Owing to their intrinsic advantages in high quality (Q) factor, small mode volume, and rich wave and quantum dynamics [1–3], optical microcavities have been intensively explored for decades and play an essential role in many practical applications ranging from microlasers [4–6] and modulators [7–9] to highly sensitive optical detection [10–12] and photonic neural networks [13–15]. Chaotic microdisks represent an important branch [16,17]. Compared with their microring counterparts, chaotic microdisks exhibit much more complicated phase space structures in the context of ray dynamics, providing more opportunities for high-density on-chip integrated systems [2,3,16,17]. On the one hand, light can still be confined in chaotic microdisk for a long time via quasi-whispering gallery modes (WGMs) and stable islands at high sinχ [2] or wave localization within the chaotic sea [16,18]. On the other hand, the widely distributed chaos and its stable and unstable manifolds [2] can greatly increase the probability of chaos-assisted tunneling (CAT) [19,20] and connect modes with completely different momentums through a series of intermediate processes, thereby greatly reducing the momentum mismatch and energy loss [21–24]. As a result, chaos-based directional output [21], broadband coupling [22], and sensing [25] have been successively proposed and demonstrated in experiment. The flip side of ultrahigh sensitivity and large mode complexity is that identifying the excited mode becomes extremely difficult. In contrast to ring resonators, many resonances in a chaotic cavity can exhibit the same resonant wavelength, free spectral range (FSR), and radiation loss [26]. In this sense, a more accurate technique than FSR estimation is highly desirable for identifying the resonant modes.

Scanning near field optical microscopy (SNOM) is the general technique to map the spatial distribution of an optical mode [27,28]. However, its imaging speed is typically slow, and the probe tip will distort the profiles of some chaotic modes, resulting in image inaccuracies. In 2015, Bruck et al. successfully observed time and frequency-resolved images of optical modes by injecting a femtosecond (fs) laser into a silicon device and exciting it with a second fs laser of shorter wavelength [29]. The broad spectral bandwidth of fs laser pulses, however, limits their applications to low-Q devices and requires large refractive index changes (Δn∼0.4) [29–31]. Recently, Wang et al. connected the spectral change to perturbations on local refractive index and directly visualized mode patterns in high-Q microdisks using nanosecond laser excitation [26]. Nonetheless, scanning the microdisks takes nearly an hour and is highly sensitive to environmental fluctuations such as temperature and humidity. More critically, heat accumulation caused by laser excitation makes it difficult to detect modes in cavities larger than 10 μm. In this study, we overcome these limitations and experimentally demonstrate a technique for robust imaging of high-Q passive silicon devices. Using this technique, a series of closely spaced resonant modes with slightly different FSRs in a chaotic microcavity has been excellently identified. The imaging speed is improved by 3 orders of magnitude and enables characterization of microcavities with radii up to tens of micrometers.

The experimental setup is schematically illustrated in Fig. 1(a). A near-infrared tunable laser (TUNICS T100S-HP-SCL, 1460–1640 nm, 400 kHz linewidth) is polarization controlled and coupled to a bus waveguide through a grating coupler. Light with resonant wavelengths couples from the waveguide into the microdisk, producing a series of dips in the transmission spectrum. The transmitted light is collected by a second grating coupler and detected by a photodetector (Newport, 1811-FC) connected to an oscilloscope (Yokogawa, DLM2034). One example of resonant dip is schematically depicted as a solid line in Fig. 1(b). By fixing the probe wavelength slightly to the right side of resonance (marked by a vertical dotted line), we then perturb the microdisk with a femtosecond laser and monitor the transmitted power. The perturbing laser is a frequency-doubled femtosecond laser (Spectra-Physics, Solstice Ace, 400 nm, 1 kHz repetition rate), reflected by a scanning galvanometer system (Sunny-technology, SS8107C) and focused onto the top surface of silicon microdisk through a 50× objective lens (NA=0.42).

Under fs laser pulse excitation, high-density free carriers are generated, locally reducing the refractive index of silicon. As a consequence, the resonant wavelength shifts to a shorter wavelength [blue dashed line in Fig. 1(b)] and induces a dramatic increase of output power from point 1 to point 2. Free carriers dissipate rapidly, and the resonant wavelength recovers over time. Since all instruments are synchronized, this transient process can be captured by the oscilloscope as a sharp peak, shown in Fig. 1(c). Following the previous reports [26,32,33], the wavelength shift and associated transmittance variation can be directly linked to the local mode field intensity |ψ0(x,y)|2. Thus, the mode pattern can be reconstructed by scanning the fs laser across the microdisk and recording transmittance signal changes.

