Webinar: Microwave Mastery with Mechanics

This blog post accompanies our webinar Microwave Mastery with Mechanics. A big thank you to Dr. Rémy Braive, associate professor at Université de Paris Cité and CNRS-C2N who presented his recent experimental results. You can find the recording here.

Thank you also to everyone who joined the webinar and participated in the lively Q&A session. The answers to all the questions, along with a summary of the content, can be found below.

Introduction

An oscillator transforms a direct current (DC) signal into an oscillatory waveform, which is essential in navigation, communication, and timing systems. Developing these systems presents several challenges, including achieving stability and precision, as well as ensuring operation at GHz frequencies to prevent frequency mixing. Additionally, designing such devices which are compact and are unaffected by electromagnetic perturbances are crucial. For the latter, often optical carriers are utilized to minimize these perturbations.

Typical examples of such oscillators include OCXO (Oven Controlled Crystal Oscillators), TCXO (Temperature Compensated Crystal Oscillators), VCO (Voltage Controlled Oscillator). For most applications they are employed as clocks for electronic systems. In most cases however, this comes with some compromises. In some situations either they are compact while the phase noise is reasonably high or have very low phase noises but are bulky. Clocks designed on optical platforms typically provide very good phase noise performances but are often too bulky due to long fibers. Therefore, a strong requirement is to have a clock which ticks both boxes i.e. is compact and has good phase noise performance.

In this webinar, Dr. Remy Braive discusses the concept of integrated photonics powered by principle of optomechanics to design clocks with small footprint and good phase noise performance. The discussion in this webinar was divided into two sections:

• Generation of low phase noise microwave clocks using a NOEMS (Nano-Opto-Electro-Mechanical Systems) platform.
• Neuromorphic computing with such oscillators.

Low phase noise signal generation:

The webinar begins with an introduction on Optomechanics which describes the coupling mechanism between optical cavities and mechanical resonator.

Typical requirements for such experiments are optical cavities with very high finesse and mechanical resonators with eigen-frequencies anywhere between kHz to GHz. In a Nano-Opto-Electro-Mechanical System or NOEMS platforms electrical connections are also added in order to control the mechanics.

The group of Dr. Braive achieves this by utilizing integrated photonics which includes a photonic crystal cavity operating at 1550nm telecom wavelength while the same photonic structure supports the so-called localized mechanical modes around 3 - 4 GHz (see Figure 1). As mentioned, the two physical domains are coupled to each other by the so-called optomechanical coupling through photo-elastic effects.

This fist part of the seminar shows how parametric amplification allows generation of self-oscillation on the mechanical resonator at the GHz frequencies. For this, the device was connected to the SHFLI 8.5 GHz Lock-in Amplifier: An RF signal was injected on one contact using the signal output of the SHFLI, while the transmitted signal was measured using the signal input channel (see blog post). Injecting a weak RF excitation around the mechanical resonance results in the so-called injection locking phenomenon which reduces the phase noise of the mechanical resonance to a very reasonable levels, this is shown in Fig. 2(a). Additional optoelectronic feedbacks allows a drastically improvement on the phase noise performance. As seen in Fig. 2 (b) the phase noise goes from - 80 dBc/sqrt(Hz) at 100 kHz offset from the carrier to -108 dBc/ sqrt(Hz) with with fibers only 200 meters long. Compared this to the existing optoelectronic oscillators with fibers that extends to few kms. This allows a significant progress towards low phase noise based clocks with significantly smaller footprints. The group is looking towards decreasing the footprint of devices while boosting up the phase noise performance. Further discussion on this topic was however outside the scope of this webinar.

Neuromorphic Computing

Second part of this webinar starts from the concepts of injection locking on this NOEMS platforms discussed in the previous section and delves into development of neuromorphic computing. The goal of this research is to build the basic building blocks of neuromorphic computers, also called the neurons out of these NOEMS platforms. It is well known that under injection locking, the system can be defined to be either in stable (injection locked) and unstable states (unlocked). Such states are then separated by a phase threshold, \(\phi_{Th}\) in the phase space. With an external perturbation \(\phi_{pert}\) < \(\phi_{Th}\), there is no excitation or firing. However. under this condition \(\phi_{pert}\) > \(\phi_{Th}\), the system goes through a \(2\pi\) rotation (see Fig. 4). 

