A range of unique capabilities in optical and microwave signal processing and generation have been demonstrated using stimulated Brillouin scattering (SBS). The need to harness SBS in mass-manufacturable integrated circuits has led to a focus on silicon-based material platforms. Remarkable progress in silicon-based Brillouin waveguides has been made, but results have been hindered by nonlinear losses present at telecommunications wavelengths. Here, we report on a new approach to surpass this issue through the integration of a high Brillouin gain material, , onto a silicon-based chip. We fabricated a compact spiral device within a silicon circuit, achieving an order-of-magnitude improvement in Brillouin amplification. To establish the flexibility of this approach, we fabricated a ring resonator with free spectral range precisely matched to the Brillouin shift, enabling the first demonstration, to our knowledge, of Brillouin lasing in a planar integrated circuit. Combining active photonic components with the SBS devices shown here will enable the creation of compact, mass-manufacturable optical circuits with enhanced functionalities.
© 2017 Optical Society of America
Stimulated Brillouin Scattering (SBS) has recently emerged as a flexible tool for optical processing and radiofrequency (RF) photonics . SBS is one of the strongest nonlinearities known to optics, hundreds of times larger than Raman scattering in SMF-28 fiber , and is capable of providing exponential gain over narrow bandwidths of the order of tens of megahertz. This narrowband amplitude response is accompanied by a strong dispersive response, capable of tailoring the phase or group delay of a counterpropagating optical signal. In light of these effects, a rich body of applications have been explored such as slow light , stored light , narrowband RF photonic filters [5–7], dynamic optical gratings [8,9], narrowband spectrometers , optical amplifiers [11,12] and RF sources  among others. When pumped in a resonator configuration, a narrow linewidth, spectrally pure SBS laser can be generated [14–16]. Highly coherent lasers are used in optical communication and LIDAR, and in the production of pure microwave sources  among other applications. While the majority of previous works have traditionally utilized SBS in optical fiber, a number of these applications have been demonstrated in integrated form factors [1,18–21]. Most recently, the demonstration of 52 dB Brillouin gain  in centimeter-scale rib waveguides proves that performance equivalent to kilometers of optical fiber is achievable in integrated devices.
The capability to embed SBS as a functional component in active photonic circuits will enable the creation of a new class of optoelectronic devices, in particular for integrated microwave photonics . The desire to harness SBS optical processing in CMOS-compatible platforms has recently culminated in demonstrations of SBS in various silicon on insulator (SOI) device architectures [24–27]. Underetching of different waveguide geometries is performed to create guided acoustic modes, generating strong SBS from the high optoacoustic overlap. Initial works have demonstrated large Brillouin gain coefficients [24–26] in excess of , times higher than single-mode optical fiber, made possible due to boundary forces which exist in these subwavelength structures . More recent work has focused on reducing propagation losses to improve amplification factors to more than 5 dB . But in general, higher gains in SOI devices have been prevented due to nonlinear losses in silicon [29,30] and linewidth broadening due to small-dimension fluctuations introduced during device fabrication .
In this work, we introduce a hybrid integration approach to generate large Brillouin gain in a silicon-based device, free from nonlinear losses. We embed a compact 5.8 cm spiral waveguide into a silicon circuit, enabling record Brillouin gain of 22.5 dB (18.5 dB net gain) on a silicon-based chip. Traditional silicon grating couplers are used for coupling in and out of the chip, with silicon tapers providing low-loss transitions between the Si and sections of the circuit. To further explore the flexibility of this approach, we fabricate precisely designed ring resonators, enabling the first demonstration, to our knowledge, of Brillouin lasing in a planar integrated circuit. This work marks a significant step towards the realization of fully integrated active SBS devices, such as integrated optoelectronic oscillators , lossless microwave photonic filters , and compact optical gyroscopes , in the near future.
