Abstract

Here we examine the waveguide dispersion property of slot waveguides, approaching/analyzing the given problem with respect to the normalized index contrast, Δnslot-core/ncore and Δncore-clad/ncore between adjacent layers. For two index contrasts of concern, it is found that their contributions to slot waveguide dispersions are substantially different, with Δnslot-core and Δncore-clad each acting preferentially on short- and long-wavelength regions. Additional degrees of freedom in the waveguide design, such as the effect of absolute refractive index and waveguide geometry are also investigated to enable flexible tuning of the waveguide dispersion. Focusing on the unexplored regime of slot waveguides design in short wavelength (<1 μm), we also study the feasibility of low-threshold super-continuum sources using a Ta2O5/TiO2/silica slot, either of two-octave spectral width (0.467–1.581 μm), or of one-octave, near unity coherence |g12(1)| = 1.

© 2012 OSA

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References

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  1. R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Quantum Electron. 12(6), 1678–1687 (2006).
    [CrossRef]
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    [CrossRef]
  3. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15(8), 4977–4993 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. 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]
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    [CrossRef] [PubMed]
  13. S. Mas, J. Caraquitena, J. V. Galán, P. Sanchis, and J. Martí, “Tailoring the dispersion behavior of silicon nanophotonic slot waveguides,” Opt. Express 18(20), 20839–20844 (2010).
    [CrossRef] [PubMed]
  14. A. E. Willner, L. Zhang, and Y. Yue, “Tailoring of dispersion and nonlinear properties of integrated silicon waveguides for signal processing applications,” Semicond. Sci. Technol. 26(1), 014044 (2011).
    [CrossRef]
  15. 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]
  16. 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]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  27. J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers (Cambridge University Press, 2010).
  28. C. Y. Tai, J. Wilkinson, N. Perney, M. Netti, F. Cattaneo, C. Finlayson, and J. Baumberg, “Determination of nonlinear refractive index in a Ta2O5 rib waveguide using self-phase modulation,” Opt. Express 12(21), 5110–5116 (2004).
    [CrossRef] [PubMed]
  29. V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79(3), 1741–1745 (1996).
    [CrossRef]
  30. J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63(4), 045117 (2001).
    [CrossRef]
  31. J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
    [CrossRef]

2011

A. E. Willner, L. Zhang, and Y. Yue, “Tailoring of dispersion and nonlinear properties of integrated silicon waveguides for signal processing applications,” Semicond. Sci. Technol. 26(1), 014044 (2011).
[CrossRef]

L. Zhang, Y. Yan, Y. Yue, Q. Lin, O. Painter, R. G. Beausoleil, and A. E. Willner, “On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses,” Opt. Express 19(12), 11584–11590 (2011).
[CrossRef] [PubMed]

2010

2009

2008

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[CrossRef]

2007

2006

2004

2001

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63(4), 045117 (2001).
[CrossRef]

2000

1996

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79(3), 1741–1745 (1996).
[CrossRef]

1992

G. A. Al-Jumaily and S. M. Edlou, “Optical properties of tantalum pentoxide coatings deposited using ion beam processes,” Thin Solid Films 209(2), 223–229 (1992).
[CrossRef]

1982

1974

S. KAWAKAMI and S. NISHIDA, “Characteristics of a doubly clad optical fiber with a low index inner cladding,” IEEE J. Quantum Electron. QE-10, 879–887 (1974).

Aggarwal, I. D.

Agrawal, G. P.

Al-Jumaily, G. A.

G. A. Al-Jumaily and S. M. Edlou, “Optical properties of tantalum pentoxide coatings deposited using ion beam processes,” Thin Solid Films 209(2), 223–229 (1992).
[CrossRef]

Almeida, V. R.

Barrios, C. A.

Baumberg, J.

Beausoleil, R. G.

Birks, T. A.

Blasco, J.

Caraquitena, J.

Cattaneo, F.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Cohen, L. G.

Dell’Olio, F.

Dimitrov, V.

