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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, "Guiding and confining light in void nanostructure," Opt. Lett. 29, 1209-1211 (2004).
    [CrossRef] [PubMed]
  2. Q. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, "Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material," Opt. Lett. 29, 1626-1628 (2004).
    [CrossRef] [PubMed]
  3. 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]
  4. 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).
  5. 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]
  6. Q. Xu and M. Lipson, "All-optical logic based on silicon micro-ring resonators," Opt. Eng. (Bellingham) 15, 924-929 (2007).
  7. T. Fujisawa and M. Koshiba, "Polarization-independent optical directional coupler based on slot waveguides," Opt. Lett. 31, 56-58 (2006).
    [CrossRef] [PubMed]
  8. C. A. Barrios, "Ultrasensitive nanomechanical photonic sensor based on horizontal slot-waveguide resonator," IEEE Photon. Technol. Lett. 18, 2419-2421 (2006).
    [CrossRef]
  9. 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]
  10. 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]
  11. 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).
  12. 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]
  13. 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]
  14. T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, 1990).
    [CrossRef]
  15. 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]
  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 (1)

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

2006 (7)

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

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).

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

2005 (3)

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 (3)

1990 (1)

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. (2)

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]

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]

Fiber Integr. Opt. (1)

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. (1)

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. (3)

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]

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]

J. Lightwave Technol. (2)

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]

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]

Opt. Eng. (Bellingham) (3)

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).

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

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).

Opt. Lett. (3)

Other (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

Equations on this page are rendered with MathJax. Learn more.

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 .

Metrics