2. SILICON-INTERFACED SPIRAL WAVEGUIDE
Figure 1(a) shows the schematic of the fabricated hybrid circuit. The circuit consists of a base silicon section and an SBS active section. Silicon grating couplers are used for chip coupling , followed by a 2 mm long silicon waveguide. The nanowire waveguide ( cross section) then linearly tapers, over a length of 100 μm, to a width of 150 nm and ends in a open silicon region of . Amorphous was deposited in the open region with a thickness of 680 nm, completely covering the silicon tapers. Overlay waveguides were processed over the silicon taper before proceeding to the rest of the circuit; a scanning electron microscopy (SEM) of the end of the taper region, before cladding deposition, is shown in Fig. 1(b). Optical propagation simulations, discussed in Supplement 1, indicate a total insertion loss on the order of 0.1 dB for transmission into the fundamental mode of the waveguide. Silica cladding of 1 μm thickness was sputtered over the sample after etching, with care taken to keep processing temperatures suitable for optimum losses . A schematic of a typical waveguide geometry is shown in Fig. 1(c), along with a cross-sectional SEM [Fig. 1(d)] and optical mode simulation of the fundamental mode of a 1.9 μm wide waveguide [Fig. 1(f)]. Further details of the fabrication process are provided in Supplement 1. The region of the circuit is confined to within a small region of , requiring significant design optimization to achieve high performance.
To maximize the physical waveguide length in the available device area (), we employ a folded spiral design with a rectangular shape and identical bends for each loop. As we will explain in further detail, the device geometry was chosen to give the highest Brillouin amplification in this confined area. The expected gain of a weak probe, , for a coupled pump power, , in the small signal gain regime of backwards SBS is given by37], which have a quartic reduction with waveguide width (i.e., ). Larger widths lead to the waveguide becoming heavily multimoded, and effective index values for the first ten guided modes are calculated for increasing widths in Fig. 1(e). Adiabatic bends based on the Euler spiral , in a matched bend configuration , are used in the design to minimize mode conversion, preventing extra loss throughout the structure.
To explore these tradeoffs more quantitatively, propagation losses for a number of waveguide widths were measured, and simulations calculating were performed for corresponding geometries. The effective lengths assuming a 6 cm long device and the peak gains are shown in Fig. 2(a). The resulting is plotted in Fig. 2(b); while widths greater than 2 μm provide further improvement, the required bend radii prevents use in the compact spiral. From this comparison, we determined an optimum waveguide width of 1.9 μm, with effective bend radii of 16.5 μm calculated through FDTD simulations; further data is provided in Supplement 1. A total device length of 5.8 cm consisted of eight loops (36 bends including external connections), with a very compact structure achieved through a small waveguide spacing of 1.4 μm. We measured a total propagation loss of 4 dB through the spiral when correcting for the coupling losses from the grating couplers and transitions. An estimated propagation loss of 0.7 dB/cm resulted in an of 3.9 cm for the nonlinear interaction. The overall form factor of this spiral represents orders-of-magnitude reduction compared to that of previous waveguides used for SBS . The typical half-etch rib geometries with multi-micrometer widths, used for the low losses , require bend radii of more than 100 μm and are incapable of high density due to the significant crosstalk introduced from the partial waveguide etch. Similarly, underetched devices require an appropriate spacing between adjacent waveguides to prevent acoustic interactions and maintain structural support; width was used for a single underetched membrane structure .
3. BACKWARDS SBS IN SPIRAL WAVEGUIDE
To experimentally investigate the behavior of different devices, we performed two sets of pump-probe SBS measurements, a coarse measurement using an optical spectrum analyzer (OSA), and a high-resolution setup with an electrical vector network analyzer (VNA). In the OSA measurement, a high-resolution OSA (0.8 pm) was used to measure the transmission of a weak probe while an amplified pump laser was counterpropagated through the sample. A schematic of the setup is provided in Supplement 1. This measurement allowed for a rough estimate of the Brillouin frequency shift in the device and enabled simultaneous monitoring of the gain and loss response. An on–off gain of was observed at 80 mW coupled power, as shown in Fig. 3(a). A Brillouin shift of was measured relative to the residual back-reflected pump (centered at 1551.18 nm), and symmetric gain and loss spectra were measured.
