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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 10 — May. 15, 2006
  • pp: 4357–4362
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Tailored anomalous group-velocity dispersion in silicon channel waveguides

Amy C. Turner, Christina Manolatou, Bradley S. Schmidt, Michal Lipson, Mark A. Foster, Jay E. Sharping, and Alexander L. Gaeta  »View Author Affiliations


Optics Express, Vol. 14, Issue 10, pp. 4357-4362 (2006)
http://dx.doi.org/10.1364/OE.14.004357


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Abstract

We present the first experimental demonstration of anomalous group-velocity dispersion (GVD) in silicon waveguides across the telecommunication bands. We show that the GVD in such waveguides can be tuned from -2000 to 1000 ps/(nm·km) by tailoring the cross-sectional size and shape of the waveguide.

© 2006 Optical Society of America

1. Introduction

In this paper we determine the waveguide geometries that allow for anomalous-GVD and investigate through numerical simulations how the waveguide cross-sectional shape and size can be used to control the resulting GVD. In agreement with our simulations, we measure experimentally that the GVD in silicon waveguides can be highly anomalous over a large bandwidth. We engineer the waveguide dimensions and experimentally measure normal- and anomalous-GVD ranging from -300 to 1100 ps/(nm·km) in the wavelength range of 1.35 to 1.55 µm. Specifically, at the telecommunications wavelength of 1.55 µm we tailor and experimentally verify the GVD to be in the range of anomalous values from 200 to 1100 ps/(nm·km) for four different sized waveguides. Careful choice of the waveguide shape and size is required to obtain anomalous-GVD at a desired wavelength.

Fig. 1. Group-velocity dispersion D as a function of wavelength for a fixed aspect ratio of 1:1.5 (height to width) and for cross-sectional areas of 0.09 µm2, 0.20 µm2, 0.40 µm2, and 0.56 µm2.

2. Analysis

The tailoring of the GVD is enabled by controlling the degree of light confinement of the waveguide. This can be seen in Figs. 1 and 2 where we plot the GVD for the low-loss TE-like mode as numerically calculated for different cross-sectional areas and shapes using a custom, full-vector, finite-difference mode solver. Sellmeier equations representing pure crystalline silicon and fused silica [5

5. M. J. Weber, “Silicon (Si)” and “Fused silica (SiO2)” in Handbook of optical materials, (CRC Press, Boca Raton, 2003).

] provide the input for the material dispersion of the core and cladding of the waveguide.

The aspect ratio of the waveguide also affects the dispersion, especially for highly confining waveguides. This can be seen in Figs. 2(a) and 2(b) where the GVD is plotted for waveguides with cross-sectional areas of 0.09 µm2 and 0.56 µm2, respectively. Figure 2(a) shows the geometric dependence of a single mode waveguide with cross-sectional area of 0.09 µm2 for different aspect ratios. One can see that at a wavelength of 1.55 µm, the maximum possible GVD for rectangular waveguide areas of 0.09 µm2 (see the green dashed curve corresponding to 212 nm×425 nm) is still normal [-160 ps/(nm·km)]. This explains why, for example, the four-wave mixing efficiency previously observed in silicon was relatively low [20

20. H. Fukada, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13, 4629–4637 (2005). [CrossRef]

, 21

21. R. L. Espinola, J. I. Dadap, R. M. Osgood Jr., S. J. McNab, and Y. A. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13, 4341–4349 (2005). [CrossRef] [PubMed]

]. For a 1:1 aspect ratio 300 nm x 300 nm (the red dashed curve in Fig. 2), the peak anomalous-GVD value is 1856 ps/(nm·km) at a wavelength of 1.35 µm.

Fig. 2. Group-velocity dispersion as a function of wavelength for varying aspect ratios and fixed cross sectional areas of (a) 0.09 µm2 and (b) 0.56 µm2.

