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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 20 — Sep. 27, 2010
  • pp: 20839–20844
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Tailoring the dispersion behavior of silicon nanophotonic slot waveguides

Sara Mas, José Caraquitena, José V. Galán, Pablo Sanchis, and Javier Martí  »View Author Affiliations


Optics Express, Vol. 18, Issue 20, pp. 20839-20844 (2010)
http://dx.doi.org/10.1364/OE.18.020839


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Abstract

We investigate the chromatic dispersion properties of silicon channel slot waveguides in a broad spectral region centered at ~1.5 μm. The variation of the dispersion profile as a function of the slot fill factor, i.e., the ratio between the slot and waveguide widths, is analyzed. Symmetric as well as asymmetric geometries are considered. In general, two different dispersion regimes are identified. Furthermore, our analysis shows that the zero and/or the peak dispersion wavelengths can be tailored by a careful control of the geometrical waveguide parameters including the cross-sectional area, the slot fill factor, and the slot asymmetry degree.

© 2010 OSA

1. Introduction

In the last few years, silicon photonics has emerged as an attractive and promising technology in the field of integrated optoelectronics. The recent progress in nanofabrication techniques has enabled the development of basic photonic building blocks on a silicon-on-insulator platform including light sources, modulators, and photodetectors [1

1. M. Lipson, “Guiding, modulating, and emitting light on silicon – Challenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005). [CrossRef]

3

3. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006). [CrossRef]

]. The silicon photonics approach provides some advantages, including lower-cost and higher-integration, compared with more traditional solutions based on other materials, e. g., III-V semiconductor compounds or LiNbO3.

In general, any silicon-based photonic component is affected by chromatic dispersion. Then, the design and optimization of silicon photonic devices requires a very precise knowledge of the dispersion properties. In this context, the chromatic dispersion of a simple silicon waveguide with ~6 μm2 cross-sectional area was first measured by Tsang et at [4

4. H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002). [CrossRef]

]. In this dimension regime, the light confinement is weak and the dispersion profile is primarily determined by the intrinsic silicon dispersion. In contrast, when the cross-sectional area is reduced, the optical confinement is stronger and, then, the effective dispersion is the result of the interplay between the material and the waveguide or geometrical dispersion [5

5. 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]

7

7. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4357. [CrossRef] [PubMed]

]. In fact, a careful control of the waveguide shape and size allows for the tailoring of the group velocity dispersion (GVD) so that normal, anomalous, or even zero GVD can be achieved in the spectral region centered at ~1.5 μm [5

5. 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]

7

7. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4357. [CrossRef] [PubMed]

].

On the other hand, the so-called silicon nanophotonic slot waveguides have been proposed and fabricated for different applications [8

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

10

10. P. Sanchis, J. Blasco, A. Martínez, and J. Martí, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” J. Lightwave Technol. 25(5), 1298–1305 (2007). [CrossRef]

]. In these waveguide structures, the optical field is strongly confined in a very thin region of low refractive index material, which is sandwiched between two silicon layers. As a result, a high optical intensity is produced in a small area so that the nonlinear optical performance is highly enhanced [10

10. P. Sanchis, J. Blasco, A. Martínez, and J. Martí, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” J. Lightwave Technol. 25(5), 1298–1305 (2007). [CrossRef]

]. An early analysis of the dispersion properties of symmetric slot waveguides was reported by Zheng et al. [11

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

]. In [11

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

], numerical simulations demonstrate that the GVD of slot waveguides is, in general, significantly quite different compared with the dispersion of traditional channel waveguides. However, the analysis by Zheng et al. was limited to a small spectral range of only 0.15 μm centered at ~1.55 μm and the dispersion control capabilities were unexplored. Simulated results of GVD in a horizontal slot waveguide filled with silicon nanocrystals have also been reported [12

12. R. Spano, J. V. Galán, P. Sanchis, A. Martínez, J. Martí, and L. Pavesi, “Group velocity dispersion in horizontal slot waveguides filled by Si nanocrystals,” International Conf. Group IV Photon., 314–316 (2008).

]. In addition, more complex slotted waveguides have been proposed for dispersion compensation purposes [13

13. L. Zhang, Y. Yue, Y. Y. Xiao-Li, R. G. Beausoleil, and A. E. Willner, “Highly dispersive slot waveguides,” Opt. Express 17(9), 7095–7101 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7095. [CrossRef] [PubMed]

].

2. Dispersion in nanophotonic slot waveguides

2.1 Symmetric slot waveguides

The effect of the slot on the waveguide dispersion is different for each particular cross-sectional area. For a cross-sectional area equal to 1 μm2, Fig. 3(a), a change in the slot fill factor translates into a relatively small variation in the GVD curve. In fact, all the dispersion profiles lie in the so-called material dispersion regime. Note that for larger fill factors, the dispersion profile exhibits a zero-GVD wavelength and, as a result, a spectral region with anomalous dispersion is found. For intermediate cross-sectional areas, ~0.5 μm2, Fig. 3(b), we find that the slot dimension strongly determines the dispersion regime in which the waveguide operates. More particularly, for the fill factors 1:5 and 1:10 we have GVD profiles in the geometrical dispersion regime while the fill factors 1:25 and 1:50 present GVD curves quite similar to the silicon material dispersion profile. For small cross-sectional areas, 0.1 μm2, Fig. 3(c), we find that the slot waveguide mostly works in the geometrical dispersion regime. Note that the dispersion curve is significantly down shifted when the slot fill factor is increased while the wavelength with maximum-GVD is nearly constant at ~1.4 μm (dashed vertical line). Transversal dimensions h = 258 nm and w = 387 nm are considered in this latter case, according to the assumed aspect ratio.

