Artist rendering of cavity

Researchers in the Netherlands have shown how an oil-filled optical cavity can generate stochastic resonance across a wide range of frequencies, thanks to the time needed for the incoming laser beam to heat up the oil. [Image: AMOLF Interacting Photons group]

Unable to detect a weak signal? Stochastic resonance could be the answer—even if the signal in question covers a broad range of frequencies.

Stochastic resonance allows a bistable system to pick up an otherwise undetectable oscillating signal, by adding in just the right amount of noise. First proposed in the 1980s to explain the recurrence of ice ages, the phenomenon has since been observed across the sciences, from physics to chemistry and biology to finance. Some systems, however, seem able to exploit the effect across a far wider range of frequencies than suggested by theory.

New research shows how such broadband stochastic resonance can be made possible by introducing memory into a system’s nonlinearity. The study also reveals that this effect could lead to a huge improvement in systems that harvest energy from vibrations, boosting their efficiency by as much as a factor of ten (Phys. Rev. Lett., doi: 10.1103/PhysRevLett.126.213901).

Getting in synch

Bistable systems rely on nonlinearity to generate two distinct outputs from a given input. With a strong enough constant input, the system yields one of the two outputs for good. On the other hand, an oscillating input—a signal—causes the system to switch back and forth continuously between the two output values.

Stochastic resonance comes into play if the bistable system is not sensitive enough to pick up the input signal unaided. If there is too much noise in the environment, the system will be swamped and continue to draw a blank. But just the right level of noise will instead cause the system to synchronize with the input signal. This in turn will amplify the signal and make it detectable.

Normally, this synchronizing phenomenon only happens when the input frequency matches the rate of random flipping induced by the noise. But, as pointed out by Said Rodriguez of AMOLF in Amsterdam, the Netherlands, the resonance condition appears to be far more relaxed for some systems in nature. Preying fish, for example, use noise to amplify signals emitted by plankton, even though the underwater environment leads to significant fluctuations in the signal frequency.

Oily cavity

In the latest research, Rodriguez and colleagues in AMOLF and the University of Oxford in the UK explore how memory might explain this broadband effect. To do so, they filled a small optical cavity formed from two moveable mirrors with oil from macadamia nuts. Into the cavity they fired a beam from a single-mode green laser, and measured the output using a photodetector.

The system’s bistability came as a result of the laser heating up the oil, which changed the oil’s refractive index and thus altered the cavity’s resonant frequency. To generate a signal, the researchers modulated the cavity length at a certain frequency, causing the output to switch between two different intensities. Setting the signal at below the detection threshold, they then added white noise to the input by passing the laser through electro-optic modulators.

Memory expands bandwidth

Rodriguez and co-workers confirmed that they had achieved stochastic resonance by varying the voltage across the modulators (and thereby changing the noise intensity), and observing a peak in the signal-to-noise ratio at intermediate voltages. More eye-catchingly, they also varied the modulation frequency and recorded how many times per cycle on average their system switched output. Switching exactly twice per cycle means perfect synchronization between signal and noise—and that is what they found across a wide range of frequencies, between about 6 and 90 Hz.

Using numerical simulations to extrapolate their data, the researchers concluded that the stochastic-resonance bandwidth of their oil-filled cavity could be at least 3,000 times greater than that of a standard Kerr-nonlinear cavity.

This far greater bandwidth, according to Rodriguez, is due to the time lapse between the laser passing through the oil and the oil’s heating-induced change in refractive index. “The heating up is not instantaneous; it takes about 10 microseconds” he says. “That is the memory time of the system. And it is that memory which makes the system less sensitive to changes in the modulation frequency.”

Harvesting energy

Having made this discovery, the researchers then asked themselves whether similar memory effects might be useful for mechanical systems that harvest energy from vibrational noise. So they simulated a piezoelectric transducer that converts this motion into electricity and gave it memory. The result was striking: they found that the memory could increase the amount of harvested energy tenfold compared to previous results.

As Rodriguez explains, such transducers only harvest energy efficiently at the resonant frequency of the oscillator used to convert mechanical strain into an electrical charge or voltage. “This makes them narrowband devices, and therefore inefficient,” he says. “There is a lot more energy they could harvest if they were broadband.”

The trick, says Rodriguez, would be to engineer such devices from materials that have memory in their nonlinear response. Unfortunately he and his colleagues don’t yet know of a material that could fit the bill. So he urges other experts to step in. “We are hopeful that our work may inspire material scientists or mechanical engineers to look for that kind of system and apply it to energy harvesting,” he says.