3. Fabrication

In order to analyze experimentally the tailoring of the GVD by varying the size and geometry, we fabricate four waveguides with a fixed height of 300 nm and create widths of different sizes using electron-beam lithography on an SOI platform with 1-µm buried oxide. The cross-sectional area for such waveguides is on the order of 0.20 µm2 which corresponds to anomalous-GVD for the fundamental TE-like mode (see Fig. 1) near the 1.55 µm region. Each end of the waveguide is terminated with an inverse taper [22

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

] in order to ensure that only the fundamental mode is excited. The 6.4-mm-long silicon waveguides are designed to have no bends in them so as to maintain propagation of the fundamental mode. The waveguides are etched using reactive-ion etching and clad with silica using plasma-enhanced chemical vapor deposition (PECVD). The measured propagation losses in the waveguides range from 1.1 to 1.4 dB/cm.

4. Experiment

In order to measure the GVD of the waveguides, we use Fourier-transform spectral interferometry (FTSI) to determine the group index as a function of wavelength for the four waveguides similar to the technique seen in Ref. 19. A picosecond laser pulse train from a tunable optical parametric oscillator is split such that one part is sent to the waveguide and the other travels through a reference arm. The waveguide branch is coupled using a laser-polished lens fiber. The polarization is optimized to excite the low-loss TE-like mode of the waveguide. The waveguide output is collected with a lens, sent through a polarizer to ensure the analysis of only the fundamental TE-like mode, and coupled back into a fiber. This signal is combined with the reference arm in a 90:10 coupler. When the output pulses are measured with an OSA one observes a wavelength-dependent modulation of the optical spectrum, or a spectral interferogram. The frequency of the modulation of the spectral interferogram is proportional to the time delay between the two pulses. By extracting the variation of the time delay as a function of the center wavelength of the pulses, one obtains the group index of refraction of the entire system. In order to find the group index solely of the waveguides, the measurements are repeated with the waveguide removed from the system. Although the measured waveguides are multimode, a very small fraction of the power is coupled into higher order modes. However, due to the extreme sensitivity of this spectral measurement technique, the signals due to these higher-order modes are easily differentiated, allowing for characterization of only the fundamental mode.

Fig. 3. Simulated (lines) and experimental (symbols) (a) group index data and (b) groupvelocity dispersion as a function of wavelength for four different waveguides. Ellipsometric measurements are done on the PECVD over-cladding and then fitted with a Sellmeier function to provide the upper-cladding material dispersion data for the simulated curves.

By tuning the wavelength of the input pulse and repeating this procedure based on FTSI, we are able to obtain the group index as a function of wavelength (Fig 3a). For the waveguides studied here, the group index increases as a function of wavelength for most of the range which is indicative of anomalous-GVD. The group delay was measured 5 times at each wavelength and the results were averaged. This produced a 0.1% error in the measurement of group index. This error does not include inaccuracies from variations in the position of the optimum focal distance with and without the waveguide and from measuring the length of the waveguide. Such errors are constant with wavelength and can lead to the observed effective “dc offset” of the group index relative to the simulated curves. However, since this offset is constant with wavelength, it does not affect the measurement of GVD which involves taking a derivative of the group index with respect to wavelength. Still, the observed offset is small; only a 4% discrepancy from the simulated values.

Figure 3(b) shows the inferred GVD as a function of wavelength for the four waveguides. The experimental GVD is calculated by fitting the group index data to a third order polynomial and differentiating the result [11

11. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).

]. There is no exact functional form for the group index of a rectangular waveguide, therefore we fit our results to a third-order polynomial as an approximation over our data range. Fitting to this third-order polynomial takes into account not only GVD, but also higher-order dispersion contributions up to fourth order. As would be expected, this approximation will breakdown near the wavelength edges of our measurement, leading to the observed disagreement. Nevertheless, the variation in magnitude of anomalous- GVD and position of the zero-GVD point with waveguide cross-section clearly follow the theoretically predicted trends.

