Nonlinear Optical Sensor Avoids Precision/Speed Trade-Off

An optical measurement method devised by a team of AMOLF researchers aims to simplify and streamline the ability to capture measurements from signals that are barely larger than the noise contained in the same system. The newly introduced approach uses a proposed single-mode Kerr-nonlinear resonator to perform sensing in noisy environments.

Specifically, the method aims to reduce the influence of noise — an important consideration in detection with optical systems — when measuring very small signals.

According to AMOLF group leader Said Rodriguez, who developed the measurement approach with researcher Kevin Peters, precision is sometimes the most important consideration in the physical measurements of a system, with the goal to reduce uncertainty about the state of the system.

In other cases, speed is most important.

In most detectors, Rodriguez said, accuracy comes at the expense of speed.

“Consider something so simple as looking at a painting: if you only see the painting for a few seconds, you will gather much less information than when you get see it for a few minutes,” Rodriguez said. “In other words, the longer we measure, the more information we gather and the more precisely we know the state of the system (the painting).”

Where a typical optical detector, based on a resonator or a cavity, provides a signal when, for example, a molecule perturbs the resonator, this signal can be so small that it barely exceeds the noise generated by the laser, Rodriguez said.

A nonlinear optical sensor outperforms the best possible linear sensor. The figure shows an optical cavity, formed by two mirrors (blue and green multilayers) facing each other. One of the mirrors is coated with a nonlinear material (pink slab). By sending laser light into this cavity, and modulating the light intensity at a high frequency, the presence of a perturbation (epsilon) to the cavity can be detected. The sensing approach works best when making fast measurements and avoiding excessive averaging. Courtesy of AMOLF.

The researchers found inspiration in an exotic physical phenomenon that occurs in open quantum systems such as optical resonators that measure the presence of molecules or viruses. “Such systems have complex eigenvalues that sometimes coincide,” Rodriguez said. “In that case we speak of an ‘exceptional point,’ and theory suggests that measurements at exactly such a point should be much more sensitive.”

In experiments, however, the signals and noise were both enhanced at these “exceptional” points. This was compounded by the complexity and difficulty in determining the exact location of the “exceptional” point at which to measure.

The researchers realized that something similar to the “exceptional” points could also be identified in the resonators with which they performed their experiments, which were nonlinear optical cavities. Nonlinear optical cavities can have what is known as optical hysteresis.

“When you ramp the laser power up, the light intensity in the cavity builds up in a certain way,” Rodriguez said. “But then, when you ramp the laser power down, the light intensity leaves the cavity in a different way. This results in hysteresis, similar to the magnetization of certain materials when a magnetic field is applied to them.”

Experiments showed that the difference in light intensity between the points where the hysteresis opens and closes was proportional to the square root of the disturbance of the resonator. The measurement of this, called a “difference signal,” was therefore very sensitive to small perturbations.

With faster measurements, the influence of noise became smaller — which contrasted what happens in conventional measurement methods, Rodriguez said.

The researchers made theoretical calculations for the proposed sensor and noted that setting the correct modulation frequency for measurements with the proposed optical resonator is easily possible with existing equipment. As a result, Rodriguez hopes to collaborate with industry to explore the idea further and use it for optical sensing.

“This way of measuring is interesting for all kinds of applications where optical sensors are already in use,” Rodriguez said. He identified chemical measurements and nanoparticle detection as possible applications for the nonlinear approach.

The research was published in Physical Review Letters (www.doi.org/10.1103/PhysRevLett.129.013901).