## Abstract

We propose highly nonlinear slot waveguides with flat and low dispersion over a wide wavelength range. Si nano-crystal and chalcogenide glass are considered as slot materials. Over a 244-nm bandwidth, dispersion of 0±0.16 ps/(nm∙m) is achieved in a silicon nano-crystal slot waveguide, with a nonlinear coefficient of 2874 /(W∙m). The As_{2}S_{3} slot waveguide exhibits dispersion of 0±0.17 ps/(nm∙m) over a bandwidth of 249 nm, with a nonlinear coefficient 16 times larger than that of As_{2}S_{3} rib waveguides and a nonlinear figure of merit three times larger than that of Si strip waveguides.

©2010 Optical Society of America

## 1. Introduction

Integrated highly nonlinear waveguides and photonic nano-wires can form the backbone of on-chip optical signal processing [1–3], especially for high bit-rate signals [4]. Such waveguides can be composed of silicon [1–3, 5–8], silicon nitride [9, 10], Si nano-crystals (Si-nc or Si-rich Si dioxide) [11, 12], III-V compound semiconductors [13, 14], and chalcogenide glasses [4, 15, 16]. Flat and low chromatic dispersion over a wide wavelength range is crucial for enhancing nonlinear interactions of optical waves. Recently, there has been much interest in tailoring dispersion in the waveguides [17–21]. A tight confinement of light with high index contrast may introduce strong and fast-changing waveguide dispersion, making it difficult to obtain a wideband and flat dispersion profile. A slotted waveguide structure [22] could provide extra design freedom to tailor the waveguide dispersion [23–27], while keeping a large fraction of the guided mode in a thin slot layer. However, there has been little reported on the wideband low dispersion in these waveguides.

We propose highly nonlinear slot waveguides for achieving a flat and near-zero dispersion profile. Two types of nonlinear materials are considered: (i) chalcogenide glass (As_{2}S_{3}), which reduces the overall two-photon-absorption (TPA) coefficient and (ii) Si-nc, which greatly increases the nonlinear Kerr coefficient compared to silicon strip waveguides. The As_{2}S_{3} slot waveguide exhibits a flat dispersion of 0±0.17 ps/(nm∙m) over a bandwidth of 249 nm, with a nonlinear coefficient of 160 /(W∙m) and a significantly improved nonlinear figure of merit (FOM). The silicon-nc slot waveguide features a flat dispersion of 0±0.16 ps/(nm∙m) over a bandwidth of 244 nm, with a high nonlinear coefficient of 2874 /(W∙m) at 1550 nm. The proposed waveguides are compared to previously published results in Table 1
, in terms of dispersion and nonlinearity properties. Accumulated dispersion in the waveguides is low, since, for most on-chip applications, the waveguides are typically a few centimeters in length.

## 2. Waveguide structure and numerical model

As shown in Fig. 1(a)
, a horizontal slot is surrounded by two silicon layers with air cladding, and waveguide substrate is 2-µm buried oxide. For the quasi-TM mode (vertically polarized), due to the discontinuity of its electric field at the interfaces of the slot and the silicon layers, a large fraction of the guided mode is confined in the slot layer [22]. The effective index of quasi-TM mode as a function of wavelength is obtained by using a finite-element mode solver (COMSOL Multiphysics 3.4), with an element size of 5, 40, and 100 nm for slot, silicon and other regions, respectively. Material dispersion is taken into account for the slot (As_{2}S_{3} [28] and Si nano-crystal [25]), silicon [29] and silica substrate. Group velocity dispersion, D = -(c/λ)∙(d^{2}n/dλ^{2}), is calculated, where n is the effective index of refraction, and c and λ are the speed of light and wavelength in vacuum, respectively.