Several issues affect the proposed imaging technique. One concern is the diffusion of free carriers. One might intuitively think that free carriers might diffuse over a larger area and greatly degrade the spatial resolution. However, in practice, the refractive index change is strongly dependent on local carrier density and the diffusion-induced change is negligible. Additionally, fs laser excitation also induces a weak thermal effect that increases the local temperature and shifts the resonance to a longer wavelength [Fig. 1(b)]. This effect has been observed as a tiny dip in signal intensity after free-carrier dissipation, as shown in Fig. 1(c). However, the thermal contribution from fs laser excitation is so weak and decays within a few nanoseconds, resulting in negligible heat accumulation. Thus, the extremely high repetition rate of the fs laser can be utilized without concern for thermal buildup. Considering the frequency of the galvanometer, we used a 1 kHz repetition rate in this experiment. Consequently, the imaging speed in this work is improved by several orders of magnitude over previous reports [26].

To demonstrate the feasibility of high-speed modes imaging using a femtosecond laser, we applied this technique to a quadrupole shaped chaotic microdisk. The microdisks were fabricated on a standard 220 nm silicon-on-insulator (SOI) wafer with a 2 μm buried oxide (BOX) layer using a combination of lithography and etching process. First, a 300-nm-thick layer of ZEP 520A photoresist was spin-coated onto the top silicon layer and soft-baked at 180°C for 30 min. Electron-beam lithography was then employed to define the patterns of microdisks, waveguides, and grating couplers in the resist layer. After development, patterns were transferred into the top silicon layer via full-depth etching using inductively coupled plasma (ICP) etching. Finally, the residual photoresist was removed to complete the fabrication. Figure 2(a) shows a top-view scanning electron microscope (SEM) image of the microdisk. Similar to the design, we can see that the cavity boundary follows the equation in polar coordinates ρ(θ)=R(1+εcos2θ) very well. Here the size and deformation parameter are R=50μm and ε=0.08, respectively. To effectively excite most of the cavity modes, we fabricated a bus waveguide with a width of 380 nm and a side-to-side distance of 80 nm from the disk.

By scanning the wavelength of the tunable laser, the transmission spectrum has been recorded and plotted in Fig. 2(b), which reveals numerous resonant dips. Since such modes appear regularly, we can categorize them into more than 10 groups by accounting their periodicity. We have selected 10 of them [marked as I–X in Fig. 2(b)] and analyzed their spectral properties. From mode I to mode X, their Q factors vary significantly from 3.8×104 to 2.1×105, clearly demonstrating their difference in light confinements. Their FSRs, however, remain around 2.184 nm with a standard deviation of 0.027 nm. Some of them have a tiny difference of only 4 pm [Fig. 2(c)]. Considering the transverse electric polarization of the resonant mode, the effective refractive index neff is 2.86. From its definition (Δλ=λ2/neffL), the corresponding orbit length is simply estimated as L=369.88μm, which differs significantly from the perimeter of the chaotic microdisk (∼314μm). In this sense, it is obvious that the estimation with FSR is insufficient for accurately identifying specific modes and their potential orbits. The FSR in a chaotic cavity can be accurately determined with the assistance of the group refractive index, but orbital information is still required.

For such a complicated case, our mode-mapping technique starts to show its intrinsic advantages. In the experiment, the wavelength of the pump laser was fixed at 2–3 pm on the right side of the resonance to ensure a linear relationship between the transmittance change and the local field intensity. Its spatial position was controlled by the galvanometer to scan the microdisk with a step size of 2.4 μm, which was chosen to balance the wide imaging range with the storage limitations of the oscilloscope. The variation of transmission ΔT was then recorded and used to reconstruct the corresponding local field intensity. For the quadrupole microdisk with R=50μm, 50×50 scanning points are enough to get the mode pattern. Considering the limitation of the galvanometer (1 kHz), an entire map was achieved within a time of 2.5 s. Then we know that the current technique can map large cavities with a speed far exceeding that of previous nanosecond laser imaging techniques.

The top panels of Fig. 2(d) illustrate the experimentally reconstructed mode patterns of resonances I–X marked in Fig. 2(b). By utilizing the effective refractive index neff, the resonances in the chaotic microdisks have also been numerically calculated and shown in bottom panels of Fig. 2(d) for a direct comparison. Both the maximal and minimal intensity positions match one another very well. By comparing the experimentally recorded mode profiles with the numerical mode profiles, despite their very similar FSRs, we can now know that modes I, II, V, VII, and IX can be attributed to higher-order diamond modes confined within the period-4 stability islands, while the other modes correspond to multibounce modes with rectangular or triangular orbits in the chaotic sea. These observations are actually quite different from the conventional understanding. In general, one may consider that the fundamental diamond mode along period-4 islands and the WGMs along cavity boundary have the highest Q factor and can be much easier to be excited, especially when most resonances can be excited in a chaotic cavity.

With the assistance of high resolution, this inconsistence between theoretical expectation and experimental results can be understood. Since the waveguide is very close to the cavity, its width and gap size, associated with the inevitable nanofabrication deviation, shall affect the wavelengths of all resonances. Due to their different field distributions, the waveguide-induced wavelength shifts of the resonances are different. In this sense, different resonances may overlap each other and some high-Q modes, which already exhibit low coupling efficiency due to stringent coupling conditions, can be easily overwhelmed by the much broader linewidths of low-Q modes, making them indistinguishable and unobservable in the transmission spectrum. By gradually increasing the gap size from 80 to 140 nm with a step size of 20 nm, we have carefully measured the transmission spectra and their corresponding field patterns of different samples. All the results are summarized in Fig. 3.

