Abstract

We report record low loss silicon-on-sapphire nanowires for applications to mid infrared optics. We achieve propagation losses as low as 0.8dB/cm at λ = 1550nm, ~1.1 to 1.4dB/cm at λ = 2080nm and < 2dB/cm at λ = 5.18 μm.

© 2011 OSA

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    [CrossRef]
  4. X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
    [CrossRef]
  5. G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
    [CrossRef] [PubMed]
  6. P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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2011 (1)

2010 (5)

T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on-sapphire integrated waveguides for the mid-infrared,” Opt. Express 18(12), 12127–12135 (2010).
[CrossRef] [PubMed]

R. A. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010).
[CrossRef]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[CrossRef]

A. Spott, Y. Liu, T. Baehr-Jones, R. Ilic, and M. Hochberg, “Silicon waveguides and ring resonators at 5.5 μm,” Appl. Phys. Lett. 97(21), 213501 (2010).
[CrossRef]

2009 (2)

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

L. Labadie and O. Wallner, “Mid-infrared guided optics: a perspective for astronomical instruments,” Opt. Express 17(3), 1947–1962 (2009).
[CrossRef] [PubMed]

2008 (1)

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

2006 (2)

2004 (2)

V. G. Ta’eed, D. J. Moss, B. J. Eggleton, D. Freeman, S. Madden, M. Samoc, B. Luther-Davies, S. Janz, and D.-X. Xu, “Higher order mode conversion via focused ion beam milled Bragg gratings in Silicon-on-Insulator waveguides,” Opt. Express 12(21), 5274–5284 (2004).
[CrossRef] [PubMed]

G. Vecchi, J. Torres, D. Coquillat, M. Le Vassor d’Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

2003 (1)

E. M. Dianov, “Single-mode As-S glass fibers,” Inorg. Mater. 39(6), 627–630 (2003).
[CrossRef]

1998 (1)

1992 (1)

G. C. Holst and S. W. McHugh, “Review of thermal imaging system performance,” Proc. SPIE 1689, 78–84 (1992).
[CrossRef]

Alic, N.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Asher, W.

Baehr-Jones, T.

T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on-sapphire integrated waveguides for the mid-infrared,” Opt. Express 18(12), 12127–12135 (2010).
[CrossRef] [PubMed]

A. Spott, Y. Liu, T. Baehr-Jones, R. Ilic, and M. Hochberg, “Silicon waveguides and ring resonators at 5.5 μm,” Appl. Phys. Lett. 97(21), 213501 (2010).
[CrossRef]

Bettiol, A. A.

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Boggio, J. M. C.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Breese, M. B. H.

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Buchwald, W. R.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguide components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[CrossRef]

Capasso, F.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

Coquillat, D.

G. Vecchi, J. Torres, D. Coquillat, M. Le Vassor d’Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Crnjanski, J.

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Dianov, E. M.

E. M. Dianov, “Single-mode As-S glass fibers,” Inorg. Mater. 39(6), 627–630 (2003).
[CrossRef]

Diehl, L.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

Divliansky, I. B.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Eggleton, B. J.

Emelett, S. J.

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguide components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[CrossRef]

Fan, J. Y.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

Freeman, D.

Fu, L.

Giusca, C.

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Go, R.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

Green, W. M. J.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[CrossRef]

Headley, W.

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Hochberg, M.

T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on-sapphire integrated waveguides for the mid-infrared,” Opt. Express 18(12), 12127–12135 (2010).
[CrossRef] [PubMed]

A. Spott, Y. Liu, T. Baehr-Jones, R. Ilic, and M. Hochberg, “Silicon waveguides and ring resonators at 5.5 μm,” Appl. Phys. Lett. 97(21), 213501 (2010).
[CrossRef]

Holst, G. C.

G. C. Holst and S. W. McHugh, “Review of thermal imaging system performance,” Proc. SPIE 1689, 78–84 (1992).
[CrossRef]

Hu, Y.

Ilic, R.

A. Spott, Y. Liu, T. Baehr-Jones, R. Ilic, and M. Hochberg, “Silicon waveguides and ring resonators at 5.5 μm,” Appl. Phys. Lett. 97(21), 213501 (2010).
[CrossRef]

T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on-sapphire integrated waveguides for the mid-infrared,” Opt. Express 18(12), 12127–12135 (2010).
[CrossRef] [PubMed]

Jackson, S. D.

Janz, S.

King, T. A.

Labadie, L.

Le Vassor d’Yerville, M.