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79(3), 1741–1745 (1996).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Edlou, S. M.

G. A. Al-Jumaily and S. M. Edlou, “Optical properties of tantalum pentoxide coatings deposited using ion beam processes,” Thin Solid Films 209(2), 223–229 (1992).
[CrossRef]

Fan, Z.

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[CrossRef]

Fathpour, S.

Finlayson, C.

Foster, M. A.

Freude, W.

Gaeta, A. L.

Galán, J. V.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Hainberger, R.

He, H.

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[CrossRef]

Hodelin, J.

Jacome, L.

Jalali, B.

Jasapara, J.

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63(4), 045117 (2001).
[CrossRef]

Jin, Y.

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[CrossRef]

KAWAKAMI, S.

S. KAWAKAMI and S. NISHIDA, “Characteristics of a doubly clad optical fiber with a low index inner cladding,” IEEE J. Quantum Electron. QE-10, 879–887 (1974).

Koos, C.

Lenz, G.

Leuthold, J.

Lin, Q.

Lipson, M.

Lumish, S.

Mammel, W. L.

Manolatou, C.

Marti, J.

Martí, J.

Martinez, A.

Mas, S.

Muellner, P.

Nampoothiri, A. V. V.

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63(4), 045117 (2001).
[CrossRef]

Netti, M.

NISHIDA, S.

S. KAWAKAMI and S. NISHIDA, “Characteristics of a doubly clad optical fiber with a low index inner cladding,” IEEE J. Quantum Electron. QE-10, 879–887 (1974).

Painter, O.

Passaro, V. M. N.

Perney, N.

Poulton, C.

Ristau, D.

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63(4), 045117 (2001).
[CrossRef]

Rudolph, W.

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63(4), 045117 (2001).
[CrossRef]

Russell, P. St. J.

Sakka, S.

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79(3), 1741–1745 (1996).
[CrossRef]

Sanchis, P.

Sanghera, J.

Schmidt, B. S.

Shao, J.

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[CrossRef]

Sharping, J. E.

Shaw, L. B.

Slusher, R. E.

Soref, R.

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

Starke, K.

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63(4), 045117 (2001).
[CrossRef]

Tai, C. Y.

Turner, A. C.

Wadsworth, W. J.

Wang, J.

Wellenzohn, M.

Wilkinson, J.

Willner, A. E.

Xiao-Li, Y.

Xu, Q.

Yan, Y.

Yao, J.

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[CrossRef]

Yin, L.

Yue, Y.

Zhang, L.

Zhao, Y.

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[CrossRef]

IEEE J. Quantum Electron.

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

S. KAWAKAMI and S. NISHIDA, “Characteristics of a doubly clad optical fiber with a low index inner cladding,” IEEE J. Quantum Electron. QE-10, 879–887 (1974).

J. Appl. Phys.

V. Dimitrov and S. Sakka, “Linear and nonlinear optical properties of simple oxides. II,” J. Appl. Phys. 79(3), 1741–1745 (1996).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Express

C. Y. Tai, J. Wilkinson, N. Perney, M. Netti, F. Cattaneo, C. Finlayson, and J. Baumberg, “Determination of nonlinear refractive index in a Ta2O5 rib waveguide using self-phase modulation,” Opt. Express 12(21), 5110–5116 (2004).
[CrossRef] [PubMed]

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]

F. Dell’Olio and V. M. N. Passaro, “Optical sensing by optimized silicon slot waveguides,” Opt. Express 15(8), 4977–4993 (2007).
[CrossRef] [PubMed]

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]

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]

P. Muellner, M. Wellenzohn, and R. Hainberger, “Nonlinearity of optimized silicon photonic slot waveguides,” Opt. Express 17(11), 9282–9287 (2009).
[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]

S. Mas, J. Caraquitena, J. V. Galán, P. Sanchis, and J. Martí, “Tailoring the dispersion behavior of silicon nanophotonic slot waveguides,” Opt. Express 18(20), 20839–20844 (2010).
[CrossRef] [PubMed]