From the transmission spectra in Fig. 3(a), we can see a series of resonant dips too. When the gap size is 100 nm, several of them, such as modes II, IV, V, and VII, appear at similar wavelengths and have almost identical patterns to Fig. 2. The others, such as modes I, III, VI, VIII, IX, and X all disappear. Interestingly, two new modes marked as modes XI and XII emerge. By comparing the transmission spectra, we know these modes now deviate from their nearby low-Q modes and can be identified. With a similar process, their field patterns have been scanned and shown in the top panel of Fig. 3(b). With a comparison to the numerical simulation (bottom panels), we know that these two modes are the quasi-WGM and fundamental diamond mode, respectively. With the increase of gap size, we find that some existing modes (IV, XI) disappear, and new modes marked as XIII and XIV emerge. From their field patterns [see Fig. 3(b)], these new modes are also higher-order diamond modes along period-4 stable islands. This information has been further confirmed with the corresponding numerical simulation.

By comparing the spectra in Figs. 2(b) and 3(a), we can see that mode II always exists and is very robust to the nanofabrication. Several of them, such as modes V, VII, XIII, and XIV, are less stable but are still much better than all the others, e.g., modes I, III, IV, VI, VIII, IX, X, XI, and XII. According to their numerical simulation and field patterns, we know that such robustness is related to the field in the waveguide–cavity coupling region. Due to the proximity effect in nanofabrication, the structural parameters in this region usually deviate a lot from the design. The stable modes, such as mode II, have a minimum within this region and thus are less affected. All the others are strongly affected and can only appear in partial samples. In this sense, different from conventional understanding, we know that mode II is more stable and should be carefully considered for practical application.

As mentioned above, less heat accumulation enables a high repetition rate of scanning. In this sense, the environmental variation can be neglected, and a much larger sample can be mapped. To quantitatively know the advantage of this new technique, we have fabricated a series of samples with radii from 5 to 50 μm and mapped their field patterns. During the experiment, the size of scan steps changes from 0.55 to 2.4 μm to maintain high image quality. The corresponding imaging time have been recorded and plotted as open squares in Fig. 4. It is evident that our technique reduces the imaging time to just a few seconds. For the smallest cavity with a 5 μm radius, the full mode pattern can be captured in approximately 0.6 s. For a direct comparison, the 7 μm microdisk has also been mapped by nanosecond laser-based imaging technique. As the cross depicted in Fig. 4, it takes several hours to complete one image [34]. In this sense, we know that our technique can not only image a larger sample but also at a faster speed. Interestingly, the imaging speed can be further increased by several orders of magnitude if a high-speed micrometer-scale system is used to manipulate the megahertz pump laser.

In additional to the scanning speed, another interesting question is about the resolution limit of this technique. By measuring the field distribution of a resonance in ring resonator, we have confirmed that the effective spatial resolution is about 1.3 μm. This resolution is mainly restricted by our optical setup. Due to the limited writing field of the electron-beam aligner, the tunable laser is coupled into and out of the bus waveguide with two grating couplers. The existence of two optical fibers wastes the field of view of the objective lens, so that its NA cannot be fully utilized. The experimentally recorded pump laser spot size is 1.16 μm, which is very close to the effective spatial resolution, indicating that the effect of carrier diffusion is only a few tens of nanometers. By utilizing an end-fire injection coupling scheme (see Fig. 1), the optical blocking problem of the fiber is solved and the objective lens with a larger NA can be fully utilized. In this sense, the focal spot is only 200 nm, and the resolution limit of our technique can be around 200–300 nm, which is good enough for resolving fine-mode structures in optical microdisks. Such a spatial resolution is still lower than conventional SNOM techniques [27,28,35] and requires optically stimulated changes in the material’s refractive index. But the noncontact perturbative imaging methods can provide a much larger imaging area, a much faster speed, and better compatibility with samples with complex or irregular structures.

In summary, we have developed a powerful technique to rapidly and accurately monitor the internal field distributions of resonances in a chaotic cavity. The corresponding image speed is 3 orders of magnitude faster than the previous report, and the impacts of environmental variations can thus be ignored, leading to a nearly real-time image of optical mode. With a chaotic microdisk, we show a counterintuitive result: the higher-order diamond mode is stabler than the quasi-WGM or fundamental diamond mode. Technically, both the scanning speed and resolution can be significantly improved by using a MEMS device and two-photon excitation to produce high-density free carriers. This concept can be extended to microcavities made of other materials whose refractive indices can be optically changed as well. In addition, nonlinear effects such as the Pockels effect and optical Hall effect, which enable local modulation of the refractive index, may also be utilized to image the field patterns in nonlinear optical microcavities. In this case, the effects of carrier diffusion can be neglected, so the spatial resolution may be comparable to conventional SNOM techniques, but at a much faster speed. We believe that this research will open up new possibilities in understanding the physical processes in optical microcavities and enhancing the corresponding light–matter interactions.