Abstract

Three-dimensional bent slot waveguides are analyzed using a combined effective-index method/modified transfer-matrix method. The effective refractive index and bending loss of the guided mode can be acquired. The results closely match those calculated by the full-vectorial finite-difference method. This method also enables the calculation of field distribution, useful in estimating power confined in the narrow slot, and can handle asymmetric bent slot waveguides, bent multiple-slot waveguides, and hybrid bent slot waveguides. This approach has advantages of simplicity, versatility, and time-saving calculation, which are beneficial for the quick design of devices using bent slot waveguides.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. C. Y. Chao and L. J. Guo, "Design and optimization of microring resonators in biochemical sensing applications," J. Lightwave Technol. 24, 1395-1402 (2006).
    [CrossRef]

2007

Q. Xu and M. Lipson, "All-optical logic based on silicon micro-ring resonators," Opt. Eng. (Bellingham) 15, 924-929 (2007).

2006

T. Fujisawa and M. Koshiba, "Polarization-independent optical directional coupler based on slot waveguides," Opt. Lett. 31, 56-58 (2006).
[CrossRef] [PubMed]

C. Y. Chao and L. J. Guo, "Design and optimization of microring resonators in biochemical sensing applications," J. Lightwave Technol. 24, 1395-1402 (2006).
[CrossRef]

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savio, A. Irrera, and F. Priolo, "Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides," Appl. Phys. Lett. 89, 241114 (2006).
[CrossRef]

C. A. Barrios, "Ultrasensitive nanomechanical photonic sensor based on horizontal slot-waveguide resonator," IEEE Photon. Technol. Lett. 18, 2419-2421 (2006).
[CrossRef]

T. Fujisawa and M. Koshiba, "Theoretical investigation of ultrasmall polarization-insensitive 1×2 multimode interference waveguides based on sandwiched structures," IEEE Photon. Technol. Lett. 18, 1246-1248 (2006).
[CrossRef]

N.-N. Feng, J. Michel, and L. C. Kimerling, "Optical field concentration in low-index waveguide," IEEE J. Quantum Electron. 42, 885-890 (2006).
[CrossRef]

P. A. Andrew, B. S. Schmidt, and M. Lipson, "High confinement in silicon slot waveguides with sharp bends," Opt. Eng. (Bellingham) 14, 9197-9202 (2006).

2005

J. Lu, S. He, and V. G. Romanov, "A simple and effective method for calculating the bending loss and phase enhancement of a bent planar waveguide," Fiber Integr. Opt. 24, 25-36 (2005).
[CrossRef]

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, "High-Q optical resonators in silicon-on-insulator-based slot waveguides," Appl. Phys. Lett. 86, 081101 (2005).
[CrossRef]

T. Baehr-Jones, M. Hochberg, G. Wang, R. Lawson, Y. Liao, P. A. Sullivan, L. Dalton, A. K.-Y. Jen, and A. Scherer, "Optical modulation and detection in slotted silicon waveguides," Opt. Eng. (Bellingham) 13, 5216-5226 (2005).

2004

1990

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: a new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Appl. Phys. Lett.

M. Galli, D. Gerace, A. Politi, M. Liscidini, M. Patrini, L. C. Andreani, A. Canino, M. Miritello, R. Lo Savio, A. Irrera, and F. Priolo, "Direct evidence of light confinement and emission enhancement in active silicon-on-insulator slot waveguides," Appl. Phys. Lett. 89, 241114 (2006).
[CrossRef]

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, "High-Q optical resonators in silicon-on-insulator-based slot waveguides," Appl. Phys. Lett. 86, 081101 (2005).
[CrossRef]

Fiber Integr. Opt.

J. Lu, S. He, and V. G. Romanov, "A simple and effective method for calculating the bending loss and phase enhancement of a bent planar waveguide," Fiber Integr. Opt. 24, 25-36 (2005).
[CrossRef]

IEEE J. Quantum Electron.

N.-N. Feng, J. Michel, and L. C. Kimerling, "Optical field concentration in low-index waveguide," IEEE J. Quantum Electron. 42, 885-890 (2006).
[CrossRef]

IEEE Photon. Technol. Lett.

