1. Introduction

Silicon (Si) is a semiconductor with an indirect bandgap and has a very low radiative recombination efficiency [1]. Consequently, electrically pumped Si lasers are difficult to realize [2]. On the other hand, Si has a large Raman gain coefficient for stimulated Raman scattering (SRS) [3]. In addition, low-loss thin-wire waveguides and small cavities with high-quality (high-Q) factors, which can enhance SRS, have been realized by using advanced microfabrication technologies [4–6]. Therefore, the research on optically pumped Raman Si lasers has made significant progress [7–11]. For example, continuous-wave (cw) laser oscillation with an energy efficiency larger than 10% [12] and cascaded Raman laser oscillation have been reported in rib-waveguide resonators [13]. Another interesting designs for Raman Si lasers are based on high-Q photonic-crystal (PC) nanocavities and PC waveguides [14–17]. The mode volume of such a PC cavity is about one cubic wavelength and the highest Q value that has so far been reported for the heterostructure nanocavity [18], is 11,000,000 by using electron beam lithography [19] and 2,500,000 by using photo lithography [20].

In 2013, we reported a Raman Si nanocavity laser with a threshold of about 1 µW [21], which exploits the fact that the strength of light–matter interactions is proportional to the ratio of Q to the cavity volume [22]. The lasing mechanism has been studied both by time-domain measurements [23] and by stimulated Raman scattering excitation spectroscopy [24]. These measurements have clarified that free carriers produced by two-photon absorption (TPA) have various effects on the lasing dynamics. In particular, the free-carrier absorption (FCA) loss is the most detrimental factor for the laser oscillation in such a device. Recently, we demonstrated the fabrication of a Raman Si nanocavity laser by complementary metal-oxide-semiconductor compatible processes [25]. We consider that interesting application schemes of such a Raman laser can be found by utilizing the abovementioned strong influences on the lasing dynamics.

In this paper, we report the behavior of a Raman Si nanocavity laser that is exposed to negatively ionized air. We find that laser oscillation quickly stops after the start of weak irradiation with ionized air, and after the irradiation has stopped, the laser output gradually recovers within several tens of seconds. We measure the Q values, the resonance wavelengths, and the output intensities during the irradiation. The results reveal that the observed laser interruption is mainly due to a transfer of the extra electrons from ionized air molecules to the Si nanocavity (Fig. 1) and the subsequent FCA loss in the Raman laser caused by these electrons.

 

Fig. 1. Schematic of the irradiation of the Si PC slab with negatively ionized air. The extra electrons (shown in blue) are transferred from the ionized air molecules to the Si slab as shown in the inset, and then these electrons can cause an increase in the FCA loss. The dashed lines represent electric field lines.

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Electrification of a material by ionized air can cause various problems, such as electronic device failures [26], fires, explosions [27], and even rocket launch failures [28], by electrostatic discharge (ESD). Methods that enable detection of ultraviolet [29] or electromagnetic waves [30] associated with an ESD event, have been developed, but they cannot detect the ionized air generated during the discharge. Electrostatic potential meters that measure the potential associated with charges have also been developed [31,32], but these sensors can be damaged by an ESD event. Therefore, the development of a novel technology to detect ionized air is important. Since a nanocavity has a small size, it may be useful in situations with limited space, and it may enable detection of ionized air with a high spatial resolution. Compared to electronic equipment, an optically pumped Raman laser, which is a passive device, can exhibit a higher resistance to ESD. Furthermore, an optical detection method has several merits compared to detection methods based on electronic equipment, for example, merits such as weight, safety, and accessibility.

2. Fundamentals of nanocavity-based Raman Si lasers

Figure 2(a) describes the design of the core region of the Raman Si nanocavity laser used in this work. This design is the same as that used in Refs. [25,33]. The core region consists of a multi-step heterostructure nanocavity (see the three different lattice constants in the figure) and two adjacent waveguides to enable excitation of the two high-Q nanocavity modes shown in the band diagram in Fig. 2(b). These cavity modes are used to confine the pump light and the Stokes Raman scattered light [16]. They will hereafter be referred to as the pump mode and the Stokes mode, respectively. The Q value and the resonance wavelength of the pump mode (the Stokes mode) are denoted by Q_p (Q_S) and λ_p (λ_S), respectively. The theoretical Q_p and Q_S calculated by the three-dimensional finite difference time domain method including effects of the excitation waveguides are about 3.0 × 10⁵ and 3.0 × 10⁶, respectively.

