1. Introduction

Silicon (Si) photonic devices fabricated on silicon-on-insulator (SOI) wafers with large diameters by complementary metal–oxide–semiconductor (CMOS)-compatible processes have made substantial progress in this decade [1–3]. Among these devices, compact Si-based lasers are considered to be useful for various applications such as opto-electronic integrated circuits, short-distance optical communication, and low-cost environmental sensors. A feasible technique that allows cost-effective mass production of such lasers would be beneficial for these applications.

Within the last thirty years, various investigations on Si-based lasers that use interband transitions, have been performed. The reported devices based on nanocrystals [4], nanolayers [5], nanowires [6], and high quality-factor (Q) photonic-crystal (PC) nanocavities [7–9] have shown promising emission properties. However, stable continuous-wave (cw) laser oscillation at room-temperature has so far not been achieved with these designs, because Si has an indirect energy band gap, resulting in a very low efficiency of radiative recombination [10]. On the other hand, several optically pumped Si lasers that use stimulated Raman scattering [11–15], have already achieved stable cw oscillation at room temperature [16]. For example, the Raman laser based on a high-Q Si ring resonator with a length of 3 cm achieved stable cw operation with a threshold of 20 mW [17]. The physical reason for the success of this type of Si laser is that the probability for stimulated Raman scattering is proportional to the Q of the resonator and inversely proportional to the volume [18,19]. It is important to understand that PC nanocavities can realize both high Q values and small volumes [20–22]. It has been shown that the heterostructure nanocavity, whose resonator length is about 10 µm, is able to achieve Q values larger than ten million [23,24]. Therefore, the heterostructure nanocavity design is considered highly beneficial for compact Raman Si lasers.

We have developed a Raman Si nanocavity laser with a lasing threshold of less than 1 µW [25,26]. To understand how the device performance can be further improved, lasing dynamics and the excitation-wavelength dependence of the Raman gain have been clarified [27,28]. We have also demonstrated the integration of two Raman Si nanocavity lasers operating at the 1.31- and 1.55-µm telecommunication bands on a single chip [29]. However, these investigations used samples fabricated by electron-beam (EB) lithography, which provides high accuracy but is a relatively time-consuming method.

Recently, high-speed optical modulators [30], wavelength demultiplexers [31,32], and beam steering devices [33] based on PCs fabricated by CMOS-compatible processes including photolithography, have been demonstrated. Furthermore, owing to the optimization of the fabrication process of heterostructure nanocavities, fabrication of nanocavities with Q values larger than 2.5 million by photolithography has been achieved [34]. However, there are still several difficulties in fabricating Raman Si nanocavity lasers by CMOS-compatible processes: Firstly, because this type of laser uses two resonant modes to confine the pump light and Stokes Raman light to the resonator, both modes require high Q values in order to enable lasing. Secondly, the frequency spacing of the two modes (Δf) needs to closely match the Raman shift of Si [35]. Thirdly, the nanocavity should be fabricated along the [100] crystal direction of Si to enhance the Raman gain [36].

In this work, we demonstrate a Raman Si laser based on a nanocavity fabricated by argon fluoride (ArF)-based immersion lithography. Here, a SOI wafer with a 45°-rotated top Si layer is employed to enhance the Raman gain and a thermal process is applied to improve the Q value of the resonant mode for the pump light. In the best sample, room-temperature cw oscillation is observed above the threshold of 1.8 µW.