2.2 Asymmetric slot waveguides

3. Conclusions

A detailed analysis of the dispersion properties of silicon-on-insulator vertical slot waveguides has been performed. Our study shows that, in general, the dispersion behavior of slot waveguides strongly depends on the slot dimension and location. Two different dispersion regimes have been qualitative distinguished by analyzing and comparing several waveguide examples with different cross-sectional areas and slot fill factors. Our results show that a careful control of the slot geometrical parameters, i.e., width and position, enables the tuning of the GVD characteristics, including the maximum and/or the zero-GVD wavelengths. Furthermore, constant dispersion in a broad wavelength range can be achieved by properly designing slot waveguides. Dispersion tailoring of slot waveguides may be interesting for controlling several relevant phenomena including ultrashort pulse propagation and nonlinear optical effects.

Acknowledgments

References and links

1.

M. Lipson, “Guiding, modulating, and emitting light on silicon – Challenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005). [CrossRef]

2.

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006). [CrossRef]

3.

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006). [CrossRef]

4.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002). [CrossRef]

5.

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]

6.

E. Dulkeith, F. Xia, L. Schares, W. M. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14(9), 3853–3863 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3853. [CrossRef] [PubMed]

7.

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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4357. [CrossRef] [PubMed]

8.

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

9.

Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]

10.

P. Sanchis, J. Blasco, A. Martínez, and J. Martí, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” J. Lightwave Technol. 25(5), 1298–1305 (2007). [CrossRef]

11.

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

12.

R. Spano, J. V. Galán, P. Sanchis, A. Martínez, J. Martí, and L. Pavesi, “Group velocity dispersion in horizontal slot waveguides filled by Si nanocrystals,” International Conf. Group IV Photon., 314–316 (2008).

13.

L. Zhang, Y. Yue, Y. Y. Xiao-Li, R. G. Beausoleil, and A. E. Willner, “Highly dispersive slot waveguides,” Opt. Express 17(9), 7095–7101 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7095. [CrossRef] [PubMed]

14.

P. A. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14(20), 9197–9202 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-20-9197. [CrossRef] [PubMed]

15.

C. Ma, Q. Zhang, and E. Van Keuren, “Analysis of symmetric and asymmetric nanoscale slab slot waveguides,” Opt. Commun. 282(2), 324–328 (2009). [CrossRef]

16.

K. Okamoto, “Beam propagation method,” in Fundamentals of Optical Waveguides (2000), Chap. 7, 273–281.

17.

B. Tatian, “Fitting refractive-index data with the Sellmeier dispersion formula,” Appl. Opt. 23(24), 4477–4485 (1984). [CrossRef] [PubMed]

18.

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-2-1300. [CrossRef] [PubMed]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides
(260.2030) Physical optics : Dispersion

ToC Category:
Integrated Optics

History
Original Manuscript: February 23, 2010
Revised Manuscript: March 31, 2010
Manuscript Accepted: April 8, 2010
Published: September 17, 2010

Citation
Sara Mas, José Caraquitena, José V. Galán, Pablo Sanchis, and Javier Martí, "Tailoring the dispersion behavior of silicon nanophotonic slot waveguides," Opt. Express 18, 20839-20844 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-20-20839


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References

  1. M. Lipson, “Guiding, modulating, and emitting light on silicon – Challenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005). [CrossRef]
  2. R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006). [CrossRef]
  3. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006). [CrossRef]
  4. H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002). [CrossRef]
  5. 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]
  6. E. Dulkeith, F. Xia, L. Schares, W. M. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14(9), 3853–3863 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-9-3853 . [CrossRef] [PubMed]
  7. 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), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4357 . [CrossRef] [PubMed]
  8. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). [CrossRef] [PubMed]
  9. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]
  10. P. Sanchis, J. Blasco, A. Martínez, and J. Martí, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” J. Lightwave Technol. 25(5), 1298–1305 (2007). [CrossRef]
  11. Z. Zheng, M. Iqbal, and J. Liu, “Dispersion characteristics of SOI-based slot optical waveguides,” Opt. Commun. 281(20), 5151–5155 (2008). [CrossRef]
  12. R. Spano, J. V. Galán, P. Sanchis, A. Martínez, J. Martí, and L. Pavesi, “Group velocity dispersion in horizontal slot waveguides filled by Si nanocrystals,” International Conf. Group IV Photon., 314–316 (2008).
  13. L. Zhang, Y. Yue, Y. Y. Xiao-Li, R. G. Beausoleil, and A. E. Willner, “Highly dispersive slot waveguides,” Opt. Express 17(9), 7095–7101 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7095 . [CrossRef] [PubMed]
  14. P. A. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14(20), 9197–9202 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-20-9197 . [CrossRef] [PubMed]
  15. C. Ma, Q. Zhang, and E. Van Keuren, “Analysis of symmetric and asymmetric nanoscale slab slot waveguides,” Opt. Commun. 282(2), 324–328 (2009). [CrossRef]
  16. K. Okamoto, “Beam propagation method,” in Fundamentals of Optical Waveguides (2000), Chap. 7, 273–281.
  17. B. Tatian, “Fitting refractive-index data with the Sellmeier dispersion formula,” Appl. Opt. 23(24), 4477–4485 (1984). [CrossRef] [PubMed]
  18. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-2-1300 . [CrossRef] [PubMed]

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