1. INTRODUCTION

Nanophotonic resonators, such as whispering gallery mode resonators, are sensitive devices that have been used to measure temperature [1], mechanical motion [2–4], and a range of biological and molecular signals with both high resolution and speed [5,6]. Further development of microfabricated resonator-based sensors and transducers necessitates new techniques for device characterization and testing; spectroscopy of optical modes is often insufficient, and rapid, noninvasive techniques for spatial mapping of the mode structures are needed. Mode mapping is also important for calibration of interaction volumes and local field enhancements, as well as for understanding the specific effects of fabrication imperfections. For one example, imperfections can break the spatial symmetry of circular resonators, resulting in spectroscopically observed resonance line splitting. However, spatial information about the imperfections can only be obtained by mapping the modes.

A number of diverse approaches have been developed for imaging nanoscale photonic and plasmonic resonators, including optical techniques such as near-field scanning optical microscopy (NSOM) and photomodulation spectroscopy (PMS) as well as electron-based techniques including cathodoluminescence (CL), electron energy loss spectroscopy (EELS), and photoemission electron microscopy (PEEM). Each approach presents a distinct set of advantages and trade-offs with regard to spatial, spectroscopic, and temporal resolution. They also vary in their ability to measure in operando, i.e., to determine the spatial distribution of a specific desired mode chosen for excitation by a single-frequency tunable source. This is particularly important for photonic structures with many high-quality-factor ($Q$), spectrally dense states.

NSOM has been widely used to map nanophotonic devices [7–9] and encompasses a broad category of tip-based scattering techniques. Advancements in this technique have allowed for local, phase-sensitive measurement of evanescent field vectors [10–12]. NSOM is fundamentally based on an interaction between the mode’s evanescent fields and an externally introduced physical scatterer, and while it allows in operando measurements, it requires a trade-off between the scattered signal strength and the probe-induced perturbation of the mode. This probe-induced perturbation has been extensively studied and can be used as a signal for high-resolution imaging [13,14]. The spatial resolution of NSOM is practically limited by the attainable probe geometries. PMS [15,16], in which a focused laser beam creates a local perturbation of the refractive index and is scanned across the surface, also allows in operando measurement. The spatial resolution of PMS is limited by diffraction to the focal spot size of the probe laser.

Electron beam techniques such as CL, EELS, and PEEM are attractive because they make use of the high spatial resolution of electron optics to extend imaging of plasmonic structures to the nanometer scale, and they avoid the type of tip-induced perturbation of the resonator seen with NSOM. A trade-off in this case is that the measurements are generally not in operando; mode excitation is typically broadband, either by an electron beam or by an ultrafast laser, with less ability to select specific modes to study unless the resonator is very small with just a few modes.

In CL measurements [17–24], a focused scanning electron beam excites the resonator, and the spectrum of the cathodoluminescence provides a map of the local optical density of states. EELS experiments are similar, except the spectrum of the optical modes is observed in the energy loss of the electrons [25]. A related technique involves excitation with an ultrafast pulsed laser and observation of the spatial distribution of the modes by synchronized ultrafast electron microscopy [26,27]. This technique has the added benefit of excellent temporal resolution, in addition to having the spatial resolution of an electron microscope. PEEM also uses a pulsed laser to excite the optical mode, and either a UV lamp or a multiphoton process to generate photoelectrons from the surface of the resonator, where mode intensity is present [28–30]. Imaging these electrons provides a map of the mode’s spatial distribution. In all these techniques, due to the broadband nature of electron or pulsed-laser excitation, it is challenging to study individual modes in spectrally dense resonators.

Recently, focused ion beams (FIBs) have been introduced as a promising alternative for in operando measurement of nanophotonic resonator modes [31] with nanometer-scale resolution. As with NSOM and PMS, a specific mode is selected for imaging by tuning an external excitation laser, and the spectral resolution is limited only by shot noise in photodetection of the resonance excitation. Similar to PMS and in contrast to NSOM, the FIB-induced interaction is localized to just below the resonator surface, without perturbing the mode’s evanescent fields. However, like electron-based methods, advantage can be taken of the high resolution of charged particle optics, and the spatial resolution is limited only by the volume of the ion collisional cascade at the point of impact on the resonator, which can be of nanometer scale. With the proper choice of ion species, beam energy, beam current, and exposure time, high-quality mode images can be obtained with minimal damage to the resonator. However, it should also be noted that focused ion beams have also been used to modify photonic devices for suppression of certain modes [32], and fine control over the location and strength of the FIB-induced modification of the resonator opens intriguing possibilities for fine-tuning of the optical modes with an unprecedented level of spatial control. For example, controllably perturbing resonators supporting multiple near-degenerate modes has been used to show phenomena such as mode coalescence and chirality at exceptional points [33,34].