2. Sample structure and fabrication method

Figure 1(a) shows a schematic of the core region of the Raman Si laser used in this work. The triangular lattice of circular air holes constitutes the two-dimensional PC (lattice constant a = 410 nm in the light-gray region). The center line-defect formed by the 27 missing air holes is a multi-heterostructure nanocavity [37]. The distance between the air holes in the x-direction is changed in steps of 5 nm as indicated by the dark-gray regions. The wider air-hole distance locally increases the effective refractive index and thus lowers the allowed frequency ranges of the two propagation bands of the line defect as shown in Fig. 1(b). As a result, two high-Q nanocavity modes are formed in the heterostructure; the mode arising from the second propagation band (blue) is used to confine the pump laser light and the mode arising from the first propagation band (red) is used to confine the Stokes Raman scattered light. They will hereafter be referred to as the pump mode and the Stokes mode, respectively. The thickness of the Si PC slab was 225.8 nm. We chose an air-hole radius of about 128 nm, because a heterostructure cavity with these dimensions has a Δf close to the Raman shift of Si. Note that, in the present cavity design, a change in the air hole radius leads to a shift of Δf with a rate of about 0.15 THz/nm [38]. Therefore, small deviations of the actual air-hole pattern from the design (due to a limited fabrication accuracy) can induce a significant shift of Δf.

 

Fig. 1. (a) Schematic of the PC heterostructure nanocavity and the two excitation waveguides used for our Raman Si laser devices. (b) Band diagram of the nanocavity. The pump mode and Stokes mode arise from the two propagation bands of the nanocavity. The white area between the first and second propagation bands presents the mode gap region.

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The two line-defects located at the top and bottom in Fig. 1(a) are the waveguides used to excite the pump mode and to excite the Stokes mode, respectively. The width of the pump excitation waveguide (that is, the distance between the air holes that define the upper line defect in the y-direction) is $0.88\sqrt 3 a$. The width of the Stokes waveguide is $1.10\sqrt 3 a$. The theoretical Q of the pump mode is 2.86 × 10⁵, which was calculated by the three-dimensional finite difference time domain method including effects of the excitation waveguides. The theoretical Q of the Stokes mode is 2.95 × 10⁶. It is noted that the experimental Q (Q_exp) values are lower than the theoretically predicted values due to imperfections of the fabricated sample. An important feature of our device design is that the x-direction of the nanocavity is along the [100] crystal direction of the Si top layer of the SOI wafer. This direction was selected in order to increase the Raman gain, which depends on the Raman tensor of Si and the electric field distributions of the two resonant modes [38].

A flow chart of the sample fabrication is provided in Fig. 2. As explained in the following, only standard CMOS processes were used for sample fabrication. We used a 300-mm SOI wafer comprising a top Si layer, a 3 µm-thick buried oxide (BOX) layer, and a Si support substrate (775 µm). Note that in this SOI wafer, the crystal orientation of the top layer is rotated by 45 degrees with respect to the substrate, i.e. the [100] direction of the top layer is parallel to [110] of the support substrate. The cleavage of this wafer is performed along to [110] of the support substrate and therefore, the cleaved sample has a top Si layer with edges along to [100] and [010]. By using this wafer, the heterostructure nanocavity can be fabricated in the direction perpendicular to the cleaved facets of the wafer and the slab warpage at the cleaved facet decreases [39].

 

Fig. 2. Sample fabrication steps.

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The sample processing related to the photolithography and plasma etching steps to form the air holes was performed using CMOS-compatible machinery in the research and development 300-mm pilot line at the National Institute of Advanced Industrial Science and Technology. We used an immersion scanner (Nikon NSR-S610C, ArF excimer laser at 193 nm) for 45-nm node volume production. We used a binary photomask with a size of 104 mm × 132 mm and projected it onto the SOI wafer by reducing the size to 26 mm × 33 mm. The patterns of the PC Raman Si lasers occupied only a small area of the photomask. Considering the present limits of the hole fabrication accuracy and their influences on Δf, we fabricated patterns containing several PC nanocavities with different hole radii. The patterns were first developed and transferred to the hardmask, and then transferred to the top Si layer by dry etching. Nearly 60 equivalent chips were fabricated on the SOI wafer. For sample characterization and the following processing steps, the wafer was separated into small pieces (800 µm × 2000 µm) along the [110] and [-110] directions of the support substrate by laser stealth dicing. Each piece contained eleven cavities with the same dimensions. Because the Q_exp values are sensitive to the Si surface quality [23,40], a thermal oxidation step (< 500 C°) and subsequent removal of the thin surface oxide were applied several times to the pieces to clean the Si surface. Prior to this cleaning procedure, the Q_exp values of the pump mode of the eleven cavities were smaller than 100,000, but in eight cavities they reached more than 100,000 owing to the cleaning (the thermal process may have also reduced surface defects, vacancies, oxygen and carbon interstitials, generated during the plasma etching step [41,42]). These final values are almost the same as the Q_exp of the pump mode of the cavity in Ref. [39], where we employed EB lithography. On the other hand, the repeated surface cleaning can result in a slight decrease of the Q_exp of the Stokes mode since it can increase the structural imperfections of the air holes [43,44]. Finally, to form an air bridge structure, the BOX layer was selectively removed using 48% hydrofluoric acid (HF) without surfactant at room temperature.

