Abstract

We analyze chromatic dispersion in tightly curved silicon strip and slot waveguides with high index contrast. It is found that the dispersion profile is changed dramatically at both polarization states, when bending radius is reduced to a few microns. Zero-dispersion wavelength may shift by more than 220 nm, which raises a critical issue in design and optimization of micro-resonator-based devices for nonlinear applications. We propose a slot structure to tailor in-cavity dispersion and obtain spectral lines with the standard deviation of frequency-dependent free spectral range of the slot-waveguide resonator made 460 times smaller than that of a strip-waveguide resonator, making it suitable for on-chip octave-spanning frequency comb generation in mid-infrared wavelength range.

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  1. E. A. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).
  2. H. F. Taylor, “Losses at corner bends in dielectric waveguides,” Appl. Opt. 16(3), 711–716 (1977).
    [CrossRef] [PubMed]
  3. E.-G. Neumann, “Curved dielectric optical waveguides with reduced transition losses,” IEE Proc. Microwaves, Antennas Propag. 129, 278–280 (1982).
  4. R. Espinola, R. Ahmad, F. Pizzuto, M. Steel, and R. Osgood, “A study of high-index-contrast 90 degree waveguide bend structures,” Opt. Express 8(9), 517–528 (2001).
    [CrossRef] [PubMed]
  5. C. Xudong, C. Hafner, R. Vahldieck, and F. Robin, “Sharp trench waveguide bends in dual mode operation with ultra-small photonic crystals for suppressing radiation,” Opt. Express 14(10), 4351–4356 (2006).
    [CrossRef] [PubMed]
  6. A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon on-insulator substrate,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L383–L385 (2001).
    [CrossRef]
  7. A. Sakai, T. Fukazawa, and T. Baba, “Estimation of polarization crosstalk at a micro-bend in Si-photonic wire waveguide,” J. Lightwave Technol. 22(2), 520–525 (2004).
    [CrossRef]
  8. Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
    [CrossRef] [PubMed]
  9. 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).
    [CrossRef] [PubMed]
  10. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express 16(6), 4309–4315 (2008).
    [CrossRef] [PubMed]
  11. Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009).
    [CrossRef]
  12. P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009).
    [CrossRef]
  13. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
    [CrossRef] [PubMed]
  14. A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
    [CrossRef] [PubMed]
  15. 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]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  18. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007).
    [CrossRef]
  19. 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]
  20. L. Zhang, Y. Yue, R. G. Beausoleil, and A. E. Willner, “Flattened dispersion in silicon slot waveguides,” Opt. Express 18(19), 20529–20534 (2010).
    [CrossRef] [PubMed]

2010

2009

Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009).
[CrossRef]

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009).
[CrossRef]

2008

2007

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

2006

2004

2001

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon on-insulator substrate,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L383–L385 (2001).
[CrossRef]

R. Espinola, R. Ahmad, F. Pizzuto, M. Steel, and R. Osgood, “A study of high-index-contrast 90 degree waveguide bend structures,” Opt. Express 8(9), 517–528 (2001).
[CrossRef] [PubMed]

1982

E.-G. Neumann, “Curved dielectric optical waveguides with reduced transition losses,” IEE Proc. Microwaves, Antennas Propag. 129, 278–280 (1982).

1977

1969

E. A. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).

Agrawal, G. P.

Ahmad, R.

Anderson, P. A.

Arcizet, O.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Baba, T.

A. Sakai, T. Fukazawa, and T. Baba, “Estimation of polarization crosstalk at a micro-bend in Si-photonic wire waveguide,” J. Lightwave Technol. 22(2), 520–525 (2004).
[CrossRef]

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon on-insulator substrate,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L383–L385 (2001).
[CrossRef]

Beausoleil, R. G.

Chen, X.

Chou, C.-Y.

Dadap, J. I.

Dai, D.

Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009).
[CrossRef]

Del’Haye, P.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Del'Haye, P.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009).
[CrossRef]

Dulkeith, E.

Espinola, R.

Fattal, D.

Foster, M. A.

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]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[CrossRef] [PubMed]

Fukazawa, T.

Gaeta, A. L.

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]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[CrossRef] [PubMed]

Gondarenko, A.

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]

Gorodetsky, M. L.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009).
[CrossRef]

Green, W. M. J.

Hafner, C.

Hara, G.

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon on-insulator substrate,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L383–L385 (2001).
[CrossRef]

He, S.

Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009).
[CrossRef]

Holzwarth, R.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Hsieh, I.-W.

Kippenberg, T. J.

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Levy, J. S.

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]

Lin, Q.

Lipson, M.

Liu, X.

Marcatili, E. A.