At wavelengths near 1.55 µm, the measured GVD ranges from about 200 ps/(nm·km) in the largest waveguide (300×650 nm), up to 1100 ps/(nm·km) in the smallest waveguide (300×500 nm), in agreement with the simulated GVD plotted in Fig. 3(b). This anomalous-GVD value is two orders of magnitude larger than SMF-28 fiber and one order of magnitude larger than commercially available microstructured fibers [17 ps/(nm·km) and ~200 ps/(nm·km), respectively] [1

1. M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12, 2880–2887 (2004). [CrossRef] [PubMed]

]. As an example, the measured value of 1100 ps/(nm·km) yields a dispersion length of 18 cm for a 0.5-ps propagating pulse. For the GVD to be neglected in pulse propagation, the dispersion length must be much greater than the propagation length [9

9. G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, Inc., 1997).

]. Since the calculated dispersion length is on the order of centimeters, one would expect the GVD to significantly influence the propagation of sub-picosecond pulses in cm-long SOI waveguides. For longer pulses, GVD will not influence pulse propagation, but will determine the phase matching for nonlinear processes such as four-wave mixing [9

9. G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, Inc., 1997).

].

5. Conclusion

In this paper we experimentally measure and numerically study the tailoring of the GVD in silicon waveguides from strongly normal- to strongly anomalous-GVD values over a wide bandwidth. We achieve anomalous values as high as 1100 ps/(nm·km) at the telecommunications wavelength of 1.55 µm. We also determine the range of sizes of silicon waveguides that allow for anomalous-GVD and investigate the effects of waveguide crosssectional shape and size on the resulting GVD through numerical simulations. This method of tailoring the GVD in a silicon waveguide can be used to customize the GVD profile for various applications requiring such regulation. The ability to demonstrate anomalous-GVD over broad bandwidths in standard silicon waveguides enables applications such as dispersion compensation and in nonlinear optics on-chip such as four-wave mixing [23

23. 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,” submitted for publication (2006).

], parametric oscillation, pulse compression and soliton communications.

Acknowledgments

This work was supported by the NSF through the Center for Nanoscale Systems under award number EEC-0117770. A.C.T. also acknowledges support under a National Science Foundation Graduate Research Fellowship. M.A.F., J.E.S., and A.L.G. also acknowledge support under the DARPA Slow-Light Program. This work was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS 03-35765).

References and links

1.

M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12, 2880–2887 (2004). [CrossRef] [PubMed]

2.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 481, 1081–1084 (2004). [CrossRef]

3.

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

4.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005). [CrossRef] [PubMed]

5.

M. J. Weber, “Silicon (Si)” and “Fused silica (SiO2)” in Handbook of optical materials, (CRC Press, Boca Raton, 2003).

6.

L. Tong, J. Lou, and E. Mazur, “Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004). [CrossRef] [PubMed]

7.

V Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Parametric Raman wavelength conversion in scaled silicon waveguides,” J. Lightwave Technol. 23, 2094–2102 (2005). [CrossRef]

8.

X. Chen, N. C. Panoiu, and R. M. Osgood Jr., “Theory of Raman-mediated pulsed amplification in siliconwire waveguides,” IEEE J. Quantum Electron. 42, 160–170 (2006). [CrossRef]

9.

G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, Inc., 1997).

10.

L. F. Mollenauer, R. H. Stolen, and J. P. Gorden, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980). [CrossRef]

11.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).

12.

D. G. Ouzounov, D. Homoelle, W. Zipfel, W. W. Webb, A. L. Gaeta, J. A. West, J. C. Fajurdo, and K. W. Koch, “Dispersion measurements of microstructured fibers using femtosecond laser pulses,” Opt. Commun. 192, 219–223 (2001). [CrossRef]

13.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809 (2000). [CrossRef]

14.

J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, and R. S. Windeler, “Four-wave mixing in microstructure fiber,” Opt. Lett. 26, 1048 (2001). [CrossRef]

15.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, “Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres,” Nature 424, 511–515 (2003). [CrossRef] [PubMed]

16.