 

Fig. 2. (a) Schematic of the core region of the Raman Si laser device containing the PC heterostructure nanocavity at the center and the two excitation waveguides. (b) Band diagram of the nanocavity. The pump mode and the Stokes mode arise from the two propagation bands of the nanocavity as a result of the three different lattice constants indicated in (a). The white area between the first and second propagation bands presents the mode gap region.

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The sample was fabricated according to the procedures explained in Refs. [33,34]. The PC pattern was defined on a resist-coated chip by electron beam lithography. The pattern was first developed and then transferred to the top Si layer by dry etching. The residues on the Si surface were removed by a standard cleaning process for Si wafers, and the surface was thoroughly cleaned by a thin thermal oxidation of the sample followed by the removal of the surface oxides. The last step in the fabrication was the formation of an air-bridge structure; the buried oxide layer underneath the PC pattern was selectively removed by 48% hydrofluoric acid at room temperature. Afterwards, the sample was rinsed with pure water for two minutes, and then it was dried under a nitrogen gas flow for two minutes. After the fabrication, the sample was stored in a low-humidity desiccator. The experiments reported here were performed more than one year after the fabrication, and therefore the surface of the sample used in the experiments had a natural oxide with a thickness of about 0.5 nm and water molecules adhered to the surface [35]. The average surface roughness Ra of a similar sample estimated by atomic force microscopy was less than 0.3 nm [36]. From scanning electron microscopy (SEM) images, the roughness of the side walls of the holes was estimated to be much larger than the surface roughness (high-resolution SEM images of the air holes are provided in Appendix A1).

The operation principle of a Raman Si nanocavity laser is important to understand the experimental results shown in Section 4, and thus it is explained briefly: When the Raman gain exceeds the cavity loss for the Stokes mode, the Raman laser starts to oscillate. Note that the cavity loss can be expressed in terms of an inverse Q factor, 1/Q_S, which can depend on various conditions. In the low pump-power regime, the Raman gain increases linearly with the photon density in the pump mode, while the cavity loss 1/Q_S is almost constant. As the photon density increases, the number of free electrons generated by TPA processes increases nonlinearly [37,38]. These electrons can absorb the Raman-scattered light via FCA, which increases the cavity loss 1/Q_S. In other words, FCA leads to a decrease in Q_S. Therefore, the initial Q_S at low pump powers should be high enough to achieve laser oscillation. The Q_S values that have been reported recently for such nanocavities, are higher than 1,000,000 [23,24,33,39]. Free carriers can also induce a shift in λ_p and λ_S via the thermo-optic effect (induced by a temperature rise due to light absorption) and the carrier plasma effect [24]. A shift in λ_p decreases the photon density in the pump mode since the detuning δλ_in between λ_p and the excitation laser wavelength λ_in increases [23]. These effects caused by free carriers play a significant role in the response of a Raman Si nanocavity laser to ionized air.

3. Experimental setup

Figure 3 shows the experimental setup used in this work. This setup is similar to that used in Ref. [33]. A cw tunable laser (Santec TSL-510) was used for excitation and the laser wavelength λ_in was measured by a high-precision wavelength meter (Agilent 86122A). The Si chip was fixed to a copper block (on the backward x–z surface of the copper block in the inset of Fig. 3) by a thermally conductive adhesive sheet. The copper block itself was fixed to the sample stage by using a further sheet of the same type. The temperature of the sample stage was maintained at room temperature by a Peltier controller. We observed the nanocavity emission towards the y-direction by using a near-infrared (NIR) camera (FLIR SC2500), and two lock-in amplifier systems were used to enable simultaneous detection of the signals from the pump mode and the Stokes mode during laser oscillation. The experiments were performed in ambient air with a relative humidity of 25%–40% and the surface of the optical table was grounded.

 

Fig. 3. Experimental setup. The inset is a photograph of the sample stage. PD: InGaAs photodiode, Pol.: polarizer, NA: numerical aperture

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The negatively ionized air for our experiment was generated by a metal tip connected to a negative ion generator (Green techno Co. Ltd., high-voltage power supply GT20). The metal tip was placed parallel to the sample surface, and the distance between the copper block and the tip in the z-direction was about 1 cm. When the potential of the tip relative to the ground (V_tip) reached 4 kV, a negative corona discharge was established and negatively ionized air was generated. As illustrated in Fig. 1, the ionized air molecules generated at the tip will move along the electric field lines [40]. In all experiments presented in this study, we used V_tip = 5 kV, which produces a weak flux with an electric (ionic) wind velocity of less than 0.5 m/s [41]. It is noted that various materials around the tip, for example the objective lenses, can affect the electric field lines, and thus the established irradiation geometry was different from the idealized geometry shown in Fig. 1.