The cross-sectional scanning electron microscope (SEM) image of one of the devices before the HF treatment is shown in Fig. 3(a). The side walls of the fabricated air holes are slightly arcuate, which decreases the Q_exp values [45]. Figure 3(b) is a cross-sectional SEM image of the sample after formation of the air bridge structure. Although the PC slab is slightly deformed due to compressive stress, this hardly decreases the Q_exp of the two modes [35,39]. Figure 3(c) is a top view of the core region of this laser device and evidences that there are no visible residues of the hardmask or the photoresist on the Si surface. The SEM image of the waveguide edge in Fig. 3(d) proves that the laser stealth dicing resulted in a cleaved facet with good quality. The waveguide extends perpendicular to the cleaved facet due to the use of the 45°-rotated SOI wafer.

 

Fig. 3. (a) SEM image of one fabricated Raman Si laser before etching of the SiO₂ layer. (b) SEM image of this sample after etching of the BOX layer. (c) Top view of the core region of this device. (d) Top view of the cleaved facet.

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3. Experimental results

The optical properties of the fabricated eleven samples were investigated using conventional micro-spectroscopy. The details of the measurement method are given in the Appendix. Figures 4(a) and 4(b) show the measured resonance spectra of the pump mode and Stokes mode of cavity #8 (details are provided further below), respectively. Here, the pump power was much smaller than the laser threshold and the insets illustrate the excitation configurations used during the measurements. The resonant wavelength λ and the full width at half-maximum Δλ of each spectrum was obtained by a fit of a Lorentz function to the data (solid curves in the figures). The resonant wavelength of the pump mode is λ = 1410.825 nm and the corresponding Δλ is 11.0 pm. For the Stokes mode we obtained λ = 1522.668 nm and Δλ = 1.5 pm. According to the relationship Q = λ/Δλ, the estimated Q_exp of the pump mode is 128,257 and that of the Stokes mode is 1,015,112. The Δf of the two modes is 15.604 THz, which closely matches the Raman shift of Si, 15.606 THz [35]. Therefore, laser oscillation can be expected in this nanocavity.

 

Fig. 4. (a) Resonance spectrum of the pump mode. (b) Resonance spectrum of the Stokes mode. (c) Laser output power as a function of the pump power coupled into the nanocavity. (d) Camera images of the nanocavity under three different excitation conditions. The pump laser light is cut off by inserting a long-pass filter.

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Figure 4(c) plots the input/output characteristics of the Raman Si nanocavity laser using cavity #8, which is the cavity with the best performance. The inset shows the excitation method (details are given in the Appendix). As shown with the red solid line, the Stokes intensity nonlinearly increases above the estimated threshold of 1.8 µW. The maximum energy efficiency of this device is 0.23% and saturation of the laser output appears for pump powers above 4 µW. This saturation is caused by the absorption due to free carriers generated by two-photon absorption [46,47]. Figure 4(d) shows three near-infrared camera images of the nanocavity at different pump powers (below and above the threshold: 1.2, 1.8, and 3.5 µW). The exposure time was 10 ms. These images clearly show the laser oscillation of a nanocavity-based Raman Si laser fabricated by photolithography.

