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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 19 — Sep. 13, 2010
  • pp: 20529–20534
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Flattened dispersion in silicon slot waveguides

Lin Zhang, Yang Yue, Raymond G. Beausoleil, and Alan E. Willner  »View Author Affiliations


Optics Express, Vol. 18, Issue 19, pp. 20529-20534 (2010)
http://dx.doi.org/10.1364/OE.18.020529


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Abstract

We propose a silicon strip/slot hybrid waveguide that produces flattened dispersion of 0 ± 16 ps/(nm∙km), over a 553-nm wavelength range, which is 20 times flatter than previous results. Different from previously reported slot waveguides, the strip/slot hybrid waveguide employs the mode transition from a strip mode to a slot mode to introduce unique waveguide dispersion. The flat dispersion profile is featured by three zero-dispersion wavelengths, which is obtained for the first time in on-chip silicon waveguides, to the best of our knowledge. The waveguide exhibits flattened dispersion from 1562-nm to 2115-nm wavelength, which is potentially useful for both telecom and mid-infrared applications.

© 2010 OSA

1. Introduction

Low-chromatic-dispersion light-guiding can be very important for a variety of applications, including: (a) phase matching of data signals for maximizing nonlinear interactions in signal processing [1

1. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002). [CrossRef]

], (b) low distortion of analog signals for accurate beam steering [2

2. M. Jarrahi, R. F. W. Pease, and T. H. Lee, “Spatial quantized analog-to-digital conversion based on optical beam-steering,” J. Lightwave Technol. 26(14), 2219–2226 (2008). [CrossRef]

], and (c) transmission of high-bandwidth data signals [3

3. H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010). [CrossRef]

]. A key challenge for optical fibers and integrated waveguides is to realize a very flat and low dispersion over a wide wavelength range. Flattened near-zero dispersion has been achieved in optical fibers [4

4. T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion flattened fibers for efficient optical signal processing applications,” Electron. Lett. 39(13), 972–974 (2003). [CrossRef]

6

6. W.-Q. Zhang, S. Afshar V, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17(21), 19311–19327 (2009). [CrossRef]

]. Although one may argue that the on-chip silicon waveguides are typically so short that the chromatic dispersion does not have a significant effect on picosecond pulse evolution, it does matter in many other important applications such as femtosecond pulse propagation [7

7. L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007). [CrossRef] [PubMed]

,8

8. I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, and R. M. Osgood, “Supercontinuum generation in silicon photonic wires,” Opt. Express 15(23), 15242–15249 (2007). [CrossRef] [PubMed]

], ultra wideband wavelength conversion [9

9. 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]

,10

10. A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010). [CrossRef] [PubMed]

] and frequency comb generation [11

11. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010). [CrossRef]

]. Moreover, an optimized dispersion profile in silicon waveguides could be beneficial to reduce phase mismatching and release the requirement for high pump power in nonlinear processes, which has potential to mitigate two-photon absorption (TPA) and achieve ‘green’ signal processing.

However, for silicon waveguides or nanophotonic wires, dispersion flattening has been a difficult task due to the tight light confinement and strong waveguide dispersion in the highly nonlinear integrated waveguides. Silicon strip and rib waveguides would have to have a quite large transverse size to produce one zero-dispersion wavelength (ZDW) in a wavelength range of interest, typically around 1550 nm [12

12. 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]

,13

13. J. I. Dadap, N. C. Panoiu, X. Chen, I.-W. Hsieh, X. Liu, C.-Y. Chou, E. Dulkeith, S. J. McNab, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood Jr., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008). [CrossRef] [PubMed]

]. If the waveguide size is shrunk to generate a smaller mode area, the ZDW is blue-shifted to even 1200 nm wavelength, where TPA is significantly higher, limiting the efficiency of nonlinear interactions. In addition, strong waveguide dispersion makes overall dispersion highly wavelength-dependent and degrades dispersion flatness (defined as max/min dispersion variation divided by bandwidth, in unit of ps/(nm2∙km)). In Table 1