To measure the SBS response in further detail, we implemented a high-resolution () pump-probe experiment through the use of a radiofrequency VNA . A laser of frequency was split into two arms to create the pump and the probe wave. The pump was upshifted in frequency by from the carrier through the use of a Mach–Zehnder intensity modulator and optical bandpass filter. The pump was then amplified with a high-power erbium-doped fiber amplifier, passed through ports of an optical circulator, and was coupled with TE polarization silicon-grating couplers into the hybrid circuit. In the probe arm, the laser underwent single-sideband with carrier modulation to produce a weak probe upshifted by frequency . The carrier and probe were both coupled to the device and passed through the hybrid circuit. After coupling at the output, the transmitted waves were routed from ports of an optical circulator, and then a bandpass filter was used to remove any residual back-reflected pump. The remaining optical waves beat on a high-speed photodetector, and the change in RF power at frequency was measured by the VNA. In the frequency region of the Brillouin shift from the pump , the modulated sideband will experience Brillouin amplification, as shown in Fig. 3(c). Further details of the measurement process can be found in Supplement 1. We measured the frequency spectrum for increasing pump powers up to 180 mW coupled power, as shown in Fig. 3(d). Net amplification was achieved above 25 mW on-chip power, overcoming the 4 dB of propagation losses, with a maximum on–off gain of 22.5 dB and a net gain of 18.5 dB. This represents a improvement of net gain compared to recent demonstrations for forward  and intermodal SBS  in suspended silicon membrane waveguides. Fitting the slope of the measured peak gain data from Fig. 3(d) results in a Brillouin gain coefficient of , a 50% increase over previous chalcogenide waveguides . This increase is primarily due to the reduction of compared to the previous partially etched rib structures.
Here, we compare the effects of pump attenuation through nonlinear losses in the devices in this work with simulated silicon geometries [Fig. 3(e)]. Nonlinear losses are a key limiting factor in integrated silicon waveguide devices at telecommunications wavelengths [42,43]. For silicon-based Brillouin systems, the effect is two-fold: a direct reduction in pump power from two-photon absorption and free-carrier absorption, leading to a power-dependent for the pump and also the direct attenuation of the probe wave through cross-photon absorption and free carriers, which are generated by the pump. We experimentally measured the transmission through a 2 mm reference hybrid waveguide, maximizing the optical power through the silicon leads of 3 mm on either side of the hybrid structure. This is a worst-case scenario, with negligible linear losses in the hybrid region and 6 mm of silicon waveguide contributing to nonlinear losses. Even so, only 0.5 dB was measured at high coupled powers of 150 mW. This is in stark contrast to pure silicon structures, with close to 4 dB of pump attenuation expected for a simulated silicon membrane and almost 6 dB for a nanowire geometry, effectively saturating the input pump power and preventing any further gain . Careful theoretical analysis [29,30] has indicated that reducing linear losses and increasing device lengths may enable higher Brillouin amplification at low pump powers, but this can be hampered by dimensional broadening as explored in the following paragraph.
We explore dimensional broadening in waveguides by measuring the SBS response of a number of different waveguide widths and lengths, including straight and spiral structures. Dimensional broadening has been identified as a key issue which reduces the expected gain, particularly in nanoscale waveguides reliant on transverse acoustic waves such as forward SBS structures [26,31]. The effect manifests in changing Brillouin lineshapes; as device lengths are modified, measured mechanical quality factors are reduced by almost half when moving from millimeter to centimeter scales in suspended membrane structures . In this work, we found that the natural linewidth did not vary with device length, and only minor fluctuations were measured for lengths of 1, 2, 4, and 40 mm; results are provided in Supplement 1. This indicates that, for these geometries, the linewidth is primarily governed by the deposited material properties of , allowing for scaling to large device lengths.
The significant increase in available gain and negligible effects of nonlinear losses will enable a number of new applications beyond the limited Brillouin signal processing currently demonstrated in silicon , including Brillouin lasing, as explored in the next section.
4. COMPACT RING RESONATOR
Brillouin lasers are capable of spectrally narrowing laser sources and, if cascaded, can produce pure microwave frequencies. Achieving Brillouin lasing in microresonators is challenging due to the requirement for the cavity free spectral range (FSR) to closely match the Brillouin shift. Initial demonstrations used highly overmoded resonators, such that two resonances between different mode families were aligned [44,45]. More recently, precise matching of the cavity FSR and the SBS shift was achieved in lithographically processed silica wedge resonators . These previous devices have extremely low losses, enabling low-threshold oscillation, but require external coupling via tapered optical fibers or free-space optics. To show a further application of the combined and Si platform, we fabricate high- ring resonators designed for Brillouin lasing and achieve the first demonstration, to our knowledge, of Brillouin lasing in a planar integrated circuit.