G. Vecchi, J. Torres, D. Coquillat, M. Le Vassor d’Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Littler, I. C.

Liu, X.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[CrossRef]

Liu, Y.

A. Spott, Y. Liu, T. Baehr-Jones, R. Ilic, and M. Hochberg, “Silicon waveguides and ring resonators at 5.5 μm,” Appl. Phys. Lett. 97(21), 213501 (2010).
[CrossRef]

Luther-Davies, B.

Lyakh, A.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

Madden, S.

Malvezzi, A. M.

G. Vecchi, J. Torres, D. Coquillat, M. Le Vassor d’Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Mashanovich, G. Z.

G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
[CrossRef] [PubMed]

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Maulini, R.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

McHugh, S. W.

G. C. Holst and S. W. McHugh, “Review of thermal imaging system performance,” Proc. SPIE 1689, 78–84 (1992).
[CrossRef]

Miloševic, M. M.

Mookherjea, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Moro, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Moss, D. J.

Nedeljkovic, M.

Osgood, R. M.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[CrossRef]

Owens, N.

Park, J. S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Patel, C. K. N.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

Pelusi, M.

Penkov, B.

Pflügl, C.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

Radic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Reed, G. T.

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Rochette, M.

Samoc, M.

Soref, R. A.

R. A. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010).
[CrossRef]

R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguide components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[CrossRef]

Spott, A.

Stankovic, S.

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Ta’eed, V. G.

Tanbun-Ek, T.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

Teo, E. J.

G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express 19(8), 7112–7119 (2011).
[CrossRef] [PubMed]

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Thomson, D.

P. Y. Yang, S. Stankovic, J. Crnjanski, E. J. Teo, D. Thomson, A. A. Bettiol, M. B. H. Breese, W. Headley, C. Giusca, G. T. Reed, and G. Z. Mashanovich, “Silicon photonic waveguides for mid- and long-wave infrared region,” J. Mater. Sci. Mater. Electron. 20(S1), 159–163 (2009).
[CrossRef]

Torres, J.

G. Vecchi, J. Torres, D. Coquillat, M. Le Vassor d’Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Tsekoun, A.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
[CrossRef]

Vecchi, G.

G. Vecchi, J. Torres, D. Coquillat, M. Le Vassor d’Yerville, and A. M. Malvezzi, “Enhancement of visible second-harmonic generation in epitaxial GaN-based two-dimensional photonic crystal structures,” Appl. Phys. Lett. 84(8), 1245–1247 (2004).
[CrossRef]

Vlasov, Y. A.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[CrossRef]

Wallner, O.

Wang, Q. J.

A. Lyakh, C. Pflügl, L. Diehl, Q. J. Wang, F. Capasso, X. J. Wang, J. Y. Fan, T. Tanbun-Ek, R. Maulini, A. Tsekoun, R. Go, and C. K. N. Patel, “1.6 W high wall plug efficiency, continuous-wave room temperature quantum cascade laser emitting at 4.6 μm,” Appl. Phys. Lett. 92(11), 111110 (2008).
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Figures (6)

Fig. 1
Fig. 1

a) Top left: device cross section. Silicon nanowire widths were 400nm, 600nm, 800nm and 1000nm. b) Top right: schematic of 1cm x 1cm chip layout. Note not all devices are shown. c) Bottom left: SEM picture of fabricated device and d) Bottom right: higher magnification image of a bend with a radius of 10μm.

Fig. 2
Fig. 2

Experimental setup for measurements at λ = 5.18 μm. QCL = quantum cascade laser. The chalcogenide fiber was single mode As2Se3 fiber.

Fig. 3
Fig. 3

Cutback loss measurements for different nanowire widths (400nm to 1000nm).at λ = 1.55 μm for TE (a) Top left) and TM (b) Top right polarizations, and at λ = 2.08 μm (c) (Bottom left TE) and d) Bottom right (TM).

Fig. 4
Fig. 4

Cutback loss measurements at λ = 5.18 μm for W = 1000nm (Top) for TE polarization along with imaged mode profiles for each length.

Fig. 5
Fig. 5

Calculated effective index vs λ for TE and TM polarizations for 1000nm wide SOS nanowires, based on Finite Element Methods (FemSim RSOFT). The mode profiles are for the Ex component. The blue line is the refractive index for sapphire and so the shaded blue region represents effective indices below cutoff.

Fig. 6
Fig. 6

Calculated relative fraction (in dB) of the mode energy in the three different regions (upper cladding, core, lower cladding) as a function of wavelength normalized to cutoff. Also shown is the relative mode area.

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