Here we present an imaging technique that uses the time-varying response of a microdisk resonator to a pulsed ion beam of ${\mathrm{Li}}^{+}$. The temporal response of the resonator includes two primary effects: a spatially dependent shift due to local modification of the device index and boundaries, and a rapid thermal shift in the resonance frequency from ion-beam heating. We refer to these as the “optical” and “thermal” responses. These two effects occur over separate time scales and can be independently measured. Both responses are useful for device characterization, the optical shift for mapping the optical mode profile and the thermal shift for measuring thermal transport within the device. In our previous work [31], a modulated ion beam was used to make linear scans of the optical mode distribution. Here, we use detailed fitting of the time-varying response to increase the signal-to-noise ratio for a given ion dose, which allows quantitative separation of the two effects. These improvements enable an increased speed of imaging, resulting in an ability to acquire two-dimensional images of the optical field without causing a significant change in the mode $Q$ or resonant wavelength. For singlet resonances, we observe azimuthally symmetric patterns as expected from the associated single-direction traveling wave fields. However, measuring on one component of a doublet line in the microdisk spectrum, we observe an azimuthally periodic standing wave pattern, which is a result of the breaking of the rotational symmetry of the microdisk, presumably by a defect or fabrication imperfections. Notably, we show that significant persistent modification in the mode spectrum and the spatial pattern can be induced by extended application of the ion beam. As our first examples of such mode editing by the focused ion beam, we show permanent shifting of the resonance line by more than a linewidth, and conversion from a spectral doublet to a singlet with the accompanying restoration of the azimuthally symmetric traveling wave pattern.

2. METHODS

The microdisk device shown in Fig. 1(a) is fabricated from a silicon-on-insulator (SOI) wafer with a device-layer thickness of $\approx 250\mathrm{nm}$. The microdisk ($\approx 10\mathrm{\mu m}$ in diameter) and integrated optical waveguides are patterned into the SOI layer using electron beam lithography and reactive ion etching. Annular silicon nitride columns support the microdisk and waveguide structures and are fabricated through an additional multistep lithographic process. The silicon dioxide cladding layer is removed via wet etching. The gap between the waveguide and the resonator ranges from $\approx 290\mathrm{nm}$ to $\approx 360\mathrm{nm}$ and sets the coupling of the waveguide to the resonator. The far ends of the waveguides are tapered to $\approx 100\mathrm{nm}$ and act as input/output couplers to optical fibers, with losses of $\approx 5.5\mathrm{dB}$ per facet. Further details of the device fabrication are described in Ref. [35].

 

Fig. 1. Ion pulse imaging of microdisk resonator modes. (a) The silicon microdisk (10 μm diameter) is housed in a ${\mathrm{Li}}^{+}$ FIB vacuum chamber with optical fibers connecting the interrogating laser and photodiode to the device. The ion beam is scanned across the resonator mode (dashed line) and perturbs small volumes in the device near the disk surface. The resonator’s mode intensity (shown in cross section) varies both radially and through the device thickness. (b) Spectroscopy of a zeroth-order transverse magnetic (TM) mode is shown with $Q\approx \mathrm{20,000}$ at $\lambda \approx 1523\mathrm{nm}$. The ion pulses incident on the microdisk shift the resonance to a longer wavelength, and this shift is read out by tuning the laser (dashed line) to the low-frequency side of the resonance and observing the time-varying change in the optical transmission of the device. (c) The change in transmission (blue lines) is shown for a series of $\approx 0.5\mathrm{ms}$ ion pulses (blue bands) incident near the mode maximum, and the absolute magnitude of the spectral shift can be calculated from the transmission measurement in (b). Between each ion pulse, the laser is adjusted (orange band) to a nominal absorption value on the side of the resonance by turning on a slow feedback circuit.