L. Zhang, Y. Yan, Y. Yue, Q. Lin, O. Painter, R. G. Beausoleil, and A. E. Willner, “On-chip two-octave supercontinuum generation by enhancing self-steepening of optical pulses,” Opt. Express 19(12), 11584–11590 (2011).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. B

J. Jasapara, A. V. V. Nampoothiri, W. Rudolph, D. Ristau, and K. Starke, “Femtosecond laser pulse induced breakdown in dielectric thin films,” Phys. Rev. B 63(4), 045117 (2001).
[CrossRef]

Rev. Mod. Phys.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Semicond. Sci. Technol.

A. E. Willner, L. Zhang, and Y. Yue, “Tailoring of dispersion and nonlinear properties of integrated silicon waveguides for signal processing applications,” Semicond. Sci. Technol. 26(1), 014044 (2011).
[CrossRef]

Thin Solid Films

J. Yao, Z. Fan, Y. Jin, Y. Zhao, H. He, and J. Shao, “Investigation of damage threshold to TiO2 coatings at different laser wavelength and pulse duration,” Thin Solid Films 516(6), 1237–1241 (2008).
[CrossRef]

G. A. Al-Jumaily and S. M. Edlou, “Optical properties of tantalum pentoxide coatings deposited using ion beam processes,” Thin Solid Films 209(2), 223–229 (1992).
[CrossRef]

Other

R. Spano, J. V. Galan, P. Sanchis, A. Martinez, J. Marti, and L. Pavesi, “Group velocity dispersion in horizontal slot waveguide filled by Si nanocrystals,” in 2008 5th IEEE International Conference on Group IV Photonics (IEEE, 2008), pp. 314–316.

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers (Cambridge University Press, 2010).

ComsolMultiphysics by COMSOL, © ver. 3.3 (2006).

G. P. Agrawal, Nonliner Fiber Optics (Academic Press, 2007).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1998)

E. V. Stryland, Handbook of Optics (McGraw–Hill, 2009).

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Figures (4)

Fig. 1
Fig. 1

(a) Cross section of horizontal slot waveguides (b) Profile of normalized refractive index for the investigated slot waveguide. Δñsc = (ncore – nslot)/ncore, and Δñcc = (ncore – nclad)/ncore.

Fig. 2
Fig. 2

(a) Waveguide dispersion (Dw), (b) Normalized intensities in slot (Islot) and core (Icore) layers, and (c) effective area (Aeff) plotted for six different sets of index contrasts, Δñsc and Δñcc. (d) Normalized modal power of quasi-TM mode (λ = 0.65–1.85μm) for slot design of index contrast Δñsc = 0.2: (d)-1, ~5 and Δñsc = 0.5: (d)-6, ~10 (Δñcc = 0.5 in solid line, Δñcc = 0.65 in dotted line). For all the plots, ncore = 3.0, w = 300 nm, h = 200 nm, ws = 40 nm.

Fig. 3
Fig. 3

(a1–c1) Waveguide dispersion (Dw). (a2–c2) Normalized intensity (Islot and Icore), and (a3–c3) Effective area (Aeff) for the slot design of; (Δñsc, Δñcc) = (0.2, 0.5); red curves and (Δñsc, Δñcc) = (0.35, 0.5); black curves, for different values of ncore = 3.5 (solid circle), 3.0 (line), and 2.5 (open circle). Core thickness h was adjusted to keep ncore × h constant. Slot thickness was changed from δ = 0.15, 0.10, and 0.05 for (a), (b), and (c) respectively.

Fig. 4
Fig. 4

(a-1,b-1) Pulse evolution and spectrum after 5mm propagation, (a-2,b-2) degree of coherence, and (a-3,b-3) chromatic dispersion (Dch = Dw + Dm, in black); for slots of normalized slot thickness (a) δ = 0.08 and (b) δ = 0.16. w = 300 nm, h = 200 nm.

Tables (1)

Tables Icon

Table 1 List of materials and their index values, within the scope of this study [2226]

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