A schematic of the ring design is shown in Fig. 4(a). To achieve low-threshold lasing in the sample, we must satisfy three competing challenges: the FSR must match the Brillouin shift, the loss throughout the cavity must be minimal, and the whole structure must be as compact as possible. The SBS shift scales () with effective index of the optical mode and acoustic velocity of the acoustic mode , such that . The FSR of a resonator depends upon the total roundtrip time of the cavity, and is related to the length and group index such that . Thus, we need to take into account the change of and with waveguide width when determining the appropriate length of the resonator, as represented in Fig. 4(b). The threshold for a Brillouin laser in a resonator with an FSR matching the Brillouin shift is given by 48], were used to transition from the heavily multimoded waveguides with widths of 2.6 μm down to few-mode structures with widths of 850 nm. These narrow waveguides were used in the directional coupler to provide coupling to the ring with as short a length as possible. A nested spiral design, again with Euler bends, was used to minimize the footprint of the resonator, and enabled the required roundtrip length () to fit within the required area. Further details on individual component design, including microscope images of the fabricated sample, are provided in Supplement 1.
Optical transmission measurements were performed on the fabricated device with the same high-resolution OSA used in the pump-probe measurements [Fig. 4(c)]. From these measurements, we observed a FSR of 7.62 GHz at 1553 nm and an extinction ratio of around 0.65 dB or, equivalently, a transmission of 85%, which corresponded to . The measured resonance linewidth was 4.5 pm, corresponding to a of . The measured factor was limited by the propagation losses in the 2.6 μm waveguide, estimated as 0.5 dB/cm, and losses due to the ring coupler on the order of 0.2 dB. This value compares favorably to previous demonstrations of planar centimeter length scale ring resonators with in on lithium niobate  and for directly written waveguides . From Eq. (2), we determine an expected threshold of 80 mW for the fabricated sample, assuming optimum matching of the SBS shift to the cavity FSR.
5. BRILLOUIN LASING
To demonstrate Brillouin lasing in the fabricated resonator, we seamlessly tuned a pump onto the resonance for a range of power levels, while monitoring the back-reflected optical waves [Fig. 4(d)]. The pump light source was an external cavity laser capable of fine-resolution tuning with a continuous step size of 10 MHz, allowing for accurate alignment to the center of the resonance. The pump was amplified before being passed through a circulator (ports ) and coupled to the chip through silicon grating couplers. Back-scattered light from SBS and the back-reflected pump wave then passed through the circulator (ports ), and was monitored on a high-resolution OSA while the RF beat was measured on an electrical spectrum analyzer (ESA). A weak reference output of the OSA was also used as a probe to measure the transmission of the resonator when desired.
For coupled powers above 50 mW, Brillouin lasing was observed on the OSA and ESA. Figure 4(e) shows a Brillouin lasing signal on the OSA, along with a reference signal at the same power level with the pump shifted just past the resonance. A single lasing signal is observed at a power level in the range of . A strong signal close to 0 dBm, at the pump wavelength, was also measured due to the back-reflection of pump from the chip grating couplers. A number of cavity side modes from the back-reflected pump were also observed; these were around 50 dB below the pump signal, in line with the pump laser specifications. To confirm that the measured signal was not due to spontaneous scattering, we measured the electrical beatnote above threshold on the ESA [Fig. 4(f)]. The measured beatnote was significantly narrower than the SBS natural linewidth of 40 MHz , plotted with a dashed line in Fig. 4(f). The frequency of the beatnote was at , and slow drifts on the order of 5 MHz were observable on the ESA over minute time scales. The lack of active locking of the pump to the resonator prevented the measurement of a slope efficiency of the Brillouin laser above the threshold level. For the weak coupling case in which we have (), a low slope efficiency of 4% is expected . Improving the coupling to the ring would drastically improve this and also reduce the lasing threshold. Finally, to confirm that the Brillouin lasing is indeed occurring on the resonances of the ring, we performed an OSA measurement while sweeping a weak probe signal to measure the resonator transmission. In this case, the coupled pump power was 75 mW. Figure 4(g) shows that the lasing signal and pump are both aligned to cavity resonances.
