Resonators made of a disk and a movable continuous-membrane Open Access

The use of microcavities¹ for detection^2–5 and studying samples in the nanoscale is a highly active field. Microcavities are useful in sensing biomolecules,^6,7 nanoparticles,^8–12 proteins,^13–15 bacteria,^16,17 viruses,^18,19 ultrasound^20,21 and magnetic fields,^22,23 temperatures,²⁴ weak forces,²⁵ refractive indices,²⁶ and angular velocities.²⁷ In addition, cavities provide resonantly enhanced access to quantum dots,^28–31 nanocrystals, and nitrogen-vacancy centers^32,33 used in fundamental studies and cavity-QED applications. In a wider perspective, non-resonant methods by interferometric detection of scattering^34,35 can sense single unlabeled molecules. Generally speaking, microcavities support multiple constructive interferences to enhance the interaction of light with an analyte. Another enhancement mechanism relates to confining the light in the dimensions perpendicular to its propagation direction. In this regard, the circulating light is confined in its transverse plane to a width comparable with the Rayleigh limit of wavelength divided by two. Accordingly, and in a more scientific language, resonance enhancement scales with the optical quality factor of the resonator, Q, divided by the volume of its electromagnetic resonance, V. To discuss this in more detail, optical interactions in microcavities usually scale with Q/V or with Q/V to an integer power, typically two. Here, we present a general technique that will permit controlled resonantly enhanced access to quantum dots, nitrogen vacancies, and nanoparticles, among other point-like analytes. Bringing an analyte to close proximity with the optical mode results in a related change in the effective refractive index, leading to scattering or increase in light absorption. These mechanisms are associated with resonance drift, resonance split, or broadening of the resonance linewidth. Accordingly, many efforts were invested in sensing methods based on these mechanisms (resonance drift, split, or quality reduction). To measure drifts in resonance frequency, locking mechanisms, such as Pound–Drever–Hall control,^36,37 were used for detecting analytes such as nanoparticles.³⁷ For measuring resonance split, beatnoting laser lines originating from a split resonance were used.³⁸ Finally, for measuring resonance broadening, cavity ring-up techniques were developed and demonstrated to operate at the fastest permitted speed.³⁸ 

A major challenge common to all of these sensors relates to the fact that their highest sensitivity is just before detecting the first analyte. After that, the detector’s sensitivity drops with any successive detection event. While washing methods can recover the resonator sensitivity, it is quite challenging to clean the resonator every few detection events. Another challenge that is common to most analyte-detection schemes relates to the fact that analytes typically fall in a random position with respect to the optical mode’s location. Relatedly, it is quite rare that an analyte falls within the position where the evanescent cavity field is maximal, and the detection sensitivity is accordingly the best. In most cases, analytes either miss the resonator or fall in a region where the evanescent field is not maximal. Hence, it is attractive to develop a method to control the analyte’s location and convey it upon request to the maximal evanescent-field region—for detection, and then removing the analytes and bringing new ones. Such an analyte conveyer will be able to leverage the current detection schemes^19,37,38 to benefit from both worlds: removing the analyte after detection to refresh the detector’s sensitivity as well as to position the analyte at the place where the evanescent field is maximal and detection sensitivity is correspondingly the highest.

Here, we present a microresonator consisting of two mechanically separate parts, a disk and a membrane, which can move one with respect to the other. Both the disk and the membrane co-host the optical modes in our hybrid resonator. The membrane can be as wide as needed, and moving it in parallel with the disk affects neither the optical mode nor its position. By spreading scatterers on the membrane and moving it laterally, we bring scatterers into the optical mode region, monitor their scattering, and then move them away and bring new ones. Although we do not demonstrate analytes detection here, our experiments prove the concept of a resonator where one of the elements is a moving continuum that can carry analytes. In addition, the membrane can serve to bring two analytes to interact. Let us explain in more detail. If the distance between two analytes on the membrane is smaller than the resonator’s diameter, then we can control their position so that both analytes overlap with the optical mode. To give just one example, controlling two objects to overlap with optical resonance might permit studies of two interacting nitrogen-vacancy centers.³⁸ The membrane can move not only parallel to the disk but also perpendicularly toward the disk. Such a perpendicular motion of the membrane, which changes the gap between the disk and the membrane, is accompanied by a resonance frequency drift. This gap–eigenfrequency relation can be used to control and tune the resonance frequency or for sensing small motion of the membrane. Since the membrane is flexible and can hence bend by weak forces, our device can serve as a sensor where drifts in resonance frequency indicate forces applied to the membrane. A mass attached to the membrane, preferably far from the optical-mode region, can make our hybrid disk–membrane resonator into an acceleration sensor. Similarly, a magnet attached to the membrane can make it a magnetic field sensor.^22,23