This experiment utilizes the capabilities of SHFLI where it is being used as the source of excitation of small RF (GHz) signals sent for injection locking. An additional optical pulse is sent for the phase perturbation. The set-up is shown in Fig. 3, The measurement is done with the SHFLI directly at the GHz frequencies. Thanks to the direct lock-in measurement at these frequencies, it is possible to look at the I and Q quadrature while constructing the system response in the phase space. This is shown in Fig. 4 (a); while the perturbation power \(P_{pert}\) = 10% \(P_0\), there is no excitation. Here, \(P_0\) is a certain power which is defined as the threshold for the switching. Careful observation on the inset also shows that the system only covers a limited regime in the phase space. On the other hand (Fig. 4 (b)), while the threshold is crossed for \(P_{pert}\) = 80% \(P_0\), the system experiences a 2\(\pi\) rotation in the phase space as indicated by the inset as well.

Conclusion

In conclusion, the webinar shows how to implement on chip NOEMS platforms based on the principle of Optomechanics. The webinar was divided into two parts: In the first part, we began by discussing on how to implement low phase noise oscillators based on such NOEMS platforms and even how to improve its performance further by utilizing the principle of injection locking. In the second part we discussed NOEMS systems as the building block for neuromorphic computing. Here we discussed how such systems can be used as the the basic building blocks for such computing schemes, which are also known as artificial neurons.

Questions and Answers:

Can you explain what is parametric amplification?

This is a method to overcome internal losses inherent to systems. For example, parametric amplification is used similar in lasers in order to “lase“ by overcoming the inherent losses.

How do you control the working frequencies of your device?

The working frequency is really by design. In the presentation you could see the holes on the beam. We can control the frequencies by controlling the size, position and shape of these holes.

What is the limiting factor for the performance of the oscillators and/or the neurons?

Like the oscillator, the mechanical quality factors are one of the limiting factor. Another very important limiting part is the thermal relaxation time of the thermal phonons. Since the system has only a very thin bridge allowing thermal dissipation, it doesn't allow fast escape for these thermal phonons. This is indeed a bottleneck for these systems.

Do you have issues with your mechanical mode heating up as a result of the optically induced thermal bath?

This is also related to the previous question; As mentioned previously the timescale of the thermal relaxations limits us on how fast we are able to operate these neurons. This problem is similar to issues on quantum optomechanical systems where they need to rely on pulsed measurements to reduce this heating effect. Our simulations also support this claim.

How is it that the optics can control the mechanics?

This is based on the principle of optomechanics where an incident laser induces the so-called “optical-spring“ effect and thereby directly controlling the spring constant i.e. the frequency of the mechanical resonator.

Why in the open loop frequency measurement, the resonance frequency varies with the laser wavelength.

This is related to the question above. As we change the wavelength, we modify the intra-cavity power. As a consequence, optical spring effect appears as well.

What is the impact of the Casimir effect (probably negligible)?

Yes in our case experiments we have not seen any clear indication of Casimir forces.

What is the strategy for a network of oscillators on neurons?

For neurons, this is still a very new research domain for us and this is where we would like to use the full functionalities of SHFLI. For network of neurons, probably we need to change the strategy of our experiment. Till now, we have been doing the perturbation in optical domain and implementing weak electric force in the electrical domain. But our assumption is that for the network of neurons we need to switch to the measurements in optical domain while perturbation in RF. This way we can control different neurons with different frequency and amplitudes. This is not so trivial and will be something for the future.
Also I would like to add that the work we are doing with optical packaging will helps us connecting different optomechanical neurons through optics.

What is the difference between this and feedback cooling?

Cooling essentially means damping the system i.e. the drive and oscillation are opposite in phase. While in our case we would like to amplify the motion and hence we are in phase.

Why don't you use piezoelectric for feedback loop

We do use an electro-mechanical excitation of the resonator thanks to the piezo-electric properties of the material.