Table 1. Dispersion and nonlinearity comparison between the published and proposed waveguides

table-icon
View This Table
, we list some simulation results on recent progresses to release the trade-off between tight mode confinement and flat dispersion bandwidth [14

14. 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]

17

17. L. Zhang, Y. Yue, Y. Xiao-Li, J. Wang, R. G. Beausoleil, and A. E. Willner, “Flat and low dispersion in highly nonlinear slot waveguides,” Opt. Express 18(12), 13187–13193 (2010). [CrossRef] [PubMed]

]. Improved flatness of dispersion curves is obtained by adding a conformal silicon nitride overlayer [16

16. 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]

] or a slot structure [17

17. L. Zhang, Y. Yue, Y. Xiao-Li, J. Wang, R. G. Beausoleil, and A. E. Willner, “Flat and low dispersion in highly nonlinear slot waveguides,” Opt. Express 18(12), 13187–13193 (2010). [CrossRef] [PubMed]

]. A laudable goal would be to continue the progress for low dispersion waveguides that can be operated over wide wavelength ranges, potentially enabling high nonlinear efficiency, low power requirements, a broad operation bandwidth and controllable propagation of femtosecond optical pulses.

2. Principle and modeling of dispersion flattening

A dielectric slot waveguide typically consists of at least two parts of high-index materials that are closely placed with a layer of low-index material between them. The electric field of light polarized normal to the interfaces of the high-index and low-index materials is enhanced in the low-index layer due to index discontinuity [18

18. 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]

]. Figure 1(a)
Fig. 1 (a) Previously reported silicon slot waveguide that exhibits convex dispersion profile. (b) A strip waveguide is added to produce additional negative waveguide dispersion. (c) The strip/slot waveguide coupler is flipped to improve sequent fabrication procedure. (d) A strip/slot hybrid waveguide with spacing layer removed for achieving flattened dispersion.
shows a horizontally slotted waveguide, in which upper and lower silicon layers have high refractive index and a low-index slot is made of Si nano-crystals (Si-nc, i.e., silicon-rich silicon dioxide) [19

19. 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]

,20

20. 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.

]. Cladding is air, and substrate is 2-μm-thick silicon dioxide.

We choose the following structural parameters: upper silicon height Hu = 265 nm, slot height Hs = 50 nm, lower silicon height Hl = 510 nm, and waveguide width W = 500 nm. The silica substrate is 2-μm-thick. A quasi-TM mode (vertically polarized) forms a slot mode [18

18. 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]

]. The slot material is silicon nano-crystal with silicon excess of 8%, annealed at 800 °C. It exhibits relatively high nonlinearity compared to samples with higher silicon excess [19

19. 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]

]. Material dispersions in Si-nc [20

20. 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.

], silicon [24

24. E. D. Palik, Handbook of Optical Constants of Solids, (San Diego, CA: Academic, 1998).

], and silica are taken into account. Over a wavelength range from 1200 to 2400 nm, material refractive index of Si-nc is between 1.72 and 1.725. Figure 2(a)
Fig. 2 (a) Material dispersion for silicon and Si-nc, calculated using Sellmeier equations [20,24]. (b) Calculated dispersion value converges as element size is reduced.
shows the material dispersions for Si-nc and silicon. We obtain the effective index of the guided mode using full-vector finite-element-method software (COMSOL), with an element size of 5, 40, and 100 nm for slot, silicon and other regions, respectively. The overall dispersion is calculated by taking the 2nd-order derivative of the effective index with respect to wavelength, i.e., D = -(c/λ)∙(d2neff/dλ2). As an example of convergence of the calculated dispersion, we show the dispersion values obtained at 1550 nm using increasingly reduced element size from 30 to 3 nm in the slot layer in Fig. 2(b). It is noted that an element size of 5 nm is good enough to produce accurate dispersion values.