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The low-energy, focused pulses of ${\mathrm{Li}}^{+}$ ions are created from a magneto-optical-trap ion source (MOTIS)-based FIB [36]. The MOTIS employs a laser-cooled gas of neutral ${}^7\mathrm{Li}$ as a high-brightness source of ions. The gas is magneto-optically trapped at a temperature of $\approx 0.5\mathrm{mK}$ and photoionized to generate ${\mathrm{Li}}^{+}$ ions with a small spread in both transverse and longitudinal velocity. The ions are accelerated in a uniform electric field to create an ion beam that is scanned and focused using standard ion optics. The ion current is controlled by modulating the photoionization laser power using an acousto-optic modulator, which is synchronized with the scanning of the beam deflectors. For this work, we operate at an accelerating voltage of $\approx 3.9\mathrm{keV}$, and the focal spot size is $\approx 50\mathrm{nm}$ with $\approx 1\mathrm{pA}$ of beam current. Details of the microscope are described in Refs. [37,38].

Spectral shifts of the microdisk resonances are observed by positioning the probing laser on the low-frequency side of a microdisk resonance and recording the transmitted power during ion dosing. The transmitted light is measured with a low-noise photodetector, and the frequency response of the disk, as shown in Fig. 1(b), is used to convert changes in optical absorption into a known spectral shift. This is calibrated by simultaneously recording the absorption spectrum from the microdisk and a Fabry–Perot cavity with a calibrated free spectral range of $\approx 1490\mathrm{MHz}$. This side-of-line spectroscopic technique provides a direct measure of the resonance shifts, but is susceptible to drift arising from amplitude and frequency noise in the laser, polarization drift in the coupling fibers, and thermal drift of the microdisk resonance. Each of these effects is found to be negligible for the measurement duration described here. Laser frequency and photodetection shot noise are the dominant noise sources. Experiments are nominally performed at room temperature.

The focused ${\mathrm{Li}}^{+}$ ion pulses are positioned using the FIB as a microscope and registering the beam position using secondary electron images of fiducial marks on the device. The beam is then stepwise rastered across the structure with a series of ion pulses between 0.2 ms and 0.5 ms in duration. The ion pulses are spaced in time by $\approx 20\mathrm{ms}$ to allow time to record the relaxation of the optical shift and to reposition the laser to a nominal position on the side of the resonance feature where the sensitivity to spectral shifts is maximal, as shown in Fig. 1(c). The tuning of the laser between ion pulses is accomplished using a sample-and-hold limited feedback circuit.

The response to a series of ion pulses across the edge of the microdisk structure is illustrated in Fig. 2. In this measurement, a sequence of $\approx 0.5\mathrm{ms}$ ion pulses containing $\approx 3000$ ${\mathrm{Li}}^{+}$ ions each are incident near the edge of the microdisk. The magnitude of the response varies as the beam is scanned across the disk edge due to the spatial dependence of the optical mode. The ion-induced shift of the microdisk resonance is analyzed independently for each pulse using least-squares fitting to a two-component model. The two components represent a spatially local shift arising from ion damage ${\mathrm{\Delta }}_{\text{optical}}$ and a position-independent shift arising from ion-beam heating ${\mathrm{\Delta }}_{\text{thermal}}$. The optical shift arises from modifications of the silicon lattice that change the local index and boundaries of the device. This modification of the device grows during the ion pulse (with length $t_d$) and relaxes afterward; we model this behavior through the piecewise-continuous function of time $t$:

 