As one can see in Fig. 1, a hybrid resonator made of a disk and a membrane lies in the center of our experiment. The resonator is made of a silica microdisk fabricated on a silicon chip similar to other such whispering gallery mode resonators.³⁹ A membrane (TEMwindows.com, silicon dioxide, 300 nm thick) is held above the disk, while the disk position is controlled using a nanopositioning system (Physics Instrument, P-611.3, NanoCube). Light is evanescently coupled into and out of the resonator using a tapered fiber.⁴⁰ The optical fiber was touching the disk, so that coupling was unaffected from the disk motion toward and from the membrane. The lateral motion was assisted by another position-control system attached to the membrane. Using this setup, we tune the incoming light wavelength, change the membrane position with respect to the disk, and monitor transmission through the resonator. The nanocube motion is calibrated using the interference between the reflection from the membrane and the reflection from the disk [Figs. 1(b) and 1(c)]. We will later use this calibration for controlling the gap with a high degree of accuracy. We call the interference pattern that originates from the membrane and disk reflections—an interferogram. As the illumination used for the interferogram is at a wavelength of 450 nm, a drift of one fringe stands for a change of 225 nm in the gap. We estimate the accuracy in measuring the gap as 22 nm, based on our ability to resolve a tenth of a fringe motion. Before we start our experiment, it is important to align the membrane so that it is parallel to the disk. For doing so, we tilt the membrane while monitoring the interference between the reflection from the disk interface and the reflection from the membrane interface [Figs. 1(a) and 1(d)]. Our first alignment is typically providing ten fringes across the disk [Fig. 1(a)]. We then tilt the membrane in a direction that reduces the number of fringes as much as we can [Fig. 1(b)]. We estimate that the disk and the membrane are parallel to within 22 nm after our alignment, for reasons similar to those related to the calibration process described earlier. To give a scale, an accuracy of 22 nm in determining the membrane–disk gap here is small compared to the membrane–disk distance that we demonstrate here to be in at the 0–620 nm range. While our setup permits gaps larger than 620 nm, the membrane did not affect the optical mode at these distances. Therefore, one can say that the error in determining the membrane position is about 3.5% of our effective scanning range.

To conclude this section, our setup provides a membrane and a disk that are mechanically disconnected and can move in 3D, one with respect to the other. As shown in Fig. 1(e), the membrane and the disk are optically evanescently coupled, as both co-host the same optical resonance. We call this resonator “continuum-coupled resonator” since the membrane is continuous in two of its dimensions. Unlike previous work where static disk resonators were fabricated on a continuous dielectric, including in silicon-on-silica configurations, our system permits controlling the position of the continuous membrane with respect to the disk, as our position control can change the disk–membrane gap as well as manage the lateral location of the membrane.

Our main claims are related to our ability to move the membrane in 3D in an almost unlimited manner while monitoring the effect of such a membrane’s motion on the resonance. We can move the membrane horizontally with no practical limit except for the membrane’s width and vertically from a state where the membrane touches the disk to a larger distance where the membrane effect on the disk vanishes, meaning that only the disk hosts the resonance at this large gap. Again, the vertical motion serves to control the resonator’s eigenfrequency, while the horizontal membrane motion permits bringing scatterers (that we previously spread on the membrane) into the optical mode upon need and removing them upon request.

In our first experiment, we measure the resonance frequency while changing the disk–membrane gap. As shown in Fig. 2, changing the membrane–disk gap from 200 to 650 nm results in a 35 GHz resonance drift. Moving the membrane more than 650 nm away from the disk does not affect the mode frequency, meaning that the disk strictly hosts the resonance at that distance. As expected, our experimental results show that the resonance frequency increases with the gap (Fig. 2, black circles). To give a qualitative explanation, increasing the gap increases the portion of the optical mode that propagates in the air. Propagation in the air is faster than propagation in silica. The integer number of wavelengths that resonate along the disk’s circumference are, therefore, circulating faster as the gap grows, resulting in an increase in the eigenfrequency. As expected, this qualitative explanation is supported by our numerical calculation using a finite-element simulation⁴¹ [Fig. 2 (red line)] that agrees with our experimental results to within their error bar. Except for the calculated eigenfrequency [Fig. 2 (red line)], we also calculate the optical mode’s spatial eigenfunction as a function of the varying gap (Fig. 2, insets). When the disk–membrane gap is 200 nm, a considerable portion of the optical mode overlaps with the membrane as well as with the air gap (Fig. 2, left inset). When the gap increases to 600 nm (Fig. 2, right inset), the overlap between the optical mode and the membrane drops to almost zero. We saw no quality degradation while bringing the membrane closer to the disk. Such degradation might be expected for resonators with small diameter, high quality factor, and thick membranes that make radiation losses larger when compared with other loss mechanisms.