We note that the Kerr nonlinear index of refraction n_{2} and TPA coefficient β_{TPA}, corresponding to the real and imaginary parts of nonlinear coefficient γ respectively, vary with wavelength [30, 31]. For silicon, the measurement results given in Refs. 30 and 31 are fitted using six-order polynomials and averaged to take the dispersion of nonlinearity into account, when we calculate γ as a function of wavelength. For As_{2}S_{3}, different n_{2} and β_{TPA} values have been reported [32–36] at individual wavelengths, and the measured n_{2} is 2.5**×**10^{−18} [32], (averaged) 3**×**10^{−18} [33,34], 2.93**×**10^{−18} [35], and 3.05**×**10^{−18} m^{2}/W [36] at 1.064, 1.31, 1.54 and 1.57 μm, respectively, which is roughly unchanged. We thus choose constant n_{2} =3**×**10^{−18} m^{2}/W and β_{TPA} = 6.2**×**10^{−15} m/W for our simulations at all wavelengths. For Si nano-crystal with 8% silicon excess, annealed at 800 °C, we choose n_{2} = 4.8**×**10^{−17} m^{2}/W and β_{TPA} = 7**×**10^{−11} m/W at 1550 nm [11]. For silica, n_{2} = 2.6**×**10^{−20} m^{2}/W is used, and β_{TPA} is neglected. Nonlinear coefficient γ is computed with a space step of 1 nm using a full-vector model [37], in which the contributions of different materials to nonlinearity are weighted by optical mode distribution, and the longitudinal electric field of the mode is also considered. We use a FOM defined as γ's real part divided by γ's imaginary part times 4π, i.e., γ_{re}/4πγ_{im}. In a scalar model with a single nonlinear material, γ_{re} = 2πn_{2}/λA_{eff} and γ_{im} = β_{TPA}/2A_{eff}, where A_{eff} is effective mode area. The FOM that we use here is equivalent to the widely used FOM n_{2}/λβ_{TPA} [38].

## 3. Dispersion and nonlinearity in chalcogenide and Si nano-crystal slot waveguides

For As_{2}S_{3} slot waveguides, we set *W* = 280 nm, *H _{u}* =

*H*= 180 nm, and

_{l}*H*= 115 nm. Figure 1(b), shows a flat dispersion profile within 0±0.017 ps/nm obtained from 1460 to 1709 nm wavelength (bandwidth of 249 nm) for a 10-cm-long waveguide on chip. There are two zero dispersion wavelengths (ZDWs), located at 1500 and 1677 nm, respectively. The maximum dispersion of 0.1695 ps/(nm∙m) occurs at 1595-nm wavelength. The flat and low dispersion is obtained by employing slot structures. As shown in Ref. 27, the effective index of a slot waveguide can change rapidly with wavelength, and this makes the effective index of the slot mode closer to that of a substrate mode at long wavelengths (e.g., around 2100 nm in this case), causing mode coupling and negative dispersion [27]. Thus, the total dispersion curve is bent and becomes small and flat at the wavelength of interest near 1550 nm.

_{s}Varying slot height can significantly increase the dispersion, and Fig. 1(b) shows an increase in the value of the dispersion peak from 0.0971 to 0.3301 ps/(nm∙m) as the slot height decreases from 120 to 105 nm. Accordingly, dispersion peak blue-shifts from 1600 to 1580 nm. Dispersion can also be tailored by changing the waveguide width, as shown in Fig. 2(a)
. Widening the waveguide produces a dispersion curve that is shifted to longer wavelength. The right ZDW red-shifts by 111 nm, from 1677 to 1788 nm as the waveguide width is changed from 280 to 310 nm, while the left ZDW blue-shifts by only 32 nm. Changing the slot height and waveguide width together enables tailoring the center wavelength and ZDWs while keeping flat and low dispersion. For example, one can start with the structure parameters given above and then increase both the waveguide width and the slot height. These modifications produce a red-shift of dispersion curves while maintaining the low peak value of dispersion. Figure 2(b) shows the tailored dispersion as the upper Si height *H _{u}* is reduced from 190 to 160 nm. It is noted that the right ZDW has a shift towards long wavelength by 65 nm, larger than the left ZDW. Moreover, the peak dispersion value is relatively tolerant to the change of

*H*, and the dispersion flatness is improved by increasing

_{u}*H*.