To provide further details on how the hybrid circuit results compared with previous demonstrations of SBS in integrated waveguides, we prepared a comparison summary in Table 1. Initial silicon devices focused on achieving the highest gain coefficients possible using highly sub-wavelength structures which harnessed radiation pressure [24–26]. Issues arising from high scattering losses, dimensional broadening, and nonlinear losses resulted in low net gain values of below 1 dB. More recent work has shifted to larger device geometries, resulting in interactions produced almost entirely through electrostriction. High sensitivity to local wafer conditions prevented the membrane structure from being folded, resulting in reduced compactness with straight waveguides up to 3 cm long. However, the reduced propagation losses enabled significantly higher net gain, up to 5 dB , than previous silicon demonstrations. In comparison it is clear that, being free from nonlinear losses, the devices are capable of significantly higher on–off gain (greater than 50 dB) compared to full silicon devices. In this work, we address the compactness limitations of previous demonstrations through the high-density and tight bends of fully etched structures while maintaining large net gain. Finally, to understand the relative efficiency of different devices, we introduce a simple figure of merit (FOM), , which is from the exponential term in Eq. (1). To achieve 20 dB of gain, which is sufficient for many microwave photonics applications , with 50 mW coupled pump power requires an FOM . None of the currently demonstrated devices have approached this regime, which is equivalent to half a km of SMF optical fiber, but further improvements to the and are expected to accomplish this goal in the near future.
One of the most desirable characteristics of Brillouin lasers is a significant linewidth narrowing of lasing Stokes lines. The key requirement for entering this regime is for the optical damping to be less than the acoustic damping or, in terms of linewidths, the cavity linewidth to be narrower than the natural linewidth of the acoustic mode . If this regime is achieved, then the Stokes spectrum will narrow and the full width at half maximum will be given by51], and experimental measurements of polymer-clad fibers saw an increase of the natural linewidth . These approaches would allow for spectral purifiers and pure microwave sources based on SBS to be implemented in fully integrated planar devices.
In this work, we have introduced a hybrid integration approach to generating large Brillouin gain in a silicon-based device. We embedded a compact 5.8 cm spiral waveguide into a silicon circuit, enabling a record Brillouin gain of 22.5 dB (18.5 dB net gain) on a silicon-based chip. Fabrication of a compact ring resonator enabled the first demonstration of Brillouin lasing, to our knowledge, in a planar integrated circuit. Combining active photonic devices, such as modulators and detectors, with the work shown here will enable the creation of compact, high-performance devices with capabilities beyond traditional RF systems.
Australian Research Council (ARC) (CE110001010, DP1096838, FL120100029).
This work has been made possible through access to the ACT and Victorian nodes of the Australian National Fabrication Facility (ANFF).
See Supplement 1 for supporting content.
1. R. Pant, D. Marpaung, I. V. Kabakova, B. Morrison, C. G. Poulton, and B. J. Eggleton, “On-chip stimulated Brillouin scattering for microwave signal processing and generation,” Laser Photon. Rev. 8, 653–666 (2014). [CrossRef]