A comparison between the above Raman Si laser characteristics and those of similar samples fabricated by EB lithography is important to identify the issues that may be investigated in future in order to improve the present approach. We note that the threshold obtained for cavity #8 is approximately three times higher than that of the comparable Raman Si nanocavity laser sample fabricated by EB lithography [39]. Furthermore, the maximum efficiency is more than twenty times smaller [39]. Although the Q_exp of the Stokes mode in cavity #8 is significantly smaller than that of the comparable sample fabricated by EB, we consider that this is not the only reason for the lower performance. This is because the sample with a Q_exp of about 1 million for the Stokes mode fabricated by EB in our previous work [26], exhibited a better laser performance. We suspect that nonlinear optical losses play an important role in our present devices [28]. As the theoretical Q values of the present design also impose a certain performance limitation, an additional improvement of the cavity design by sophisticated techniques will also be important [48,49]. We have recently confirmed that the theoretical Q of the two modes can be increased by several times compared to those in this study [50].

Next, we briefly discuss the magnitude of the variation in the Δf of the cavities on the investigated piece. Figure 5 compares the Δf of eleven nanocavities that have the same structure as shown in Fig. 1(a). The red line shows the Raman shift of Si [35]. The Δf values are scattered over a relatively broad range due to fluctuations in the air hole positions and radii [43]. The standard deviation of this distribution is 3.28 × 10⁻² THz, which approximately 1.2 times larger than that for the Raman Si nanocavity lasers fabricated by EB lithography [38]. It has been shown that a large statistical variation in Δf decreases the fabrication yield of nanocavity-based Raman Si lasers [38]. In order to reduce the magnitude of the structural fluctuations, it may be useful to enhance the accuracy of the photomask pattern.

 

Fig. 5. Frequency spacing Δf between the resonant frequencies of pump and Stokes modes for eleven nanocavities with the same dimensions as shown in Fig. 1(a). Dotted lines show the standard deviation of the distribution.

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Finally, we comment on the potential of using photolithography for fabrication of other PC lasers. The photolithography is particularly suitable for patterning the circular nanoholes. In the present work, we performed the ArF immersion lithography process with a binary photomask. When fabricating circular holes with a diameter less than 150 nm using this method, the fabrication accuracy could gradually become worse as the diameter becomes smaller. For devices that require smaller circular holes, it can be advantageous to use a halftone photomask [51]. Besides circular air holes, also nanoholes with other shapes, such as an ellipse [52], a triangle [53], or a square [54], can be used to fabricate a PC laser. It has been proposed that the performance of a Raman Si nanocavity laser can be enhanced using a slotted nanostructures [55]. Also for these other types of nanoholes, it can be advantageous to use a halftone photomask.

4. Summary

We have demonstrated the operation of a nanocavity-based Raman Si laser that was fabricated by photolithography and CMOS-compatible machinery. We employed a SOI wafer with a 45°-rotated top Si layer to enhance the Raman gain and applied a thermal process to improve the Q value of the pump mode. The achieved lasing threshold was 1.8 µW and the maximum energy efficiency was 0.23%. The results prove that fabrication of nanocavity-based Raman Si lasers by photolithography is possible, but further optimization is required for realization of mass production of nanocavity-based Raman Si lasers. We believe that further improvements in the fabrication process and the cavity design are required to enhance the laser performance and to increase the fabrication yield.