3. Flattened dispersion profiles

We now examine the dependence of the dispersion properties on the slot height, Hs, with Hu = 265 nm, Hl = 510 nm, and W = 500 nm. Figure 4(a)
Fig. 4 In silicon strip/slot hybrid waveguides, dispersion profiles are tailored by changing (a) slot height and (b) waveguide width, respectively.
shows that, as Hs increases from 44 to 56 nm, the dispersion curve rotates, with a nearly zero dispersion value at around 1866 nm. In this way, one can modify the third order dispersion (i.e., dispersion slope), without changing the average dispersion much. Another important parameter is the waveguide width. With Hu = 265 nm, Hs = 50 nm, and Hl = 510 nm, we calculate the dispersion curves for different widths ranging from 420 to 540 nm. As seen in Fig. 4(b), the dispersion at a long wavelength is more sensitive to the width and becomes more negative, with the local minimum value shifting from a wavelength of 1902 nm to 2025 nm as the width decreases. Dispersion flatness is thus destroyed. This is because the decreased width causes a reduced effective index of the guided mode and makes it more likely to be coupled with the substrate mode, and such a mode transition also results in negative dispersion at longer wavelengths.

The influence of the lower silicon height, Hl, on the dispersion is also examined, with Hs = 50 nm, Hu = 265 nm, and W = 500 nm, as shown in Fig. 5(a)
Fig. 5 In silicon strip/slot hybrid waveguides, dispersion profiles are tailored by changing (a) lower silicon height and (b) upper silicon height, respectively.
. The dispersion profile is almost entirely moved up without a dramatic change in its shape and slope, as the lower silicon height Hl is increased from 490 to 530 nm. At 1850-nm wavelength, the dispersion value increases from –104 to 80 ps/(nm∙km), with a rate of 45 ps/(nm∙km) per 10 nm. As mentioned above, the dispersion is flattened by the mode transition. When the lower silicon height is decreased, the effective index of the strip mode drops with wavelength more rapidly, which causes a sharper mode transition from the strip mode to the slot mode and over-balanced dispersion, and moves the whole dispersion curve down. The averaged dispersion value can be changed more effectively by modifying the upper silicon height Hu. When keeping Hs = 50 nm, Hl = 510 nm, and W = 500 nm, we change Hu from 235 to 295 nm. As shown in Fig. 5(b), the dispersion curve is moved down, and the dispersion value at 1850-nm wavelength is reduced from 162 to −153 ps/(nm∙km), with a rate of 52 ps/(nm∙km) per 10 nm. In this case, the dispersion slope is slightly changed.

Although the goal of this paper is to show a flattened near-zero dispersion profile, we would emphasize that this just serves as an example of dispersion tailorability enabled by the mode transition in the proposed strip/slot hybrid waveguide. For a specific application, a perfectly flat dispersion may not be most desirable, since many other important parameters such as the nonlinear coefficient and loss are not as flat as the dispersion over wavelength. We find that an appropriate combination of the slot height and lower silicon height provides a very effective way to tailor the dispersion profile, which is critically important for manipulating ultrafast pulse dynamics and nonlinear signal processing in silicon photonics. More sophisticated dispersion tailoring (e.g., designing 4th- and 5th-order dispersion terms) may be needed for a specific application, in which case advanced optimization algorithm such as generic algorithm [5

5. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13(10), 3728–3736 (2005). [CrossRef] [PubMed]

,6

6. W.-Q. Zhang, S. Afshar V, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17(21), 19311–19327 (2009). [CrossRef]

] could be used.

4. Discussion

To calculate the nonlinear coefficient, we choose a nonlinear Kerr index n2 = 4.8 × 10−17 m2/W and TPA coefficient βTPA = 7 × 10−11 m/W for Si-nc with 8% silicon excess, annealed at 800 °C [19

19. 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]

], along with n2 = 4.06 × 10−18 m2/W and βTPA = 7.45 × 10−12 m/W for silicon at 1550 nm [25

25. 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]

,26

26. 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]

]. To obtain the parameters in silicon, we fit the measurement results in Refs. 25 and 26 using six-order polynomials and average them. The value of n2 is close to the commonly used one [27

27. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

]. Using a full-vector model [28

28. 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]

], the nonlinear coefficient γ in high-index-contrast waveguides is computed with contribution of both transverse and longitudinal field components. We obtain γ = 134 + j28 /(W∙m) at 1550-nm wavelength, and the imaginary part of γ characterizes the TPA property of the waveguide.