In our second experiment, we laterally move a membrane containing scatterers while monitoring both the optical resonance using a photodetector (Fig. 3, graphs) and scattering using an infrared camera (Fig. 3, photographs). We spread the particles (Creative Diagnostics, silica nanoparticles, 10 nm) on the membrane by mixing them with water and letting the mixture dry on the membrane. Using this method, nanoparticles tend to aggregate to 1-μm clusters. We choose a concentration of 100 nanoparticles per microliter since it resulted in scatterer density such that moving the membrane laterally typically introduces one scatterer into the optical-mode region [Figs. 3(a) and 3(b)], sometimes two scatterers [Fig. 3(c)], and rarely three scatterers. Simple geometrical considerations imply that when a pair of scatterers fall separated to a distance smaller than the resonator’s diameters, it is always possible to bring both of them to overlap with a region on the circumference, at the region where the evanescent field is maximal. Indeed, aligning two scatters to overlap with the optical mode appeared to be a relatively easy task. The scatterers are spread on the upper part of the membrane. Putting the particles above the membrane, as we did, trades off stability, as the membrane can touch the disk, for a slightly lower evanescent field, when compared to the other side of the membrane. Afterward, the membrane is set to touch the disk to increase the overlap between the scatterer and the resonance. In this mode, where the disk touches the membrane, our resonator exhibited stability identical to that of regular resonators. This is since the act of touching prevents relative motion between the disk and the membrane. We now move the membrane laterally until the infrared camera monitors a light-scattering event (Fig. 3, left) appearing as a bright point. As expected, the strongest scattering is observed when the scatterer is near the maximal intensity region, similar to the region calculated in Fig. 1(c). It is also not surprising that the strongest scattering is monitored when the laser frequency is at the center of the resonance, as indicated by the detector. Our optical quality factor was 10⁵, as was calculated from the resonance linewidth. Our relatively low quality factor prevents us from estimating the particle size using a measurement of the resonant shift, and we are now working on increasing the optical quality factor to allow doing so. After performing the optical experiment, we analyzed the scatterers using an electron microscope (Fig. 4). The electron microscope micrographs reveal that the nanoparticles tend to cluster into spherical structures with almost identical sizes.

There are several methods to calculate the frequency shift due to the dielectric particle added to the membrane. Most accurate, in our view, is a 3D numerical simulation of the resonator–particle system.⁴² Such a 3D simulation is challenging since a resonator–particle system is not axially symmetric. One, therefore, cannot reduce the problem from a Cartesian 3D coordinate system to a cylindrical coordinate system and then to a Cartesian 2D system with rotation symmetry. Such a simplification is generally referred to as 2.5 dimensional⁴¹ coordinates. To make the particle–resonator system 3D possible to simulate, it is useful to cut a narrow 3D slice of the axially symmetrical circular resonator and add the particle on the relevant interface as explained in Ref. 42. Another alternative relies on estimating the 3D particle–resonator system as a 2D system. In such an approximation, both the particle and resonator are simulated as cylinders.⁴³ Although challenging, one can also extend such a 3D simulation to consider the scattering losses, caused by the particle, and their effect on linewidth broadening.

Although resonators such as silicon on silica were reported in the past, with modes partially propagating in a continuous silica plate, moving the continuous plate toward the disk or parallel to the disk was challenging in such structures. Here, we broke the traditional disk–membrane configuration into two mechanically disconnected elements (a dielectric disk and a continuous membrane) that are movable in respect to one another. By doing so, we can perpetually bring analytes to interact with light while benefiting resonance enhancement or measure the gap between the membrane and the disk by monitoring the resonance–frequency drift. Our continuum-coupled resonator might help in the task of bringing quantum dots, nitrogen-vacancy centers, and analytes to the maximum intensity region. Maybe even more important, after optically interrogating one object, one can remove it by laterally moving the membrane and then proceeding to the next analyte. This process can then be repeated perpetually with seemingly no limit on the number of analytes that a resonator can handle. Our vision in this regard includes a field-deployable sensor where one can bring and remove particles to (and from) the optical resonance. We propose that the configuration will include an XY stage that moves the membrane while it touches the disk. Stability is expected in such a touch-mode operation since the membrane and disk are restricted from moving, except when we remove a particle and bring another. Another possible application relates to the flexibility of the membrane. Putting a magnet on the membrane can make it into a magnetic field sensor,^22,23 where forces on the magnet deform the membrane and drift resonance. Similarly, a mass placed on the membrane will make it sensitive to acceleration or changes in gravity. In such a realization, lateral motion of the membrane would be unnecessary.

The authors declare no conflicts of interest.

This research was supported by the United States-Israel Binational Science Foundation (BSF) (Grant No. 2016670) and the Israeli Science Foundation (Grant Nos. 1572/15, 537/20, and 1802/12).

The data that support the findings of this study are available from the corresponding author upon reasonable request.