2. G. Agrawal, “Stimulated Raman scattering,” in Nonlinear Fiber Optics (Elsevier, 2013), pp. 295–352.
3. L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2, 474–481 (2008). [CrossRef]
4. Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748–1750 (2007). [CrossRef]
5. B. Vidal, M. A. Piqueras, and J. Martí, “Tunable and reconfigurable photonic microwave filter based on stimulated Brillouin scattering,” Opt. Lett. 32, 23–25 (2007). [CrossRef]
6. D. Marpaung, B. Morrison, R. Pant, and B. J. Eggleton, “Frequency agile microwave photonic notch filter with anomalously high stopband rejection,” Opt. Lett. 38, 4300–4303 (2013). [CrossRef]
7. W. Zhang and R. Minasian, “Ultrawide tunable microwave photonic notch filter based on stimulated Brillouin scattering,” IEEE Photon. Technol. Lett. 24, 1182–1184 (2012). [CrossRef]
8. K. Y. Song, W. Zou, Z. He, and K. Hotate, “All-optical dynamic grating generation based on Brillouin scattering in polarization-maintaining fiber,” Opt. Lett. 33, 926–928 (2008). [CrossRef]
9. M. Santagiustina, S. Chin, N. Primerov, L. Ursini, and L. Thévenaz, “All-optical signal processing using dynamic Brillouin gratings,” Sci. Rep. 3, 1594 (2013). [CrossRef]
10. J. Domingo, J. Pelayo, F. Villuendas, C. Heras, and E. Pellejer, “Very high resolution optical spectrometry by stimulated Brillouin scattering,” IEEE Photon. Technol. Lett. 17, 855–857 (2005). [CrossRef]
11. K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Hansch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336, 441–444 (2012). [CrossRef]
12. S. M. F. Raupach, A. Koczwara, and G. Grosche, “Brillouin amplification supports 1×10−20 uncertainty in optical frequency transfer over 1400 km of underground fiber,” Phys. Rev. A 92, 021801 (2015). [CrossRef]
13. X. S. Yao, “High-quality microwave signal generation by use of Brillouin scattering in optical fibers,” Opt. Lett. 22, 1329–1331 (1997). [CrossRef]
14. A. Debut, S. Randoux, and J. Zemmouri, “Linewidth narrowing in Brillouin lasers: theoretical analysis,” Phys. Rev. A 62, 1–4 (2000). [CrossRef]
15. S. P. Smith, F. Zarinetchi, and S. Ezekiel, “Narrow-linewidth stimulated Brillouin fiber laser and applications,” Opt. Lett. 16, 393–395 (1991). [CrossRef]
16. J. Geng, S. Staines, Z. Wang, J. Zong, M. Blake, and S. Jiang, “Highly stable low-noise Brillouin fiber laser with ultranarrow spectral linewidth,” IEEE Photon. Technol. Lett. 18, 1813–1815 (2006). [CrossRef]
17. M. C. Gross, P. T. Callahan, T. R. Clark, D. Novak, R. B. Waterhouse, and M. L. Dennis, “Tunable millimeter-wave frequency synthesis up to 100 GHz by dual-wavelength Brillouin fiber laser,” Opt. Express 18, 13321–13330 (2010). [CrossRef]
18. J. Li, H. Lee, T. Chen, and K. J. Vahala, “Characterization of a high coherence, Brillouin microcavity laser on silicon,” Opt. Express 20, 20170–20180 (2012). [CrossRef]
19. J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013). [CrossRef]
20. R. Pant, A. Byrnes, C. G. Poulton, E. Li, D.-Y. Choi, S. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering,” Opt. Lett. 37, 969–971 (2012). [CrossRef]
21. A. Casas-Bedoya, B. Morrison, M. Pagani, D. Marpaung, and B. J. Eggleton, “Tunable narrowband microwave photonic filter created by stimulated Brillouin scattering from a silicon nanowire,” Opt. Lett. 40, 4154–4157 (2015). [CrossRef]
22. A. Choudhary, B. Morrison, I. Aryanfar, S. Shahnia, M. Pagani, Y. Liu, K. Vu, S. Madden, D. Marpaung, and B. J. Eggleton, “Advanced integrated microwave signal processing with giant on-chip Brillouin gain,” J. Lightwave Technol. 35, 846–854 (2017). [CrossRef]
23. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photon. Rev. 7, 506–538 (2013). [CrossRef]
24. H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat. Commun. 4, 1944 (2013). [CrossRef]
25. R. Van Laer, B. Kuyken, D. Van Thourhout, and R. Baets, “Interaction between light and highly confined hypersound in a silicon photonic nanowire,” Nat. Photonics 9, 199–203 (2015). [CrossRef]
26. R. V. Laer, A. Bazin, B. Kuyken, R. Baets, and D. V. Thourhout, “Net on-chip Brillouin gain based on suspended silicon nanowires,” New J. Phys. 17, 115005 (2015). [CrossRef]