_{u}We examine the nonlinear coefficient γ and FOM as a function of wavelength with varied slot height in Fig. 3(a)
. For a slot height *H _{s}* = 115 nm, γ decreases from 178.3 to 135.6 /(W∙m) as wavelength increases from 1400 to 1800 nm. A similar trend is found for other slot heights. In contrast, the FOM increases with wavelength from 0.87 to 1.52 for

*H*= 115 nm. This is explained as follows. First, the dispersion of nonlinearity in silicon is considered. From 1400 to 1800 nm, silicon's material FOM defined as n

_{s}_{2}/λβ

_{TPA}increases from 0.252 to 0.739. Second, we assume that n

_{2}and β

_{TPA}in As

_{2}S

_{3}do not change with wavelength, so As

_{2}S

_{3}material FOM decreases with wavelength. Third, the material index and mode distribution change with wavelength, and contributions of different materials to FOM depend on wavelength. With

*H*of around 120 nm and a smaller index contrast between Si and As

_{s}_{2}S

_{3}(compared to Si and Si-nc), the field enhancement in the As

_{2}S

_{3}slot is less than that shown in Fig. 5 insets for an 120-nm Si-nc slot, and thus contribution of silicon layers to FOM is more than that of the As

_{2}S

_{3}slot. This is why the overall FOM increases with wavelength. The third factor has limited effect. For a larger slot height, more power is confined in the As

_{2}S

_{3}slot, and the FOM value becomes higher. There are similar changes in γ and FOM versus wavelength in Fig. 3(b), with the waveguide width changed, but the FOM is insensitive to the width change.

For silicon nano-crystal slot waveguides, we choose *W* = 500 nm, *H _{u}* =

*H*= 180 nm, and

_{l}*H*= 47 nm. Figure 4(a) shows a flat dispersion profile within 0±0.16 ps/(nm∙m) obtained over a 244-nm wavelength range, from 1539 to 1783 nm. There are two ZDWs at 1580 and 1751 nm, respectively. The peak dispersion of 0.156 ps/(nm∙m) is found at 1670 nm. Figure 4(a) shows that the dispersion peak value is decreased from 0.2101 to 0.0508 ps/(nm∙m) as slot height

_{s}*H*varies from 46 to 49 nm, at a rate of 0.053 ps/(nm∙m) per nm. We note that, as compared to As

_{s}_{2}S

_{3}slot waveguides, the Si nano-crystal slot waveguides have a larger index contrast between the slot and silicon layers and a smaller slot height, and this causes stronger field enhancement in the slot. The overall dispersion is dominated by waveguide dispersion, which results in the high sensitivity of dispersion to the slot height. We examine the dispersion change caused by increasing the lower silicon height

*H*, as shown in Fig. 4(b). The thicker the lower silicon layer, the flatter the dispersion profile near its peak value. The dispersion curve is red-shifted for a larger

_{l}*H*. The right ZDW shifts by 106 nm, from 1696 to 1802 nm as

_{l}*H*is changed from 170 to 190 nm. Generally, similar trends of dispersion tailoring are found for the As

_{l}_{2}S

_{3}and Si nano-crystal slot waveguides as a structural parameter is changed, so we do not show dispersion profiles with varied

*W*and

*H*repeatedly. However, for a smaller slot height, dispersion is more sensitive to a change in the slot height. As an example, Fig. 5 shows dispersion profiles modified by a 10-nm change of

_{u}*H*in a 10-cm-long Si nano-crystal slot waveguide when

_{s}*H*= 40, 80 and 120 nm, (

_{s}*W*= 500 nm,

*H*=

_{u}*H*= 180 nm), and accordingly dispersion value is changed by 0.698, 0.339, and 0.195 ps/(nm∙m) at 1650-nm wavelength. A small

_{l}*H*induces strong field enhancement shown in Fig. 5 insets, and light is tightly confined in a small area, which causes an increased dispersion sensitivity to the slot height.