Fig. 2. Optical and thermal response of the microdisk resonator to ion dose. (a) A cross section of the optical mode intensity (color scale) for the zeroth radial order mode shown in Fig. 1(b) is shown relative to the data in (b) and (c). (b) The ion beam is scanned radially across the edge of the microdisk with a series of $\approx 0.5\mathrm{ms}$ ion pulses, and the time-varying shift (blue lines) is recorded. Insets show the thermal response to the ion pulses (blue bands) off the disk, where no response is observed [inset (i)], and on the disk, where the overlap with the optical mode is minimal and only the thermal response of the resonator is observed [inset (ii)]. Each inset trace (blue points) is an average of eight consecutive ion pulses with fitting for the thermal shift (dashed line) superposed. (c) The maximum optical shifts (closed circles) and thermal shifts (open circles) are plotted as a function of beam position. Each value is extracted from fitting the time-varying response to Eq. (1), as shown in inset (iii). The optical response is compared to a numerical simulation of the optical mode intensity at the disk surface (red line), and the thermal response is shown to be constant across the disk surface (blue line). Both responses account for the finite size of the ion beam. Inset (iv) shows the orientation of the $\approx 3\mathrm{\mu m}$ scan (red bar) using a FIB secondary electron image of the device. Error bars indicate the standard error of the mean; some are smaller than the data points.

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The optical shift dynamics during the ion dose ($0<t\le t_d$) are modeled as linear growth with exponential saturation to capture the finite bound on damage to the device. The relaxation of the shift ($t>t_d$) with magnitude ${\mathrm{\Delta }}_{\text{relax}}$ is modeled as exponential decay, similar to the model used to describe damage from 3 keV ${\mathrm{He}}^{+}$ ions in graphite [39], and is motivated by the linear response to ion damage and relaxation through interstitial–vacancy recombination in the dilute damage limit. Time scales for damage saturation and relaxation in this model are set by ${\tau }_s$ and ${\tau }_r$, respectively. The maximum optical shift ${\mathrm{\Delta }}_{\text{optical}}$ is taken as the value of this fit at $t_d$, as shown in Fig. 2(iii), and the statistical uncertainty in ${\mathrm{\Delta }}_{\text{optical}}$ is the fitting uncertainty in this parameter. The thermal response is a constant shift for the duration of the ion pulse and is represented using a stepwise function to capture the rapid thermal shift and recovery of the device, as shown in Fig. 2(ii). The magnitude and time scale of the optical and thermal responses afford easy separation through two-component fitting. The optical response is compared with a numerically calculated intensity profile of the optical mode intensity near the disk surface in Fig. 2(c). Commercial finite element software was used to model the optical modes, solving full-wave vector Maxwell’s equations in the frequency domain. The finite size of the ion beam, as well as other sources of technical noise, blurs the measured signal, and we include this in the data analysis as Gaussian blur. The thermal shift of the resonance is observed to be uniform across the disk surface, and is also limited by the finite probe size at the microdisk edge. Both responses are consistent with a blurring root-mean-square (rms) radius of 100 nm.

3. RESULTS

The optical shift of the microdisk resonances is understood by considering the effect of the ion beam on the silicon structure, including surface swelling and modification of its optical index [31]. The ions interact with the microdisk through a collisional cascade, damaging the Si lattice as the ions scatter and slow in the device. The light mass of the ${\mathrm{Li}}^{+}$ ion creates a disperse volume of damage with minimal material sputtering [40]. A numerical simulation of the cascade in SRIM [41] shows that 3.9 keV ${\mathrm{Li}}^{+}$ ions penetrate to a depth of $\approx 31\mathrm{nm}$ with an rms deviation of $\approx 15\mathrm{nm}$. The primary source of damage is knock-out collisions that create $\approx 70$ silicon interstitial–vacancy pairs per incident ion. Surface sputtering is $\approx 0.3$ Si per incident ${\mathrm{Li}}^{+}$, and $\approx 7\%$ of the ions backscatter from the device, while the rest remain as interstitials in the crystalline silicon (c-Si) lattice. The lateral rms deviation in ion position is $\approx 22\mathrm{nm}$. Considering a single ion pulse with 3000 ions and a conservative 100 nm estimation of the beam size, the expected ion flux is $\approx 5\times {10}^{12}{\mathrm{cm}}^{-2}$ and the vacancy density is $\approx 0.2\%$ in the center of the damaged volume.