Appendix

Figure 6 describes the experimental setup used for obtaining the experimental results shown in Figs. 4 and 5. For excitation, we used light from a cw tunable laser (Santec TSL-510). The emission wavelength was determined by a high precision wavelength meter (Agilent 86122A). To obtain the transverse-electric field component, the excitation light was passed through a polarizer. Then, the beam size was expanded to the size of the pupil diameter of the objective lens (with numerical aperture, NA = 0.4) by a beam expander. The light is focused on either the facet of the pump excitation waveguide or that of the Stokes excitation waveguide. To precisely control the position of the sample, we used a high-precision six-axis stage. In order to stabilize the λ [56], the sample temperature was stabilized at 297 °C by a Peltier device.

 

Fig. 6. Experimental setup to measure the resonance spectra of the two nanocavity modes and the laser characteristics. The colors of the incident light and the emitted light correspond to the measurement of the data shown in Figs. 4(c) and 4(d). The 1500-nm long-pass filter (LPF) is removed for the measurement of the resonance spectra in Figs. 4(a) and 4(b).

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For each measurement, the wavelength of the tunable laser is scanned in order to detect the resonant wavelength of the cavity mode of interest (either pump mode or Stokes mode). When the incident wavelength matches the resonant wavelength, a part of the pump light is extracted by the nanocavity and emitted in the direction perpendicular to the slab. To characterize the cavities, we collected the emitted light by another objective lens (NA = 0.65) placed on a 3-axis stage. By precisely adjusting the position of the objective lens using an InGaAs camera (FLIR SC2500), we were able to detect the emitted light without leakage by the photodiode indicated in the figure. To obtain the resonance spectra shown in Figs. 4(a) and 4(b), the intensities of the emitted light were measured with aid of a lock-in amplifier system (NF Corporation LI5630) as a function of the excitation laser wavelength. For this measurement, no long-pass filter was employed.

However, when the pump resonant mode is strongly excited, both pump light and stimulated Raman scattered light are emitted from the cavity via the two resonant modes. Therefore, the laser emission was measured by inserting a long-pass filter with a cutoff wavelength of 1500 nm to suppress the signal from the pump mode. Each data point in Fig. 4(c) corresponds to the peak value of the recorded resonance spectrum at a certain excitation intensity [28]. The power coupled into the pump mode, that is, the x-axis in Fig. 4(c), was estimated from the emission by the pump mode in the low-excitation power regime using the assumption that this intensity is linearly proportional to the power of the cw laser.

Funding

Japan Society for the Promotion of Science (18H01479); Support Center for Advanced Telecommunications Technology Research Foundation; Kyoto Technoscience Center.

Acknowledgments

T. Yasuda was supported by a fellowship from the ICOM Foundation.

Disclosures

The authors declare no conflicts of interest.

References

1. J. K. Doylend and A. P. Knights, “The evolution of silicon photonics as an enabling technology for optical interconnection,” Laser Photonics Rev. 6(4), 504–525 (2012). [CrossRef]  

2. K. K. Mehta, J. S. Orcutt, O. Tehar-Zahav, Z. Sternberg, R. Bafrali, R. Meade, and R. J. Ram, “High-Q CMOS-integrated photonic crystal microcavity devices,” Sci. Rep. 4(1), 4077 (2015). [CrossRef]  

3. T. Horikawa, D. Shimura, H. Okayama, S. H. Jeong, H. Takahashi, J. Ushida, Y. Sobu, A. Shiina, M. Tokushima, K. Kinoshita, and T. Mogami, “A 300-mm silicon photonics platform for large-scale device integration,” IEEE J. Sel. Top. Quantum Electron. 24(4), 1–15 (2018). [CrossRef]  

4. Y. Kanemitsu, T. Ogawa, K. Shiraishi, and K. Takeda, “Visible photoluminescence from oxidized Si nanometer-sized spheres: Exciton confinement on a spherical shell,” Phys. Rev. B 48(7), 4883–4886 (1993). [CrossRef]  

5. D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, “Quantum confined luminescence in Si/SiO₂ superlattices,” Phys. Rev. Lett. 76(3), 539–541 (1996). [CrossRef]  

