Abstract

The undercut long-wave infrared (LWIR) waveguide components with air-gap beneath are analyzed and fabricated on the Si-wafer with simple manufacturing process. A 1 × 2 multimode interference (MMI) splitter based on this structure is presented and measured under the 10.6μm wavelength experimental setup. The uniformity of the MMI fabricated is 0.76 dB. The relationship among the output power, slab thickness and air-gap width is also fully discussed. Furthermore, undercut straight waveguides based on SOI platform are fabricated for propagation loss evaluation. Ways to reduce the loss are discussed either.

© 2011 OSA

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References

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  1. R. Soref, S. J. Emelett, and W. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
    [CrossRef]
  2. 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]
  3. 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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
    [CrossRef]
  4. B. Jalali, “Silicon photonics nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
    [CrossRef]
  5. V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a mid-infrared silicon Raman amplifier,” Opt. Express 15(22), 14355–14362 (2007).
    [CrossRef] [PubMed]
  6. X. P. 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]
  7. X. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, Y. A. Vlasov, and M. J. Green, “ Mid-infrared pulse dynamics in Si nanophotonic wires near the two-photon absorption edge,” in Conference on Lasers and Electro-optics, Technical Digest (CD) (Optical Society of America, 2009), paper CFR5, http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2009-CFR5 .
  8. www.irphotonics.com .
  9. G. T. Reed, Silicon Photonics: the State of the Art (Wiley, 2008).
  10. R. Soref, “Towards silicon-based longwave integrated optoelectronics (LIO),” Proc. SPIE 6898, 689809 (2008).
    [CrossRef]
  11. M. M. Milošević, P. S. Matavulj, P. Y. Yang, A. Bagolini, and G. Z. Mashanovich, “Rib waveguides for mid-infrared silicon photonics,” J. Opt. Soc. Am. B 26(9), 1760–1766 (2009).
    [CrossRef]
  12. 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]
  13. G. Z. Mashanovich, W. R. Headley, M. M. Milosevic, N. Owens, E. J. Teo, B. Q. Xiong, P. Y. Yang, M. Nedeljkovic, J. Anguita, I. Marko, and Y. Hu, “Waveguides for mid-infrared group IV photonics,” in 7th IEEE International Conference on Group IV Photonics 2010, (IEEE, 2010), pp. 374–376.
  14. 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]
  15. R. Shankar, R. Leijssen, I. Bulu, and M. Lončar, “Mid-infrared photonic crystal cavities in silicon,” Opt. Express 19(6), 5579–5586 (2011).
    [CrossRef] [PubMed]
  16. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985), Vol.1.
  17. R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
    [CrossRef]
  18. www.rsoftdesign.com .
  19. G. T. Reed, “An introduction to silicon photonics,” in Optical Interconnects: the Silicon Approach (Springer, 2006), pp. 161–204.

2011 (2)

2010 (4)

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]

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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

B. Jalali, “Silicon photonics nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
[CrossRef]

X. P. 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]

2009 (2)

M. M. Milošević, P. S. Matavulj, P. Y. Yang, A. Bagolini, and G. Z. Mashanovich, “Rib waveguides for mid-infrared silicon photonics,” J. Opt. Soc. Am. B 26(9), 1760–1766 (2009).
[CrossRef]

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]

2008 (1)

R. Soref, “Towards silicon-based longwave integrated optoelectronics (LIO),” Proc. SPIE 6898, 689809 (2008).
[CrossRef]

2007 (1)

2006 (1)

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

1991 (1)

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Baehr-Jones, T.

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]

Bagolini, A.

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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Borlaug, D.

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

Bulu, I.

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]

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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Emelett, S. J.

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

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]

Green, W. M. J.

X. P. 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.

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]

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]

Jalali, B.

Leijssen, R.

Liu, X. P.

X. P. 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]

Loncar, M.

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]

M. M. Milošević, P. S. Matavulj, P. Y. Yang, A. Bagolini, and G. Z. Mashanovich, “Rib waveguides for mid-infrared silicon photonics,” J. Opt. Soc. Am. B 26(9), 1760–1766 (2009).
[CrossRef]

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]

Matavulj, P. S.

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 sorce,” 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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Nedeljkovic, M.

Osgood, R. M.

X. P. 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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Petermann, K.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Raghunathan, V.

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]

Rice, R. R.

Schmidtchen, J.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[CrossRef]

Shankar, R.

Soref, R.

R. Soref, “Towards silicon-based longwave integrated optoelectronics (LIO),” Proc. SPIE 6898, 689809 (2008).
[CrossRef]

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

Soref, R. A.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[CrossRef]

Spott, A.

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]

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]

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]

Vlasov, Y. A.

X. P. 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]

Xiong, B.

Yang, P. Y.

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]

M. M. Milošević, P. S. Matavulj, P. Y. Yang, A. Bagolini, and G. Z. Mashanovich, “Rib waveguides for mid-infrared silicon photonics,” J. Opt. Soc. Am. B 26(9), 1760–1766 (2009).
[CrossRef]

Zlatanovic, 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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

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]

IEEE J. Quantum Electron. (1)

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971–1974 (1991).
[CrossRef]

J. Mater. Sci. Mater. Electron. (1)

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]

J. Opt. A, Pure Appl. Opt. (1)

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

J. Opt. Soc. Am. B (1)

Nat. Photonics (3)

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 sorce,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

B. Jalali, “Silicon photonics nonlinear optics in the mid-infrared,” Nat. Photonics 4(8), 506–508 (2010).
[CrossRef]

X. P. 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]

Opt. Express (3)

Proc. SPIE (1)

R. Soref, “Towards silicon-based longwave integrated optoelectronics (LIO),” Proc. SPIE 6898, 689809 (2008).
[CrossRef]

Other (7)

G. Z. Mashanovich, W. R. Headley, M. M. Milosevic, N. Owens, E. J. Teo, B. Q. Xiong, P. Y. Yang, M. Nedeljkovic, J. Anguita, I. Marko, and Y. Hu, “Waveguides for mid-infrared group IV photonics,” in 7th IEEE International Conference on Group IV Photonics 2010, (IEEE, 2010), pp. 374–376.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985), Vol.1.

www.rsoftdesign.com .

G. T. Reed, “An introduction to silicon photonics,” in Optical Interconnects: the Silicon Approach (Springer, 2006), pp. 161–204.

X. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, Y. A. Vlasov, and M. J. Green, “ Mid-infrared pulse dynamics in Si nanophotonic wires near the two-photon absorption edge,” in Conference on Lasers and Electro-optics, Technical Digest (CD) (Optical Society of America, 2009), paper CFR5, http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2009-CFR5 .

www.irphotonics.com .

G. T. Reed, Silicon Photonics: the State of the Art (Wiley, 2008).

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic cross section of the silicon undercut waveguide. (b) Rib waveguide based on silicon wafer with an air-gap beneath

Fig. 2
Fig. 2

Slab thickness vs. normalized output power under different Wair

Fig. 3
Fig. 3

BPM Simulation results of the undercut 1 × 2 MMI splitter.

Fig. 4
Fig. 4

(a) Output and (b) Input port of the multimode interference area of the undercut MMI splitter under confocal microscopy scan after the second round wet etching.

Fig. 5
Fig. 5

Cross section of input and multimode interference area of the undercut MMI under confocal microscopy scan.

Fig. 6
Fig. 6

Experimental set-up for LWIR waveguides

Fig. 7
Fig. 7

Propagation loss of the SOI undercut straight waveguides.

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