27. E. A. Kittlaus, H. Shin, and P. T. Rakich, “Large Brillouin amplification in silicon,” Nat. Photonics 10, 463–467 (2016). [CrossRef]
28. P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated Brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012). [CrossRef]
29. C. Wolff, P. Gutsche, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Impact of nonlinear loss on stimulated Brillouin scattering,” J. Opt. Soc. Am. B 32, 1968–1978 (2015). [CrossRef]
30. C. Wolff, P. Gutsche, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Power limits and a figure of merit for stimulated Brillouin scattering in the presence of third and fifth order loss,” Opt. Express 23, 26628–26638 (2015). [CrossRef]
31. C. Wolff, R. V. Laer, M. J. Steel, B. J. Eggleton, and C. G. Poulton, “Brillouin resonance broadening due to structural variations in nanoscale waveguides,” New J. Phys. 18, 025006 (2016). [CrossRef]
32. M. Merklein, B. Stiller, I. V. Kabakova, U. S. Mutugala, K. Vu, S. J. Madden, B. J. Eggleton, and R. Slavík, “Widely tunable, low phase noise microwave source based on a photonic chip,” Opt. Lett. 41, 4633–4636 (2016). [CrossRef]
33. Y. Liu, D. Marpaung, A. Choudhary, and B. J. Eggleton, “Lossless and high-resolution RF photonic notch filter,” Opt. Lett. 41, 5306–5309 (2016). [CrossRef]
34. J. Li, M.-G. Suh, and K. Vahala, “Microresonator Brillouin gyroscope,” Optica 4, 346–348 (2017). [CrossRef]
35. D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006). [CrossRef]
36. D. Y. Choi, A. Wade, S. Madden, R. Wang, D. Bulla, and B. Luther-Davies, “Photo-induced and thermal annealing of chalcogenide films for waveguide fabrication,” Phys. Procedia 48, 196–205 (2013). [CrossRef]
37. C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 1306–1321 (2006). [CrossRef]
38. M. Cherchi, S. Ylinen, M. Harjanne, M. Kapulainen, and T. Aalto, “Dramatic size reduction of waveguide bends on a micron-scale silicon photonic platform,” Opt. Express 21, 17814–17823 (2013). [CrossRef]
39. A. Melloni, P. Monguzzi, R. Costa, and M. Martinelli, “Design of curved waveguides: the matched bend,” J. Opt. Soc. Am. A 20, 130–137 (2003). [CrossRef]
40. A. Loayssa, R. Hernández, D. Benito, and S. Galech, “Characterization of stimulated Brillouin scattering spectra by use of optical single-sideband modulation,” Opt. Lett. 29, 638–640 (2004). [CrossRef]
41. E. Kittlaus, N. T. Otterstrom, and P. T. Rakich, “Inter-modal Brillouin scattering in an integrated waveguide,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2017), paper STu3N.3.
42. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010). [CrossRef]
43. R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12, 2774–2780 (2004). [CrossRef]
44. I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102, 043902 (2009). [CrossRef]
45. M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) Rates,” Phys. Rev. Lett. 102, 113601 (2009). [CrossRef]
46. H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012). [CrossRef]
47. T. Kippenberg, S. Spillane, B. Min, and K. Vahala, “Theoretical and experimental study of stimulated and cascaded Raman scattering in ultrahigh-Q optical microcavities,” IEEE J. Sel. Top. Quantum Electron. 10, 1219–1228 (2004). [CrossRef]
48. Y. Fu, T. Ye, W. Tang, and T. Chu, “Efficient adiabatic silicon-on-insulator waveguide taper,” Photon. Res. 2, A41–A44 (2014). [CrossRef]
49. Y. Zhou, X. Xia, W. T. Snider, J. Kim, Q. Chen, W. C. Tan, and C. K. Madsen, “Two-stage taper enhanced ultra-high Q As2S3 ring resonator on LiNbO3,” IEEE Photon. Technol. Lett. 23, 1195–1197 (2011). [CrossRef]
50. S. Levy, M. Klebanov, and A. Zadok, “High-Q ring resonators directly written in As2S3 chalcogenide glass films,” Photon. Res. 3, 63–67 (2015). [CrossRef]
51. C. G. Poulton, R. Pant, and B. J. Eggleton, “Acoustic confinement and stimulated Brillouin scattering in integrated optical waveguides,” J. Opt. Soc. Am. B 30, 2657–2659 (2013). [CrossRef]
52. J.-C. Beugnot, R. Ahmad, M. Rochette, V. Laude, H. Maillotte, and T. Sylvestre, “Reduction and control of stimulated Brillouin scattering in polymer-coated chalcogenide optical microwires,” Opt. Lett. 39, 482–485 (2014). [CrossRef]