The mode transition to a quasi-slot mode at long wavelengths helps lift the guided mode up, which is beneficial to reduce the loss by substrate leakage. The proposed waveguide is multi-mode, and the higher-order mode has greatly different dispersion profiles, which requires a careful mode excitement. A single-mode nano-taper [29

29. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [CrossRef] [PubMed]

] may be helpful in doing beam coupling and mode screening simultaneously. The dispersion is highly polarization dependent, and the quasi-TE mode has a strong anomalous dispersion >1000 ps/(nm∙km) when the wavelength is beyond 1500 nm.

5. Conclusion

We have proposed the use of slot structures to achieve flat and near-zero chromatic dispersion in silicon waveguides. Flattened dispersion of 0 ± 16 ps/(nm∙km) was obtained over a 553-nm wavelength range, with three ZDWs. The dispersion profile was found to be highly tailorable in terms of the average dispersion value and dispersion slope.

Acknowledgments

The authors would thank Prof. Lorenzo Pavesi, Dr. Rita Spano, and Dr. Qiang Lin for helpful discussions. This work is supported by Defense Advanced Research Projects Agency (DARPA) (HR0011-09-C-0124) and the HP Labs.

References and links

1.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002). [CrossRef]

2.

M. Jarrahi, R. F. W. Pease, and T. H. Lee, “Spatial quantized analog-to-digital conversion based on optical beam-steering,” J. Lightwave Technol. 26(14), 2219–2226 (2008). [CrossRef]

3.

H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010). [CrossRef]

4.

T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion flattened fibers for efficient optical signal processing applications,” Electron. Lett. 39(13), 972–974 (2003). [CrossRef]

5.

F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13(10), 3728–3736 (2005). [CrossRef] [PubMed]

6.

W.-Q. Zhang, S. Afshar V, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17(21), 19311–19327 (2009). [CrossRef]

7.

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007). [CrossRef] [PubMed]

8.

I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, and R. M. Osgood, “Supercontinuum generation in silicon photonic wires,” Opt. Express 15(23), 15242–15249 (2007). [CrossRef] [PubMed]

9.

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]

10.

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010). [CrossRef] [PubMed]

11.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010). [CrossRef]

12.

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]

13.

J. I. Dadap, N. C. Panoiu, X. Chen, I.-W. Hsieh, X. Liu, C.-Y. Chou, E. Dulkeith, S. J. McNab, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood Jr., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008). [CrossRef] [PubMed]

14.

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]

15.

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]

16.

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]

17.

L. Zhang, Y. Yue, Y. Xiao-Li, J. Wang, R. G. Beausoleil, and A. E. Willner, “Flat and low dispersion in highly nonlinear slot waveguides,” Opt. Express 18(12), 13187–13193 (2010). [CrossRef] [PubMed]

18.

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]

19.

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]

20.

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.

21.

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]

22.

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

23.

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]

24.

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

25.

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]

26.

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]

27.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

28.

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]

29.

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [CrossRef] [PubMed]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(130.4310) Integrated optics : Nonlinear
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(260.2030) Physical optics : Dispersion
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(130.3990) Integrated optics : Micro-optical devices

ToC Category:
Integrated Optics

History
Original Manuscript: August 2, 2010
Revised Manuscript: August 26, 2010
Manuscript Accepted: August 29, 2010
Published: September 10, 2010

Citation
Lin Zhang, Yang Yue, Raymond G. Beausoleil, and Alan E. Willner, "Flattened dispersion in silicon slot waveguides," Opt. Express 18, 20529-20534 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-20529


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References

  1. J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8(3), 506–520 (2002). [CrossRef]
  2. M. Jarrahi, R. F. W. Pease, and T. H. Lee, “Spatial quantized analog-to-digital conversion based on optical beam-steering,” J. Lightwave Technol. 26(14), 2219–2226 (2008). [CrossRef]
  3. H. C. H. Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010). [CrossRef]
  4. T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion flattened fibers for efficient optical signal processing applications,” Electron. Lett. 39(13), 972–974 (2003). [CrossRef]
  5. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13(10), 3728–3736 (2005). [CrossRef] [PubMed]
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