_{s}Calculated nonlinear coefficient γ and FOM with the slot height *H _{s}* of 47 nm are 2874 /(W∙m) and 0.447, respectively, at 1550-nm wavelength. A small change in the slot height

*H*, from 46 to 49 nm, does not change γ and FOM much. Due to the strong field enhancement in the slot, FOM is dominated by the material properties of the Si-nc slot. This is confirmed by noting that silicon's material FOM is 0.352 at 1550-nm wavelength, but the Si-nc’s material FOM n

_{s}_{2}/λβ

_{TPA}is 0.4424, which is close to the computed FOM. Due to the lack of measurements on the dispersion of nonlinearity in Si-nc, γ is not calculated as a function of wavelength.

## 4. Discussion and conclusion

Chalcogenide glasses are good photonic platforms for on-chip nonlinear signal processing [15, 39]. Typically, the nonlinear coefficient γ of As_{2}S_{3} rib waveguides is found to be ~10 /(W∙m) [39, 40], which is much lower than that of silicon waveguides [1, 3, 20]. This is partially because the As_{2}S_{3} waveguides have a smaller index contrast and larger mode area, compared to silicon waveguides. However, the relatively small refractive index in As_{2}S_{3} allows the formation of a chalcogenide slot waveguide, greatly enhancing light confinement and increasing γ from ~10 to 160 /(W∙m). Moreover, a benefit of introducing the As_{2}S_{3} slot is that it increases the waveguide FOM from ~0.35 (for Si) to 1.15 at 1.55 μm, which approaches saturation of nonlinear performance [15]. By properly combining different materials, one can have a slot waveguide with a designable (instead of geometry independent) FOM. Though the Si nano-crystal slot waveguides have relatively small FOMs, the high nonlinear coefficient γ allows a great reduction of pump power for nonlinear optical signal processing on a chip. Nonlinear length L_{NL} = 1/γP may still be comparable to dispersion length for high-speed signals [4], which requires the optimization of the dispersion properties of the waveguides.

We have proposed highly nonlinear slot waveguides with flat and low dispersion for on-chip nonlinear signal processing. Flat dispersion within 0±0.16 ps/(nm∙m) is obtained over a 244-nm wavelength range for Si nano-crystal slot waveguides, and nonlinear coefficient is 2874 /(m∙W) at 1550 nm. We have shown that As_{2}S_{3} slot waveguides can produce a dispersion profile within 0±0.17 ps/(nm∙m) over a 249-nm bandwidth, with greatly increased nonlinear coefficient as compared with previously reported chalcogenide rib waveguides.

## Acknowledgments

The authors would thank Prof. Jurgen Michel, Prof. Lorenzo Pavesi, Dr. Rita Spano, Dr. Shahraam Afshar V. and Dr. Qiang Lin for helpful discussions. This work is sponsored by DARPA (under contract number HR0011-09-C-0124) and HP Laboratories.

## References and links

**1. **C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express **15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

**2. **Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express **15**(25), 16604–16644 (2007). [CrossRef] [PubMed]

**3. **R. M. Osgood Jr, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. Green, and Y. A. Vlasov, “Engineering nonlinearities in nanoscale optical systems: physics and applications in dispersion-engineered silicon nanophotonic wires,” Adv. Opt. Photon. **1**, 162–235 (2009). [CrossRef]

**4. **M. Galili, J. Xu, H. C. Mulvad, L. K. Oxenløwe, A. T. Clausen, P. Jeppesen, B. Luther-Davis, S. Madden, A. Rode, D.-Y. Choi, M. Pelusi, F. Luan, and B. J. Eggleton, “Breakthrough switching speed with an all-optical chalcogenide glass chip: 640 Gbit/s demultiplexing,” Opt. Express **17**(4), 2182–2187 (2009). [CrossRef] [PubMed]