E. A. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).

McNab, S.

McNab, S. J.

Neumann, E.-G.

E.-G. Neumann, “Curved dielectric optical waveguides with reduced transition losses,” IEE Proc. Microwaves, Antennas Propag. 129, 278–280 (1982).

Osgood, R.

Osgood, R. M.

Oxborrow, M.

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007).
[CrossRef]

Panoiu, N. C.

Pizzuto, F.

Robin, F.

Sakai, A.

A. Sakai, T. Fukazawa, and T. Baba, “Estimation of polarization crosstalk at a micro-bend in Si-photonic wire waveguide,” J. Lightwave Technol. 22(2), 520–525 (2004).
[CrossRef]

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon on-insulator substrate,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L383–L385 (2001).
[CrossRef]

Schliesser, A.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Schmidt, B. S.

Sekaric, L.

Sheng, Z.

Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009).
[CrossRef]

Steel, M.

Taylor, H. F.

Turner, A. C.

Turner-Foster, A. C.

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]

Vahldieck, R.

Vlasov, Y.

Vlasov, Y. A.

Wang, J.

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Willner, A. E.

Xia, F.

Xiao-Li, Y.

Xu, Q.

Xudong, C.

Yin, L.

Yue, Y.

Zhang, L.

Appl. Opt.

Bell Syst. Tech. J.

E. A. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).

IEE Proc. Microwaves, Antennas Propag.

E.-G. Neumann, “Curved dielectric optical waveguides with reduced transition losses,” IEE Proc. Microwaves, Antennas Propag. 129, 278–280 (1982).

IEEE J. Sel. Top. Quantum Electron.

Z. Sheng, D. Dai, and S. He, “Comparative study of losses in ultrasharp silicon-on-insulator nanowire bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007).
[CrossRef]

J. Lightwave Technol.

Jpn. J. Appl. Phys.

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon on-insulator substrate,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L383–L385 (2001).
[CrossRef]

Nat. Photonics

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]

P. Del'Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009).
[CrossRef]

Nature

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Opt. Express

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[CrossRef] [PubMed]

Y. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express 16(6), 4309–4315 (2008).
[CrossRef] [PubMed]

R. Espinola, R. Ahmad, F. Pizzuto, M. Steel, and R. Osgood, “A study of high-index-contrast 90 degree waveguide bend structures,” Opt. Express 8(9), 517–528 (2001).
[CrossRef] [PubMed]

C. Xudong, C. Hafner, R. Vahldieck, and F. Robin, “Sharp trench waveguide bends in dual mode operation with ultra-small photonic crystals for suppressing radiation,” Opt. Express 14(10), 4351–4356 (2006).
[CrossRef] [PubMed]

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]

L. Zhang, Y. Yue, R. G. Beausoleil, and A. E. Willner, “Flattened dispersion in silicon slot waveguides,” Opt. Express 18(19), 20529–20534 (2010).
[CrossRef] [PubMed]

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., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[CrossRef] [PubMed]

Opt. Lett.

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Figures (5)

Fig. 1
Fig. 1

A horizontal slot waveguide has a low-index slot between upper and lower high-index layers. When the upper layer and the slot are removed (Hu = 0, Hs = 0), the waveguide becomes a strip waveguide. In waveguide bends and micro-resonators, traveling optical mode feels an effective bending radius, Reff, that is greater than structural bending radius, R0.

Fig. 2
Fig. 2

In curved strip waveguides, effective bending radius Reff, relative to structural bending radius R0, changes with wavelength, producing additional waveguide dispersion. (a) quasi-TE mode (b) quasi-TM mode. Dispersion curves with a different bending radius R0 from 1300 to 1800 nm. (c) quasi-TE mode (d) quasi-TM mode. ZDW is shifted, relative to that in straight strip waveguides, by waveguide bending. (e) quasi-TE mode (f) quasi-TM mode.

Fig. 3
Fig. 3

Dispersion change induced by waveguide bending in horizontal slot waveguides. (a) effective banding radius, (b) dispersion profile and (c) ZDW shift.

Fig. 4
Fig. 4

(a) Dispersion inside the cavity is changed as R0 is reduced from 16 to 3 μm. Both averaged value and flatness of the dispersion profiles are varied. (b) FSR's standard deviation changes rapidly with R0.

Fig. 5
Fig. 5

Spectral response of a single-ring resonator is sliced with a frequency spacing equal to the averaged FSR. All the spectrum pieces are plotted together to show the uniformity of the resonance peaks. Proposed slot-waveguide resonator has well-aligned resonance peaks over a 563-nm wavelength band, in contrast with a strip-waveguide resonator.

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