Ion damage shifts the microdisk resonances due to local expansion of the structure and modification of its refractive index. The magnitude of the observed shift in Fig. 2 is $\approx 1.5\mathrm{pm}$ for $\approx 3000$ ions—this is a fractional shift of the resonant wavelength of $\approx {10}^{-6}$. The contribution of total shift due to modification of the refractive index can be estimated from the amorphization fraction, the known $\approx 10\%$ index difference between crystalline and amorphous Si [42], and the fraction of the mode volume that is damaged. The estimated shift is $\approx 0.15\mathrm{pm}$, which is in the same direction as the signal but constitutes only a tenth of the observed value [31,43]. Calculation of the contribution from surface swelling can be done through optical eigenmode perturbation theory [31], and an expansion of $\approx 0.6\mathrm{nm}$ would accommodate the observed 1.5 pm shift. The low-energy-${\mathrm{Li}}^{+}$-induced expansion of c-Si is unknown, and comparison to other measurements of ion-induced expansion is complicated by the variation in expansion with ion species, dose, and accelerating voltage. Measurements with 80 keV ${\mathrm{He}}^{+}$ implanted in c-Si show expansion at the percent level and suggest that surface swelling is likely the explanation for the presently observed signal [44]. Generically, the amplitude of the optical response is expected to differ for fields normal and perpendicular to the disk surface. For the modes explored in this work, the electric field normal to the microdisk surface is negligible, and the expected response can be approximated using the mode intensity. The proximity of the ion damage to the disk surface may also play a role in the magnitude of this effect, as self-interstitial silicon has been observed to migrate to the surface instead of remaining as lattice interstitials [45].

In addition to the spatially varying optical response, there is also the rapid thermal shift of the resonance, as shown in Fig. 2(ii), caused by ion-beam heating of the microdisk. This response appears independent of beam location on the microdisk due to rapid thermalization across the structure. The thermalization time constant of the microdisk is estimated as $L^2/4D_T\approx 300\mathrm{ns}$, where $D_T$ is the thermal diffusivity of c-Si ($\approx 0.8{\mathrm{cm}}^2{\mathrm{s}}^{-1}$) and $L$ is the diameter of the disk. Thermalization with the substrate is limited by conduction through the silicon nitride support structure, and the temperature increase of the disk can be estimated through the balance of the ion heating ($\approx 4\mathrm{nW}$) and thermal conduction of the nitride column ($\mathrm{\Delta }T{C}_{\text{SiN}}A/H$), where $\mathrm{\Delta }T$ is the increase in temperature of the microdisk, $A$ is the cross-sectional area of the support ($\approx 1.4{\mathrm{\mu m}}^2$), and $H$ is the height of the support ($\approx 2\mathrm{\mu m}$). The thermal conductivity of the nanofabricated silicon nitride structures $C_{\text{SiN}}$ is estimated as $\approx 5{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ [46]. Using these values, we estimate the temperature rise of the disk at $\mathrm{\Delta }T\approx 0.5\mathrm{mK}$. The thermo-optic coefficient of c-Si ($dn/dT\approx 2\times {10}^{-4}{\mathrm{K}}^{-1}$ near 1550 nm, $T\approx 300\mathrm{K}$) [47] predicts an expected thermal shift of $\approx 0.15\mathrm{pm}$ given this temperature increase and is consistent with observed values of $\approx 0.12\mathrm{pm}$ seen in Fig. 2. The role of thermal expansion is minimal given the low thermal expansion coefficient of c-Si at $\approx 2.6\times {10}^{-6}{\mathrm{K}}^{-1}$, two orders of magnitude smaller than the effect from the change in index. In general, microdisk resonators are extraordinarily sensitive thermometers, and the data in Fig. 2(ii) show similar capability to state-of-the-art microdisk thermometers [48,49].

Using the understanding of the time-varying response of the microdisk to ion pulses, images of the optical mode intensity were acquired with a high signal-to-noise ratio. Two-dimensional images of the zeroth- and first-order radial TM modes on two separate devices are shown in Fig. 3 to demonstrate this ability. For each of these images, an array of ion pulses was positioned near the microdisk edge and the two-component fitting procedure described in Eq. (1) was used to extract the optical and thermal responses from each ion pulse. The images are composed of 864 and 900 ion pulses lasting 250 μs and 300 μs, respectively (total of $\approx 2$ million ions); total image acquisition time is less than 20 s. The measured optical shifts are compared to numerical simulations of the mode intensity. The finite beam width and technical noise are again modeled as a Gaussian blurring of the expected mode profile. The comparison to the predicted mode shows strong agreement that is most visible in the azimuthally averaged data shown in Figs. 3(b) and 3(d). Notably, the agreement indicates that nonlinear effects from ion damage are minimal and the ion dose can be considered in the linear-response regime. A higher ion dose leading to significant amorphization is known to have a nonlinear scaling and would limit this technique at fluences in the regime of ${10}^{16}{\mathrm{cm}}^{-2}$ [50].