The negatively ionized air molecules that reach the Si surface, can transfer electrons to Si. The transferred electrons can follow various paths: they can be trapped at localized surface states, diffuse into the Si slab, diffuse to the sample stage, or again escape into the air. The electrons can produce heat by releasing their excess energy. Those electrons that are in the Si nanocavity, can cause various effects that are detrimental for a Raman Si laser, such as FCA induced by TPA.

4. Experimental results

Figures 4(a) and 4(b) show the resonance spectra of the nanocavity pump and Stokes modes, respectively, that were observed while the negative ion generator was off. The laser intensity incident on the excitation waveguides was small enough to ignore TPA. The open circles in Figs. 4(a) and 4(b) represent the experimental data. The solid curves are the fitting results using Lorentzian functions, from which we obtain the peak position λ and the full width at half-maximum (Δλ). The pump mode has a λ_p of 1423.367 nm and a Δλ_p of 13.59 pm. The values for the Stokes mode are λ_S = 1537.235 nm and Δλ_S = 1.25 pm. According to the relation Q = λ/Δλ, we estimate Q_p = 1.05 ´ 10⁵ and Q_S = 1.22 ´ 10⁶. The lower experimental Q values compared to the theoretical values are due to imperfections of the fabricated sample [42,43]. The frequency difference Δf between these two modes is 15.5973 THz, which closely matches the Raman shift of Si, 15.606 THz [44]. These values should be sufficient for laser oscillation [45].

 

Fig. 4. (a) Resonance spectrum of the pump mode (open circles). The continuous curve is the fitting result. (b) Resonance spectrum of the Stokes mode. (c) Stokes output power as a function of the pump power coupled into the nanocavity. The closed black circles were obtained in the absence of ion irradiation, and the open blue circles were obtained during ion irradiation. The insets in (a)−(c) depict the excitation of the nanocavity pump (blue) and Stokes (red) modes. (d) NIR camera images of the nanocavity emission for three different values of δλ_in. Here, we used no ion irradiation and the pump laser signal was cut off by inserting a long-pass filter (cutoff wavelength 1500 nm).

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The closed black circles in Fig. 4(c) are the input/output characteristics of the Raman laser when the device was not exposed to ionized air. For each data point, the λ_in was adjusted to the actual λ_p, which gradually redshifts due to the free carriers generated by TPA as the pump power increases [24]. Above the estimated threshold (I_th) of 1.3 µW, the Stokes intensity starts to increase strongly (see the red solid line). We can confirm that the Stokes power tends to saturate as the pump power further increases. This saturation is caused by the FCA loss induced by TPA [11,37,38].

Figure 4(d) shows the NIR camera images of the nanocavity at a pump power of 1.2 × I_th for three different values of the detuning δλ_in (= λ_in−λ_p). The Raman laser intensity is maximized when δλ_in = 0. For a detuning of δλ_in = – 4 pm, the Raman laser intensity is already significantly smaller due to the reduction of the photon density in the pump mode [24]. Laser oscillation stops for conditions where δλ_in < − 8 pm. This lower limit of δλ_in for laser oscillation is related to the irradiation-induced mechanism of the laser interruption as demonstrated later.

The blue open circles in Fig. 4(c) show the input/output characteristics measured while the negative ion generator was on (V_tip = 5 kV) and the nanocavity was continuously irradiated with ionized air. Under this condition, Raman laser oscillation was not observed at any excitation power even when the λ_in was adjusted to the shifted λ_p. We recorded a movie (Visualization 1) of the temporal change of the Raman laser oscillation. In this experiment, the device was irradiated with ionized air for two seconds under the conditions 1.2 × I_th, δλ_in = 0 pm, and V_tip = 5 kV. Figure 5 (Visualization 1) shows that the Raman laser oscillation stops abruptly after the start of the irradiation and then gradually recovers after the irradiation has ended. In this movie, the Raman laser intensity recovered almost completely, that is, it almost reached the intensity before irradiation, within 6 seconds from the irradiation stop. These results demonstrate that the ionized air molecules supply extra electrons to the Si nanocavity as illustrated in Fig. 1, and this is detrimental for the Raman laser performance. As the electrons escape from the nanocavity after the irradiation, the Raman laser emission recovers.