C. A. Barrios, "Ultrasensitive nanomechanical photonic sensor based on horizontal slot-waveguide resonator," IEEE Photon. Technol. Lett. 18, 2419-2421 (2006).
[CrossRef]

T. Fujisawa and M. Koshiba, "Theoretical investigation of ultrasmall polarization-insensitive 1×2 multimode interference waveguides based on sandwiched structures," IEEE Photon. Technol. Lett. 18, 1246-1248 (2006).
[CrossRef]

C. Y. Chao and L. J. Guo, "Reduction of surface scattering loss in polymer microrings using thermal-reflow technique," IEEE Photon. Technol. Lett. 16, 1498-1500 (2004).
[CrossRef]

J. Lightwave Technol.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: a new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

C. Y. Chao and L. J. Guo, "Design and optimization of microring resonators in biochemical sensing applications," J. Lightwave Technol. 24, 1395-1402 (2006).
[CrossRef]

Opt. Eng. (Bellingham)

T. Baehr-Jones, M. Hochberg, G. Wang, R. Lawson, Y. Liao, P. A. Sullivan, L. Dalton, A. K.-Y. Jen, and A. Scherer, "Optical modulation and detection in slotted silicon waveguides," Opt. Eng. (Bellingham) 13, 5216-5226 (2005).

Q. Xu and M. Lipson, "All-optical logic based on silicon micro-ring resonators," Opt. Eng. (Bellingham) 15, 924-929 (2007).

P. A. Andrew, B. S. Schmidt, and M. Lipson, "High confinement in silicon slot waveguides with sharp bends," Opt. Eng. (Bellingham) 14, 9197-9202 (2006).

Opt. Lett.

Other

T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, 1990).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Schematics of an asymmetric bent single-slot waveguide: (a) top view and (b) cross-sectional view in the cylindrical coordinate system.

Fig. 2
Fig. 2

Schematic of a 3D bent single-slot waveguide.

Fig. 3
Fig. 3

Effective refractive index and (b) bending loss of an air-clad silicon bent single-slot waveguide ( η = 0.5 , w = 400 nm , and h = 250 nm ) as a function of the bending radius for the fundamental quasi-TE mode under various slot sizes.

Fig. 4
Fig. 4

Bending loss of an air-clad silicon bent single-slot waveguide ( w = 400 nm and h = 250 nm ) as a function of η for (a) fixed g at 50 nm and (b) fixed R at 2.5 μ m .

Fig. 5
Fig. 5

Normalized E r of the fundamental quasi-TE mode in an air-clad silicon bent single-slot waveguide with w = 400 nm , h = 250 nm , g = 50 nm , and R = 2.5 μ m for various η (0.3, 0.5, and 0.7).

Fig. 6
Fig. 6

(a) Schematic of a curved double-slot waveguide; (b) normalized E r of an air-clad silicon bent double-slot waveguide with w = 400 nm , h = 250 nm , g 1 = g 2 = 50 nm , R = 2.5 μ m , and η 1 = η 2 = 0.25 for the fundamental quasi-TE mode. The effective refractive index of this structure is equal to 1.55619.

Equations (3)

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d 2 ψ d Z i 2 Z i ψ = 0 ,
Z i = k 0 2 n i 2 + β 2 1 4 R 2 a x a 2 3 .
det [ Ai [ Z 1 ( x 1 ) ] Ai [ Z 2 ( x 1 ) ] Bi [ Z 2 ( x 1 ) ] 0 0 0 0 0 Ai [ Z 1 ( x 1 ) ] n 1 2 Ai [ Z 2 ( x 1 ) ] n 2 2 Bi [ Z 2 ( x 1 ) ] n 2 2 0 0 0 0 0 0 Ai [ Z 2 ( x 2 ) ] Bi [ Z 2 ( x 2 ) ] Ai [ Z 3 ( x 2 ) ] Bi [ Z 3 ( x 2 ) ] 0 0 0 0 Ai [ Z 2 ( x 2 ) ] n 2 2 Bi [ Z 2 ( x 2 ) ] n 2 2 Ai [ Z 3 ( x 2 ) ] n 3 2 Bi [ Z 3 ( x 2 ) ] n 3 2 0 0 0 0 0 0 Ai [ Z 3 ( x 3 ) ] Bi [ Z 3 ( x 3 ) ] Ai [ Z 4 ( x 3 ) ] Bi [ Z 4 ( x 3 ) ] 0 0 0 0 Ai [ Z 3 ( x 3 ) ] n 3 2 Bi [ Z 3 ( x 3 ) ] n 3 2 Ai [ Z 4 ( x 3 ) ] n 4 2 Bi [ Z 4 ( x 3 ) ] n 4 2 0 0 0 0 0 0 Ai [ Z 4 ( x 4 ) ] Bi [ Z 4 ( x 4 ) ] j Ai [ Z 5 ( x 4 ) ] Bi [ Z 5 ( x 4 ) ] 0 0 0 0 0 Ai [ Z 4 ( x 4 ) ] n 4 2 Bi [ Z 4 ( x 4 ) ] n 4 2 j Ai [ Z 5 ( x 4 ) ] n 5 2 Bi [ Z 5 ( x 4 ) ] n 5 2 ] = 0 .

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