 

Fig. 3. Two-dimensional imaging of nanophotonic modes. (a) Image of the zeroth-order radial mode showing the spatially dependent optical shift; (b) data from (a) are compared with a 2D model of the mode intensity (inset). The optical shift (closed circles) is compared with the numerically calculated mode intensity (red line) averaged by the radial position on the microdisk after fitting. The thermal shift (open circles) shows the effects of nonlinear driving of the resonance at the mode position. Inset (i): The thermal response away from the optical mode position shows a hysteretic response, in which the original temperature is not restored after the ion pulse. This resonance is the same as described in Fig. 2 and was interrogated using 250 μs, 1 pA pulses ($\approx 1500\mathrm{ions}$). (c) Image of a first-order radial mode showing the optical response to 300 μs ion pulses on a separate device with $Q\approx 5000$ and $\lambda \approx 1538\mathrm{nm}$; (d) the optical response (closed circles) is compared to the numerically calculated mode profile (red line, inset), and the thermal response (open circles) again shows a hysteretic response that is uniform across the disk except at the mode maximum.

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The thermal shifts shown in Fig. 3 are observed to be constant across the disk surface, except near the modal maxima. The resonances used for these images were excited in a quasi-linear regime in which the optical mode spectrum is skewed by a thermal shift due to the absorbed optical power, increasing the apparent slope on the low-frequency shoulder of the mode’s absorption line. While this nonlinear driving is useful for increasing sensitivity to small frequency shifts, it induces hysteretic behavior in the thermal response of the system. This hysteresis is due to the interplay between ion heating and rapid modification of the resonance absorption and is evident in the modification of the shape of the thermal response, shown in Fig. 3(i), away from a step response and in the shift’s partial recovery after the ion pulse. We model this behavior by fitting to a heuristic function, and the plotted values correspond to the maximum of that function.

Repeated imaging of a disk mode is ultimately limited by the broadening of the optical resonances, attributed to increased optical losses due to ion damage. Nevertheless, it is possible to image large areas with minimal device degradation. The imaging in Fig. 3(c) was repeated six separate times with an estimated total dose of $\approx 2\mathrm{pC}$ ($\approx 0.6\mathrm{pC}$ in the mode volume). During this process the mode $Q$ decreased by approximately a factor of 2. The loss of sensitivity can be partially offset by increasing the optical power and thereby decreasing the detection shot noise. A careful measurement of the mode spectrum changes in a doublet resonance during ion imaging is shown in Fig. 4(a). Starting from the pristine resonator with the mode used in Fig. 3(c), we measure the spectrum before, in the middle, and after two imaging sequences. The spectrum is observed to globally shift to a longer wavelength by $\approx 100\mathrm{pm}$ per image, with $\approx \mathrm{750,000}$ ions incident on the portion of the microdisk occupied by the mode. At the same time, the lower frequency peak was broadened by $\approx 75\mathrm{pm}$ per image. The process of adjusting the interrogation laser frequency to follow the resonance is shown in Fig. 4(b) during one of the imaging sequences. Here the stepwise shifting of the mode follows the rastering of the ion beam across the disk surface, demonstrating a gradual and controlled shift of the mode line by more than a linewidth. We note that associated with this shift is an inevitable, but relatively minor, change in $Q$. Understanding and limiting this change in $Q$ is a subject for a future study.

 

Fig. 4. Persistent spectroscopic shifts of microdisk modes due to ion imaging. (a) A doublet mode [same as Fig. 3(c)] spectrum is measured interleaved with two separate 2D imaging sequences. The curves correspond to the initial spectrum (black) and the spectrum after the first (blue) and second (red) 2D images. The spectra show that the modes are redshifted and broadened during imaging, and that coupling to the lower-wavelength mode becomes dramatically reduced. (b) The wavelength of the laser is monitored using an optical wavemeter during the second imaging sequence (shaded area) and shows the stepwise shift of the disk resonance as the pulsed ion beam is rastered across the microdisk surface. The inset shows the resulting map of the optical mode.