 

Fig. 5. Influence of a flux of ionized air on the Raman Si nanocavity laser oscillation: (a) before irradiation, (b) a short time after the start of the irradiation, and (c) several seconds after the irradiation. The figure shows representative frames recorded by the NIR camera, which were extracted from Visualization 1. The sample was exposed to negatively ionized air for two seconds from 5.5 to 7.5 seconds. The inserted time corresponds to the time in the Visualization 1. This movie was recorded using an exposure time of 10 milliseconds, a frame rate of 25 frames per second, and a camera resolution of 320 × 256 pixels.

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We confirmed the abovementioned laser interruption due to a short irradiation with ionized air many times on different days. We found that the degree of the laser oscillation recovery varied in each experiment. Since we manually controlled the high-voltage power supply, we consider that the total amount of charges delivered to the cavity varied from experiment to experiment. Additionally, the Si chip was not directly connected to the ground, and such a condition can also decrease the reproducibility of the electron escape rate from the cavity. For example, in another experiment where the copper block was connected to the ground, we observed that the variation in the laser oscillation recovery was reduced, and the recovery time tended to be slightly shorter. Probably, the reproducibility is also affected by humidity. Since the Q values stayed almost unchanged before and after the experiment, we believe that the Si surface was not modified by the ionized air irradiation at V_tip = 5 kV. Note that Q_S values larger than one million can be maintained even if the surface condition is slightly changed [46].

Next, we investigate the reason why the Raman laser oscillation was interrupted under the exposure to negatively ionized air by comparing the resonance spectra with and without irradiation. Since the time required for measuring one spectrum was 2 minutes, we performed experiments under continuous irradiation, instead of the short irradiation used for Visualization 1. The solid lines in Figs. 6(a) and 6(b) are the resonance spectra of the pump mode and Stokes mode, respectively, measured with continuous irradiation at V_tip = 5 kV. The laser intensities incident onto the excitation waveguides were the same as those for Figs. 4(a) and (b), and the broken curves are the same spectra as shown in Figs. 4(a) and 4(b).

 

Fig. 6. Resonance spectra of (a) the pump mode and (b) the Stokes mode in the presence of ionized air (solid curves). The broken curves are the same data as in Figs. 4(a) and 4(b).

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We find that the λ_p redshifts by 12.7 pm due to the irradiation, and the λ_S redshifts by 6.0 pm. The difference in the magnitude of the redshift is probably due to the variation in the total amount of the delivered charge as explained above (the setup shown in Fig. 3 does not allow us to simultaneously measure the resonance spectra of the two modes). The Δf between the two peaks of the solid curves in Figs. 6(a) and 6(b) is 15.5964 THz. The change in the Δf due to the irradiation should thus be less than 0.0009 THz (we measured the spectra many times under the same condition, and the change in the Δf was not larger than 0.001 THz). This is much smaller than the width of the Raman gain of Si, ≈ 0.08 THz [47]. In addition, we have observed Raman laser operation in a range of Δf from 15.582 THz to 15.630 THz [45]. Hence, this irradiation-induced change in Δf cannot be the main cause for the laser interruption.

To explain the redshift, we consider the electrons that have been transferred from the ionized air to the nanocavity. These electrons can induce a blueshift of λ via the carrier plasma effect while they can induce a redshift of λ via the thermo-optic effect induced by a temperature rise. This temperature rise is considered to be mainly due to the release of the excess energy of the transferred electrons and the FCA of pump photons by the transferred electrons. Due to the competition between both effects, the sign of the actual shift is determined by the experimental conditions such as the thermally conductive contact between the sample and the copper block, and humidity. We in fact were also able to observe opposite shifts in λ_p and the λ_S under different measurement conditions; we found that blue shifts are more likely to be observed when the conductive contact is imperfect. In this case, the electric potential of the Si chip (copper block) rapidly increases to a value close to 5 kV due to a slower electron diffusion to the sample stage, and then the ionized air cannot further supply charges to the Si chip. As a result, the temperature rise is suppressed while the magnitude of the carrier plasma effect is not changed.