**5. **O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express **12**(21), 5269–5273 (2004). [CrossRef] [PubMed]

**6. **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] [PubMed]

**7. **M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature **441**(7096), 960–963 (2006). [CrossRef] [PubMed]

**8. **Q. Lin, J. D. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express **14**(11), 4786–4799 (2006). [CrossRef] [PubMed]

**9. **K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/ silicon dioxide waveguides,” Opt. Express **16**(17), 12987–12994 (2008). [CrossRef] [PubMed]

**10. **J. S. Levy, A. Gondarenko, A. C. Turner-Foster, M. A. Foster, A. L. Gaeta, and M. Lipson, “Four-wave mixing in integrated silicon nitride waveguides,” in *Conference on Lasers and Electro-Optics*, (OSA, 2009), CMFF5.

**11. **R. Spano, N. Daldosso, M. Cazzanelli, L. Ferraioli, L. Tartara, J. Yu, V. Degiorgio, E. Giordana, J. M. Fedeli, and L. Pavesi, “Bound electronic and free carrier nonlinearities in Silicon nanocrystals at 1550nm,” Opt. Express **17**(5), 3941–3950 (2009). [CrossRef] [PubMed]

**12. **Z. Yuan, A. Anopchenko, N. Daldosso, R. Guider, D. Navarro-Urrios, A. Pitanti, R. Spano, and L. Pavesi, “Silicon Nanocrystals as an Enabling Material for Silicon Photonics,” Proc. IEEE **97**(7), 1250–1268 (2009). [CrossRef]

**13. **J. J. Wynne, “Optical third-order mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. **178**(3), 1295–1303 (1969). [CrossRef]

**14. **H. Q. Le and S. D. Cecca, “Ultrafast, room-temperature, resonance-enhanced third-order optical susceptibility tensor of an AlGaAs/GaAs quantum well,” Opt. Lett. **16**(12), 901–903 (1991). [CrossRef] [PubMed]

**15. **V. Ta’eed, N. J. Baker, L. Fu, K. Finsterbusch, M. R. E. Lamont, D. J. Moss, H. C. Nguyen, B. J. Eggleton, D.-Y. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express **15**(15), 9205–9221 (2007). [CrossRef] [PubMed]

**16. **J. Hu, V. Tarasov, N. Carlie, N.-N. Feng, L. Petit, A. Agarwal, K. Richardson, and L. Kimerling, “Si-CMOS-compatible lift-off fabrication of low-loss planar chalcogenide waveguides,” Opt. Express **15**(19), 11798–11807 (2007). [CrossRef] [PubMed]

**17. **L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. **31**(9), 1295–1297 (2006). [CrossRef] [PubMed]

**18. **E. Dulkeith, F. N. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express **14**(9), 3853–3863 (2006). [CrossRef] [PubMed]

**19. **A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express **14**(10), 4357–4362 (2006). [CrossRef] [PubMed]

**20. **X. Liu, W. M. J. Green, X. Chen, I.-W. Hsieh, J. I. Dadap, Y. A. Vlasov, and R. M. Osgood Jr., “Conformal dielectric overlayers for engineering dispersion and effective nonlinearity of silicon nanophotonic wires,” Opt. Lett. **33**(24), 2889–2891 (2008). [CrossRef] [PubMed]

**21. **M. R. Lamont, C. M. de Sterke, and B. J. Eggleton, “Dispersion engineering of highly nonlinear As(_{2)}S(_{3}) waveguides for parametric gain and wavelength conversion,” Opt. Express **15**(15), 9458–9463 (2007). [CrossRef] [PubMed]

**22. **V. R. Almeida, Q. F. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. **29**(11), 1209–1211 (2004). [CrossRef] [PubMed]