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Ion imaging can also be used to explore mode doublets. For perfectly circular disks, clockwise (CW) and counterclockwise (CCW) whispering gallery modes are degenerate due to rotational symmetry of the disk. However, small fabrication imperfections and defects are in some cases sufficient to break the symmetry, leading to doublets in the mode spectrum. These doublets correspond to pairs of standing wave modes with slightly different energies, arising from the mixing of CW and CCW propagating waves. The nodal position of the lower- and higher-energy standing waves is dictated by the details of the spatial-symmetry-breaking disorder. Modifying the symmetry-breaking disorder and/or modifying the photon lifetime (linewidth) can cause the relative coupling of the two modes to change, as is shown in Fig. 4(a). In this data, repeated ion dosing dramatically reduces the contrast of the high-frequency mode. Additionally, distinct standing wave modes can be individually measured using this technique, as shown in Fig. 5(a), where a TM zeroth-radial-order mode is imaged. Given sufficient spectral separation between the modes, independent addressing and imaging can be achieved. Here we image the lower-frequency mode of a doublet and observe five peaks on the standing wave pattern. The interferometric visibility of the observed standing wave is $\approx 0.28$. The maximum theoretically expected value for the visibility is $\approx 0.7$ due to the 90° phase shift of the azimuthal electric field relative to the radial and normal components of the field. The finite resolution of the ion beam and finite spectral mode overlap shown in Fig. 5(d) also contributes to a reduction in the standing wave visibility. Assuming Gaussian blurring with an rms radius of 100 nm, one expects a visibility of $\approx 0.29$ in the mode response, in strong agreement with the data shown in Fig. 5(b). Additionally, the mode order is found to be $\ell =35$, in agreement with spectroscopy of the disk modes. Further imaging of this microdisk leads to permanent broadening of the mode’s spectrum. When the photon lifetime becomes shorter than the CW–CCW scattering rate, the mode splitting and the resulting standing wave are no longer resolved. Imaging of the mode distribution after this broadening in Fig. 5(e) shows no visible standing wave and demonstrates the ability to spatially image and permanently edit high-$Q$ optical modes.

 

Fig. 5. Imaging of an optical standing wave and ion-beam mode editing. (a) 2D image of a zeroth-radial-order TM standing wave showing ${\mathrm{\Delta }}_{\text{optical}}$ at each point in space. This image is an average of four data sets taken of the same area; scale bars (white) are 0.5 μm. (b) Comparison of the imaged mode to a numerical mode simulation showing interferometric visibility of $\approx 0.28$; (c) FIB secondary electron image of the microdisk device showing the orientation of the images in parts (a) in red and (e) in white; (d) optical transmission spectrum of the standing wave resonance before acquiring the image in (a). Light solid and dashed lines indicate the two separate resonances. (e) A larger area scan at the same microdisk location after the ion-beam dose shows no standing wave visibility. No standing wave is apparent in these data. (f) A comparison to the expected traveling wave mode shape.

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4. CONCLUSIONS

We have imaged the optical and thermal responses of microdisk resonators to pulses of low-energy ions from a focused beam. This has enabled us to form images of the device’s optical mode intensity in the linear response regime with both higher sensitivity and speed. With a higher cumulative dose, we demonstrate persistent editing of mode spectra and spatial patterns. Future extensions of this technique using focused ion beams to locally perturb optical structures at higher spatial and temporal resolutions will allow for improved imaging of subwavelength structures. Fundamentally, the technique is only limited by the volume of the ion cascade in the material, and this volume can be minimized using high-resolution, low-energy beams that are currently being developed using MOTIS and similar sources [51]. There is also an opportunity to use high-energy ions that will penetrate deeper into nanophotonic devices to allow for the mapping of optical structures using ${\mathrm{He}}^{+}$ and other forms of ion microscopy. Additionally, a detailed understanding of the time-varying optical response will provide insight into the process of thermal annealing of ion damage, which is of relevance to a broad range of electronic and optical materials.