumPy/SciPy. The stepper motor and its driver (PMD07CV) are quite peculiar with a motor winding topology that seem to be used only in Japan; luckily the driver was in good working order and Oriental Motor emailed me its datasheet (in Japanese). The rest was pretty straightforward. Analyzing the combined output of two CWDM lasers produced peaks at the expected positions on the spectrum. Even incoherent light can be analyzed, with limited resolution, using this setup when the carriage crosses the point of zero optical path difference. Connecting a low-cost EDFA with the firmware configured in ACC mode (constant pump current) and no signal at its input produced the textbook spectrum of erbium-doped glass ASE. Considering the very high price of NIR CCD sensors (including linear ones), this is probably what typically needs to be done instead of trying to use a grating-based spectrometer in this wavelength region; additionally, for coherent light sources, the resolution is higher than what could be achieved with a simple and compact grating-based spectrometer.
August 2020
In most lasers, the spacing between the modes noticeably deviates from the FSR of the laser cavity. Indeed, the gain medium "pulls" the frequencies of the resonating modes towards the maximum the gain curve, which results in a small detuning from the frequencies that would be expected if the cavity contained vacuum. This phenomenon is easy to observe using a short two-mode HeNe laser tube and a software defined radio. We need the HeNe tube to be short so that at most two modes are oscillating (short tubes have a higher FSR which means that only one or two modes can be under the narrow neon gain curve at any given time). This in turn results in a beat note between the modes at around 1GHz, which is the signal we will be looking at. For information about the workings and procurement of HeNe lasers, see Sam's Laser FAQ.
Direct the beam into a polarizer oriented at approximately 45 degrees relative to the tube's polarization axes (in red HeNe lasers, the modes are polarized orthogonally from each other) and into a silicon photodiode connected directly to the SDR's antenna input. The signal is strong with plenty of room for inefficiencies, so, it does not really matter if the polarizer is not very well aligned, if the photodiode is not a particularly high-speed model, if the SDR's 50-ohm input is not a great photodiode frontend, if your SDR is cheap, etc. If you want a photodiode that is guaranteed to work, the Hamamatsu S5973 is a good choice, though many cheaper ones will also produce a usable signal. Telecom photodiodes for 1310nm/1550nm will NOT work as their semiconductor material is not sensitive to visible light. To increase signal if necessary, you can use a lens to focus the beam onto the photodiode's active area. If your SDR has a bias-T function, it can be turned on to reduce the photodiode's capacitance, but make sure that the photodiode is reverse-biased otherwise damage will occur. An external bias-T can also be used instead and typically can reach higher bias voltages.
A HeNe tube freshly turned on and warming up will go through cycles of mode sweeping, as its cavity expands from the temperature rising. This causes the cavity modes to move under the neon gain curve, as explained in detail on Sam's Laser FAQ. The frequency pulling effect causes the distance between the modes to vary substantially and non-monotonically (much more than what would be expected from the small and monotonic decrease in the FSR caused by the expansion) and is clearly seen on the SDR's waterfall display. The RF signal also vanishes periodically as the tube crosses into regions of single-frequency operation.
Thanks to frequency pulling, we have information about where the cavity modes fall on the neon gain curve, and we can use it to stabilize the HeNe laser tube. There are multiple ways to control a HeNe cavity length, and many are described in Sam's Laser FAQ. The technique used here is based on a small induction heater with the heating coil that goes around the tube's metallic mirror mount.
The induction heater (see detailed circuit photo) is simply a MCP1407 MOSFET driver which feeds a resonant LC tank through a series inductor. External MOSFETs are not necessary as the MCP1407 itself can already provide enough power to make the HeNe tube go through dozens of cycles of mode-sweeping. The power delivered to the mirror mount can be varied by taking the LC tank further from or closer to resonance by changing the drive frequency. This is accomplished by connecting the input of the MCP1407 to a low-cost MHS5200A function generator that can be controlled over USB. This method is very power-efficient (the heatsink seen on the pictures is not really necessary) and does not need a DAC. The LC tank capacitor must be one specified for induction heating applications; general-purpose capacitors are not designed for being constantly charged and discharged hundreds of thousands of times per second at high current and they will heat up and burn (the current circulating in the tank is much higher than the 6A that the MCP1407 can supply!). Additionally, external protection diodes that clamp to the power rails must be added on the output pin of the MCP1407. Otherwise, if the circuit is powered down with the tank at resonance, the stored energy will discharge into the MCP1407 and cause part of its die to literally explode (Photo: Sascha Naske). Also, beware that the HeNe tube's electrodes may be at a very high electrical potential (it can be in excess of 10kV before the tube strikes), and design things so that the tube's mirror mount won't arc to the heater coil (for example, ground the tube's cathode and install the heater coil there - study your HeNe power supply to check if this solution would work).
A software-based P controller that adds an offset to the induction heater's drive frequency proportional to the difference between the beat note between the modes and a reference value is sufficient to lock the laser. After trying a few algorithms for lock acquisition and not being very successful at making them reliable, I simply added a second offset to the drive frequency which is chosen randomly when the laser lock times out after a few seconds. This may not be the fastest or most beautiful technique but it is simple to implement and pretty foolproof.
With the laser stabilized in a two-mode region and the mode beat ("REF") signal already digitized by the SDR, all that it takes to build a DMI is to follow the techniques for the two-frequency interferometer described on Sam's Laser FAQ with just that different laser source and a SDR to process the signals. Without the Zeeman split, the tube already emits two orthogonal linear polarizations so the waveplates are not necessary. You need a two-channel coherent SDR for this experiment, such as the bladeRF. With complex (IQ) samples such as those acquired by the bladeRF, the displacement is proportional to the unwrapped argument of the MEAS signal multiplied pointwise by the conjugate of the REF signal. This computation can be implemented with just one line of Python/NumPy code :)
The results are seen in this screenshot, with the moving corner cube mounted on a speaker driven by a sine wave. I have not attempted to quantitatively characterize it or optimize it, but the system subjectively seems a bit noisier than the Zeeman-split ones from HP. Nevertheless, displacements can be tracked with about a dozen nanometer accuracy.