An important result in Fig. 6 is that the Q values and the emission intensities are significantly lower in the case of irradiation with ionized air. These reductions are due to the FCA that is caused by the transferred electrons. The Q_p in the case of irradiation (Q_{p_ion}) is7.93 × 10⁴, and the corresponding Q_S is Q_{S_ion} = 4.05 × 10⁵. The reduction of the peak intensity in the Stokes mode is larger than in the pump mode, because Q_S is larger than Q_p. As explained in Section 2, Raman laser oscillation is possible when the Raman gain exceeds the cavity loss for the Stokes mode, 1/Q_S. While we have so far measured many laser samples (more than fifty) that exhibited cw oscillation, most of them had a Q_S > 1,000,000 [21,23,24,33,39,45]. In other words, we have not yet observed cw oscillation in a nanocavity with Q_S < 500,000. A numerical simulation based on coupled-mode theory indicates that the sample used in this study cannot exhibit laser oscillation if the initial Q_S is less than 8.0 × 10⁵ [23,24]. Therefore, the reduction of Q_S (due to FCA) as shown in Fig. 6(b) should be an important factor for the interruption of laser oscillation observed in our experiments.

To be able to use the effect shown in Fig. 5 for sensing applications, it is important to estimate the change of the carrier density in the nanocavity due to the irradiation with ionized air. The additional Q_{add_loss} value due to the increase of FCA caused by the ionized air, is defined by

Here, α_FCA is the absorption coefficient that determines the strength of FCA, and n₀ is the refractive index at λ_S. By substituting the above value of Q_{S_add_loss} for Q_FCA, we obtain α_FCA = 2.40 × 10⁻¹ cm⁻¹. The free-electron density (N_FCA) can be evaluated by using the relation

By using two lock-in amplifiers as shown in Fig. 3, we simultaneously measured the changes in the emission intensities of the two nanocavity modes of the Raman laser after a short irradiation with the ionized air. The circles in Fig. 7 show the emission from the pump mode measured using a short-pass filter, while the triangles represent that from the Stokes mode measured using a long-pass filter. The measurement time was two minutes, and the pump mode was excited at an intensity of 1.2 × I_th. The λ_in was fixed at the wavelength where the Raman laser without ionized-air irradiation reaches the maximum output. The intensities were recorded every 1.5 seconds and ionized air was generated for two seconds (from 30 to 32 s as indicated by the shaded area in Fig. 7). The temporal responses shown in Fig. 7 enable a detailed discussion of the mechanism of the Raman laser interruption. For the discussion, we divided the data into four different time regions (i)–(iv).

 

Fig. 7. Temporal behavior of the emission intensities of the pump and Stokes modes measured at the same time. The shaded area represents the time where the device was exposed to ionized air. The four illustrations on the right-hand side show temporal changes of the TPA carriers (open circles) and the transferred electrons (filled circles) in the nanocavity.

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In time region (i), which lasts thirty seconds, both intensities are stable. The Raman laser intensity slightly fluctuates, because the slope of the input/output characteristic at 1.2 × I_th is large as shown in Fig. 4(c). Although free carriers due to TPA exist in the nanocavity, the number of these carriers is relatively small since we used an excitation intensity close to the threshold [23].

In time region (ii), the emission intensity of the pump mode decreases by 15% within a few seconds after the irradiation and then gradually recovers to the value before irradiation. The initial reduction is due to the wavelength shift and the increase in the FCA loss caused by the exposure to ionized air. We were not able to identify the phenomenon that contributed the most to the reduction. From the resonance spectrum shown in Fig. 4(a) and the intensity decrease by 15%, the magnitude of the wavelength shift is estimated to be less than 2.7 pm. The subsequent recovery of the intensity indicates that the influences of free carriers on the pump mode are negligible at the end of region (ii). On the other hand, the Stokes intensity exhibits a drastic change; it starts to decrease immediately after the irradiation and decreases by about 97% within a few seconds after the irradiation, where the laser oscillation stops although the photon density in the pump mode is still larger than that at the threshold (85% of 1.2 × I_th equals 1.02 × I_th). At the end of region (ii), Raman laser oscillation occurs again, but the Stokes emission intensity has recovered to just 11% in spite of the fact that the photon density in the pump mode has recovered to a density corresponding to 1.2 × I_th. Since the Q_S is 10 times larger than the Q_p, it takes a longer time before the influence of FCA becomes negligible again.