J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “Optical parametric oscillator based on four-wave mixing in microstructure fiber,” Opt. Lett. 271675–1677 (2002). [CrossRef]

17.

M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, “Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires,” Opt. Express 136848–6855 (2005). [CrossRef] [PubMed]

18.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

19.

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, 416–418 (2002). [CrossRef]

20.

H. Fukada, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13, 4629–4637 (2005). [CrossRef]

21.

R. L. Espinola, J. I. Dadap, R. M. Osgood Jr., S. J. McNab, and Y. A. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13, 4341–4349 (2005). [CrossRef] [PubMed]

22.

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

23.

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,” submitted for publication (2006).

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(130.2790) Integrated optics : Guided waves
(230.7380) Optical devices : Waveguides, channeled

ToC Category:
Integrated Optics

History
Original Manuscript: February 17, 2006
Revised Manuscript: April 28, 2006
Manuscript Accepted: May 1, 2006
Published: May 15, 2006

Citation
Amy C. Turner, Christina Manolatou, Bradley S. Schmidt, Michal Lipson, Mark A. Foster, Jay E. Sharping, and Alexander L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-10-4357


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References

  1. M. A. Foster, K. D. Moll, and A. L. Gaeta, "Optimal waveguide dimensions for nonlinear interactions," Opt. Express 12, 2880-2887 (2004). [CrossRef] [PubMed]
  2. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, "All-optical control of light on a silicon chip," Nature 481, 1081-1084 (2004). [CrossRef]
  3. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 1731-1739 (2003). [CrossRef] [PubMed]
  4. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005). [CrossRef] [PubMed]
  5. M. J. Weber, "Silicon (Si)" and "Fused silica (SiO2)" in Handbook of optical materials, (CRC Press, Boca Raton, 2003).
  6. L. Tong, J. Lou, and E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Express 12, 1025-1035 (2004). [CrossRef] [PubMed]
  7. V Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, "Parametric Raman wavelength conversion in scaled silicon waveguides," J. Lightwave Technol. 23, 2094-2102 (2005). [CrossRef]
  8. X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron. 42, 160-170 (2006). [CrossRef]
  9. G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons, Inc., 1997).
  10. L. F. Mollenauer, R. H. Stolen, and J. P. Gorden, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095-1098 (1980). [CrossRef]
  11. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).
  12. D. G. Ouzounov, D. Homoelle, W. Zipfel, W. W. Webb, A. L. Gaeta, J. A. West, J. C. Fajurdo, and K. W. Koch, "Dispersion measurements of microstructured fibers using femtosecond laser pulses," Opt. Commun. 192, 219-223 (2001). [CrossRef]
  13. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000). [CrossRef]
  14. J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, and R. S. Windeler, "Four-wave mixing in microstructure fiber," Opt. Lett. 26, 1048 (2001). [CrossRef]
  15. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424,511-515 (2003). [CrossRef] [PubMed]
  16. J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, "Optical parametric oscillator based on four-wave mixing in microstructure fiber," Opt. Lett. 271675-1677 (2002). [CrossRef]
  17. M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, "Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires," Opt. Express 136848-6855 (2005). [CrossRef] [PubMed]
  18. J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000). [CrossRef]
  19. 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, 416-418 (2002). [CrossRef]
  20. H. Fukada, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, "Four-wave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005). [CrossRef]
  21. R. L. Espinola, J. I. Dadap, R. M. OsgoodJr., S. J. McNab, and Y. A. Vlasov, "C-band wavelength conversion in silicon photonic wire waveguides," Opt. Express 13, 4341-4349 (2005). [CrossRef] [PubMed]
  22. V. R. Almeida, R. R. Panepucci, and M. Lipson, "Nanotaper for compact mode conversion," Opt. Lett. 28, 1302-1304 (2003). [CrossRef] [PubMed]
  23. 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," submitted for publication (2006).

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