**23. **J. Jágerská, N. Le Thomas, R. Houdré, J. Bolten, C. Moormann, T. Wahlbrink, J. Ctyroký, M. Waldow, and M. Först, “Dispersion properties of silicon nanophotonic waveguides investigated with Fourier optics,” Opt. Lett. **32**(18), 2723–2725 (2007). [CrossRef] [PubMed]

**24. **A. Di Falco, L. O'Faolain, and T. F. Krauss, “Dispersion control and slow light in slotted photonic crystal waveguides,” Appl. Phys. Lett. **92**(8), 083501 (2008). [CrossRef]

**25. **R. Spano, J. V. Galan, P. Sanchis, A. Martinez, J. Martí, and L. Pavesi, “Group velocity dispersion in horizontal slot waveguides filled by Si nanocrystals,” International Conf. on Group IV Photonics, pp. 314–316, 2008.

**26. **Z. Zheng, M. Iqbal, and J. Liu, “Dispersion characteristics of SOI-based slot optical waveguides,” Opt. Commun. **281**(20), 5151–5155 (2008). [CrossRef]

**27. **L. Zhang, Y. Yue, Y. Xiao-Li, R. G. Beausoleil, and A. E. Willner, “Highly dispersive slot waveguides,” Opt. Express **17**(9), 7095–7101 (2009). [CrossRef] [PubMed]

**28. **W. S. Rodney, I. H. Malitson, and T. A. King, “Refractive index of arsenic trisulfide,” J. Opt. Soc. Am. **48**(9), 633–636 (1958). [CrossRef]

**29. **E. D. Palik, Handbook of Optical Constants of Solids. San Diego, CA: Academic, 1998.

**30. **A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. **90**(19), 191104 (2007). [CrossRef]

**31. **Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near-infrared region,” Appl. Phys. Lett. **91**(2), 021111 (2007). [CrossRef]

**32. **F. Smektala, C. Quemard, L. Leneindre, J. Lucas, A. Barthelemy, and C. De Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non-Cryst. Solids **239**(1-3), 139–142 (1998). [CrossRef]

**33. **M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photon. Technol. Lett. **4**(4), 362–365 (1992). [CrossRef]

**34. **K. S. Bindra, H. T. Bookey, A. K. Kar, B. S. Wherrett, X. Liu, and A. Jha, “Nonlinear optical properties of chalcogenide glasses: observation of multiphoton absorption,” Appl. Phys. Lett. **79**(13), 1939–1941 (2001). [CrossRef]

**35. **Y. Ruan, B. Luther-Davies, W. Li, A. Rode, V. Kolev, and S. Madden, “Large phase shifts in As_{2}S_{3} waveguides for all-optical processing devices,” Opt. Lett. **30**(19), 2605–2607 (2005). [CrossRef] [PubMed]

**36. **Y. Ruan, W. Li, R. Jarvis, N. Madsen, A. Rode, and B. Luther-Davies, “Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching,” Opt. Express **12**(21), 5140–5145 (2004). [CrossRef] [PubMed]

**37. **S. Afshar V and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express **17**(4), 2298–2318 (2009). [CrossRef] [PubMed]

**38. **V. Mizrahi, K. W. Delong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. **14**(20), 1140–1142 (1989). [CrossRef] [PubMed]

**39. **M. D. Pelusi, V. Ta'eed, L. Fu, E. Maqi, M. R. E. Lamont, S. Madden, D.-Y. Choi, D. A. P. Bulla, B. Luther-Davies, and B. J. Eggleton, “Applications of highly-nonlinear chalcogenide glass devices tailored for high-speed all-optical signal processing,” IEEE J. Sel. Top. Quantum Electron. **14**(3), 529–539 (2008). [CrossRef]

**40. **M. R. E. Lamont, B. Luther-Davies, D. Y. Choi, S. Madden, and B. J. Eggleton, “Supercontinuum generation in dispersion engineered highly nonlinear (γ = 10 /W/m) As_{2}S_{3}) chalcogenide planar waveguide,” Opt. Express **16**(19), 14938–14944 (2008). [CrossRef] [PubMed]