6. L. T. Canham, “Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers,” Appl. Phys. Lett. 57(10), 1046–1048 (1990). [CrossRef]  

7. S. Iwamoto, Y. Arakawa, and A. Gomyo, “Observation of enhanced photoluminescence from silicon photonic crystal nanocavity at room temperature,” Appl. Phys. Lett. 91(21), 211104 (2007). [CrossRef]  

8. M. Fujita, B. Gelloz, N. Koshida, and S. Noda, “Reduction in surface recombination and enhancement of light emission in silicon photonic crystals treated by high-pressure water-vapor annealing,” Appl. Phys. Lett. 97(12), 121111 (2010). [CrossRef]  

9. T. Ihara, Y. Takahashi, S. Noda, and Y. Kanemitsu, “Enhanced radiative recombination rate for electron-hole droplets in a silicon photonic crystal nanocavity,” Phys. Rev. B 96(3), 035303 (2017). [CrossRef]  

10. J. M. Shainline, “Silicon as an emissive optical medium,” Laser Photonics Rev. 1(4), 334–348 (2007). [CrossRef]  

11. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of stimulated Raman amplification in silicon waveguides,” Opt. Express 11(15), 1731–1739 (2003). [CrossRef]  

12. M. Krause, H. Renner, and E. Brinkmeyer, “Analysis of Raman lasing characteristics in silicon-on-insulator waveguides,” Opt. Express 12(23), 5703–5710 (2004). [CrossRef]  

13. R Jones, H Rong, A. Liu, A Fang, D. Paniccia, D Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13(2), 519–525 (2005). [CrossRef]  

14. X. Checoury, Z. Han, and P. Boucaud, “Stimulated Raman scattering in silicon photonic crystal waveguides under continuous excitation,” Phys. Rev. B 82(4), 041308 (2010). [CrossRef]  

15. T. Datta and M. Sen, “LED pumped micron-scale all-silicon Raman amplifier,” Superlattices Microstruct. 110, 273–280 (2017). [CrossRef]  

16. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005). [CrossRef]  

17. H. Rong, S. Xu, Y. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007). [CrossRef]  

18. X. Yang and C. W. Wong, “Coupled-mode theory for stimulated Raman scattering in high-Q/Vm silicon photonic band gap defect cavity lasers,” Opt. Express 15(8), 4763–4780 (2007). [CrossRef]  

19. Y. Takahashi, R. Terawaki, M. Chihara, T. Asano, and S. Noda, “First observation of Raman scattering emission from silicon high-Q photonic crystal nanocavities,” Proceedings of Conference on Lasers and Electro-Optics (CLEO) (2011), paper QWC3.

20. Y. Takahashi, Y. Tanaka, H. Hagino, T. Sugiya, Y. Sato, T. Asano, and S. Noda, “Design and demonstration of high-Q photonic heterostructure nanocavities suitable for integration,” Opt. Express 17(20), 18093–18102 (2009). [CrossRef]  

21. Y. Taguchi, Y. Takahashi, Y. Sato, T. Asano, and S. Noda, “Statistical studies of photonic heterostructure nanocavities with an average Q factor of three million,” Opt. Express 19(12), 11916–11921 (2011). [CrossRef]  

22. K. Maeno, Y. Takahashi, T. Nakamura, T. Asano, and S. Noda, “Analysis of high-Q photonic crystal L3 nanocavities designed by visualization of the leaky components,” Opt. Express 25(1), 367–376 (2017). [CrossRef]  

23. T. Asano, Y. Ochi, Y. Takahashi, K. Kishimoto, and S. Noda, “Photonic crystal nanocavity with a Q factor exceeding eleven million,” Opt. Express 25(3), 1769–1777 (2017). [CrossRef]  

24. M. Nakadai, K. Tanaka, T. Asano, Y. Takahashi, and S. Noda, “Statistical evaluation of Q factors of fabricated photonic crystal nanocavities designed by using a deep neural network,” Appl. Phys. Express 13(1), 012002 (2020). [CrossRef]  

25. Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013). [CrossRef]  

26. D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “A sub-microwatt threshold Raman silicon laser using a high-Q nanocavity,” Proceedings of Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) (2015), paper 28J2_3.