In time region (iii), the Raman laser intensity gradually recovers to the initial value. The time required for the Stokes light recovery was 15 seconds longer than that of the recovery of the light emitted from the pump mode. This time is much longer than the carrier lifetime that has been observed when only the nanocavity was photoexcited locally [23,50]. Since in our experiment the entire Si chip and the sample stage had been charged up by ionized air, it took a long time for the electrons to escape. In time region (iv), the influences of free carriers completely disappear and we confirmed that the Raman laser is stable for more than 1 minute.

The temporal responses in Fig. 7 suggest that the reduction of Q_S due to an increased FCA loss is the most significant factor for the observed Raman laser interruption. The wavelength shift of the pump mode only contributes to the initial behavior of the laser interruption.

Finally, future prospects are discussed. In this report, we investigated the laser interruption that occurs at an excitation power of 1.2 × I_th due to exposure to negatively ionized air generated at V_tip = 5 kV. With a much higher excitation intensity, for example more than 5 × I_th, it might be possible to quantitatively detect air ions by measuring the decrease in the Raman laser intensity, instead of simply judging whether or not laser oscillation has stopped. In that case, a high sensitivity could be expected if the device has a higher Q_S (Raman nanocavity laser with a much higher Q_S, which is designed by using a deep neural network, was demonstrated recently [51]). Instead of the present Raman laser design, high-Q L3-type nanocavities or PC waveguides may also be used for the detection of ionized air [52–54], since the emission from the high-Q nanocavity mode or the transmission of the waveguide will be influenced by the adsorption of ionized air. The detection of ionized air with a high spatial resolution is possible by employing arrays of nanocavities with an excitation waveguide [55–57]. In such devices, use of broadband light from a superluminescent diode has advantages since it can excite all cavities simultaneously and is hardly affected by shifts in λ [58]. If a Raman Si nanocavity laser with SLD excitation can be developed, it may stimulate research for sensing applications [59,60]. By using Raman lasers for detection, a higher sensitivity can be expected because the output intensity from the cavity changes significantly with a small amount of charges. Since stimulated Raman scattering in Si involves a wavelength conversion with an input–output separation of more than 100 nm, stray light with the same wavelength as that of the excitation light will not affect the signal-to-noise ratio.

Regarding future experiments using a similar approach as in this work, the following aspects may be considered. In the spectral measurement shown in Fig. 6, the decrease of Q due to the exposure to ionized air may not have been accurately evaluated because the sample may not have been in thermal equilibrium during the measurement. A time-domain measurement is required to evaluate the decrease of Q with a high accuracy [61]. The evaluation of the spatial density of the air ions that impinge on the nanocavity, is also an important issue. Furthermore, an experiment using positively ionized air is also considered significant because ESD can be also caused by positive charges. In general, positive ions do not move in the orbits shown in Fig. 1 [40], and thus we employed negative ions here.

5. Summary

The detection of negatively ionized air by using a Raman Si nanocavity laser has been reported. We found that the Raman laser oscillation stops abruptly after an exposure to a weak flux of negatively ionized air for two seconds. Spectral measurements revealed that the observed laser interruption is mainly caused by an increase in the FCA loss that is induced by the ionized air via a transfer of extra electrons from the ionized air molecules to the Si nanocavity. After the generation of ionized air had stopped, laser oscillation gradually recovered as these additional electrons escaped from the nanocavity. Thus, the detection of ionized air by this device is repeatable. The results reported here show how ionized air can be detected using optical technologies. We believe that such a method can be useful in situations where the use of electronic devices for detection is difficult.

Appendix

A1. SEM images of the air holes

Figure 8 shows two SEM images of the air holes. In Fig. 8(a), the edges of the air holes appear as white circles. Based on an image analysis, we consider that the standard deviation of the edge roughness might be less than 1 nm. From Fig. 8(b), it can be seen that the side wall surface is rougher than the top surface of the slab.

 

Fig. 8. (a) SEM image of the air holes in the presently used sample. (b) SEM image of the PC slab tilted by 20 degrees. Platinum was coated on the surface to make the side walls visible.

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Funding

Inamori Foundation; Japan Society for the Promotion of Science (18H01479, 21H01373); Japan Science and Technology Agency (JPMJST2032).

Acknowledgments

Yuki Takahashi was supported by a fellowship from the ICOM Foundation.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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51. T. Kawakatsu, T. Asano, S. Noda, and Y. Takahashi, “Sub-100-nW-threshold Raman silicon laser designed by a machine-learning method that optimizes the product of the cavity Q-factors,” accepted in Opt. Express.

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