27. D. Yamashita, Y. Takahashi, J. Kurihara, T. Asano, and S. Noda, “Lasing dynamics of optically-pumped ultralow-threshold Raman silicon nanocavity lasers,” Phys. Rev. Appl. 10(2), 024039 (2018). [CrossRef]  

28. D. Yamashita, T. Asano, S. Noda, and Y. Takahashi, “Strongly asymmetric wavelength dependence of optical gain in nanocavity-based Raman silicon lasers,” Optica 5(10), 1256–1263 (2018). [CrossRef]  

29. M. Kuwabara, S. Noda, and Y. Takahashi, “Ultrahigh-Q photonic nanocavity devices on a dual thickness SOI substrate operating at both 1.31- and 1.55-µm telecommunication wavelength bands,” Laser Photonics Rev. 13(2), 1800258 (2019). [CrossRef]  

30. H. C. Nguyen, N. Yazawa, S. Hashimoto, S. Otsuka, and T. Baba, “Sub-100 µm photonic crystal Si optical modulators: spectral, athermal, and high-speed performance,” IEEE J. Sel. Top. Quantum Electron. 19(6), 127–137 (2013). [CrossRef]  

31. Y. Ooka, T. Tetsumoto, N. A. B. Daud, and T. Tanabe, “Ultrasmall in-plane photonic crystal demultiplexers fabricated with photolithography,” Opt. Express 25(2), 1521–1528 (2017). [CrossRef]  

32. K. Ashida, M Okano, M. Ohtsuka, M Seki, N. Yokoyama, K Koshino, M Mori, K Koshino, T Asano, S. Noda, T Asano, and Y. Takahashi, “Ultrahigh-Q photonic crystal nanocavities fabricated by CMOS process technologies,” Opt. Express 25(15), 18165–18174 (2017). [CrossRef]  

33. G. Takeuchi, Y. Terada, M. Takeuchi, H. Abe, H. Ito, and T. Baba, “Thermally controlled Si photonic crystal slow light waveguide beam steering device,” Opt. Express 26(9), 11529–11537 (2018). [CrossRef]  

34. K. Ashida, M. Okano, M. Ohtsuka, M. Seki, N. Yokoyama, K. Koshino, K. Yamada, and Y. Takahashi, “Photonic crystal nanocavities with an average Q factor of 1.9 million fabricated on a 300-mm-wide SOI wafer using a CMOS-compatible process,” J. Lightwave Technol. 36(20), 4774–4782 (2018). [CrossRef]  

35. D. Yamashita, Y. Takahashi, T. Asano, and S. Noda, “Raman shift and strain effect in high-Q photonic crystal silicon nanocavity,” Opt. Express 23(4), 3951–3959 (2015). [CrossRef]  

36. Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “High-Q resonant modes in a photonic crystal heterostructure nanocavity and applicability to a Raman silicon laser,” Phys. Rev. B 88(23), 235313 (2013). [CrossRef]  

37. B.S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). [CrossRef]  

38. J. Kurihara, D. Yamashita, N. Tanaka, T. Asano, S. Noda, and Y. Takahashi, “Detrimental fluctuation of frequency spacing between the two high-quality resonant modes in a Raman silicon nanocavity laser,” IEEE J. Sel. Top. Quantum Electron. 26(2), 1–12 (2020). [CrossRef]  

39. Y. Yamauchi, M. Okano, H. Shishido, S. Noda, and Y. Takahashi, “Implementing a Raman silicon nanocavity laser for integrated optical circuits by using a (100) SOI wafer with a 45-degree-rotated top silicon layer,” OSA Continuum 2(7), 2098–2112 (2019). [CrossRef]  

40. H. Sekoguchi, Y. Takahashi, T. Asano, and S. Noda, “Photonic crystal nanocavity with a Q-factor of ∼9 million,” Opt. Express 22(1), 916–924 (2014). [CrossRef]  

41. A. Sagara, A. Uedono, and S. Shibata, “Thermal behavior of residual defects in low-dose arsenic- and boron-implanted silicon after high-temperature rapid thermal annealing,” IEEE Trans. Semicond. Manufact. 28(1), 92–95 (2015). [CrossRef]  

42. Y. Sato, S. Shibata, A. Uedono, K. Urabe, and K. Eriguchi, “Characterization of the distribution of defects introduced by plasma exposure in Si substrate,” J. Vac. Sci. Technol., A 37(1), 011304 (2019). [CrossRef]  

43. H. Hagino, Y. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Effects of fluctuation in air hole radii and positions on optical characteristics in photonic crystal heterostructure nanocavities,” Phys. Rev. B 79(8), 085112 (2009). [CrossRef]  

44. The repeated thermal process was not necessary in the previous studies [34,39]. We consider that improvements of the fabrication process to increase the Q_exp of both cavity modes without the thermal process should be possible.

45. T. Asano, B.-S. Song, and S. Noda, “Analysis of the experimental Q factors (∼1 million) of photonic crystal nanocavities,” Opt. Express 14(5), 1996–2002 (2006). [CrossRef]  

46. T. Liang and H. Tsang, “Nonlinear absorption and Raman scattering in silicon-on-insulator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 10(5), 1149–1153 (2004). [CrossRef]  

47. H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85(12), 2196–2198 (2004). [CrossRef]  

48. T. Nakamura, Y. Takahashi, T. Asano, and S. Noda, “Improvement in the quality factors for photonic crystal nanocavities via visualization of the leaky components,” Opt. Express 24(9), 9541–9549 (2016). [CrossRef]  

49. T. Asano and S. Noda, “Optimization of photonic crystal nanocavities based on deep learning,” Opt. Express 26(25), 32704–32716 (2018). [CrossRef]  

50. T. Kawakatsu, T. Asano, S. Noda, and Y. Takahashi, “Experimental evaluation of Raman silicon nanocavity laser designed by machine learning ,” in Spring Meeting Japan Society of Applied Physics, Abstract (The Japan Society of Applied Physics, 2020), 14a-B415-1.

51. T. Terasawa, N. Hasegawa, H. Fukuda, and S. Katagiri, “Imaging characteristics of multi-phase-shifting and halftone phase-shifting masks,” Jpn. J. Appl. Phys. 30(Part 1, No. 11B), 2991–2997 (1991). [CrossRef]  

52. M. Yoshida, M. D. Zoysa, K. Ishizaki, Y. Tanaka, M. Kawasaki, R. Hatsuda, B Song, J. Gelleta, and S. Noda, “Double-lattice photonic-crystal resonators enabling high-brightness semiconductor lasers with symmetric narrow-divergence beams,” Nat. Mater. 18(2), 121–128 (2019). [CrossRef]  

53. K. Kitamura, M. Kitazawa, and S. Noda, “Generation of optical vortex beam by surface-processed photonic-crystal surface-emitting lasers,” Opt. Express 27(2), 1045–1050 (2019). [CrossRef]  

54. Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Topological photonic crystal nanocavity laser,” Commun. Phys. 1(1), 86 (2018). [CrossRef]  

55. A. K. Pradhan and M. Sen, ““An integrable all-silicon slotted photonic crystal Raman laser” J,” Appl. Phys. 126(23), 233103 (2019). [CrossRef]  

56. R. Shiozaki, T. Ito, and Y. Takahashi, “Utilizing broadband light from a superluminescent diode for excitation of photonic crystal highQ nanocavities,” J. Lightwave Technol. 37(10), 2458–2466 (2019). [CrossRef]