Abstract

We propose a nanometer-scale hollow core waveguide that can be fabricated with standard methods on a silicon-on-insulator substrate. High optical confinement in the core is possible, making such a waveguide structure suitable for sensing applications, applications making use of strong optical nonlinearities, and optofluidics applications. We extend a historical method (Marcatili’s method) to provide analytical solutions for field distributions in the device and simulate power confinement, intensity, and parametric dependencies with beam propagation and finite-difference time-domain methods for two polarizations. In an example worked out, the optical confinement in the air core is 40% of the total waveguide power, which is favorable to that of a standard slot waveguide. The intensity per μm2 in the hollow core is 95% higher than in the silicon cladding region, indicating that avoiding optical nonlinearities is also possible.

© 2010 Optical Society of America

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References

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2009

2008

2007

2006

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, “On-chip microfluidic tuning of an optical microring resonator,” Appl. Phys. Lett. 88, 111107 (2006).
[CrossRef]

P. A. Anderson, B. S. Schmidt, and M. Lipson, “High confinement in silicon slot waveguides with sharp bends,” Opt. Express 14, 9197–9202 (2006).
[CrossRef] [PubMed]

D. Psaltis, S. R. Quake, and C. H. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

D. Erickson, T. Rockwood, T. Emery, A. Scherer, and D. Psaltis, “Nanofluidic tuning of photonic crystal circuits,” Opt. Lett. 31, 59–61 (2006).
[CrossRef] [PubMed]

2005

2004

W. P. Risk, H. C. Kim, R. D. Miller, H. Temkin, and S. Gangopadhyay, “Optical waveguides with an aqueous core and a low-index nanoporous cladding,” Opt. Express 12, 6446–6455 (2004).
[CrossRef] [PubMed]

D. Yin, J. P. Barber, A. R. Hawkins, D. W. Dreamer, and H. Schmidt, “Integrated optical waveguides with liquid cores,” Appl. Phys. Lett. 85, 3477–3479 (2004).
[CrossRef]

V. R. Almeida, Q. F. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004).
[CrossRef] [PubMed]

C. A. Barrios, “High-performance all optical silicon microswitch,” Electron. Lett. 40, 862–863 (2004).
[CrossRef]

1969

E. A. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).

Almeida, V. R.

Anderson, P. A.

Ang, Y. L.

Barber, J. P.

D. Yin, J. P. Barber, A. R. Hawkins, D. W. Dreamer, and H. Schmidt, “Integrated optical waveguides with liquid cores,” Appl. Phys. Lett. 85, 3477–3479 (2004).
[CrossRef]

Barrios, C. A.

Campbell, K.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, “On-chip microfluidic tuning of an optical microring resonator,” Appl. Phys. Lett. 88, 111107 (2006).
[CrossRef]

Chan, S. P.

Chen, L.

Daldosso, N.

Dell’Olio, F.

Dreamer, D. W.

D. Yin, J. P. Barber, A. R. Hawkins, D. W. Dreamer, and H. Schmidt, “Integrated optical waveguides with liquid cores,” Appl. Phys. Lett. 85, 3477–3479 (2004).
[CrossRef]

Emery, T.

Erickson, D.

Fainman, Y.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, “On-chip microfluidic tuning of an optical microring resonator,” Appl. Phys. Lett. 88, 111107 (2006).
[CrossRef]

Fedeli, J. -M.

Gangopadhyay, S.

Groisman, A.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, “On-chip microfluidic tuning of an optical microring resonator,” Appl. Phys. Lett. 88, 111107 (2006).
[CrossRef]

Guider, R.

Hawkins, A. R.

D. Yin, J. P. Barber, A. R. Hawkins, D. W. Dreamer, and H. Schmidt, “Integrated optical waveguides with liquid cores,” Appl. Phys. Lett. 85, 3477–3479 (2004).
[CrossRef]

Jordana, E.

Kim, H. C.

Levy, U.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, “On-chip microfluidic tuning of an optical microring resonator,” Appl. Phys. Lett. 88, 111107 (2006).
[CrossRef]

Lim, S. T.

Lipson, M.

Marcatili, E. A.

E. A. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).

Miller, R. D.

Mookherjea, S.

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, “On-chip microfluidic tuning of an optical microring resonator,” Appl. Phys. Lett. 88, 111107 (2006).
[CrossRef]

Ong, E. A.

Passaro, V. M. N.

Pavesi, L.

Pitanti, A.

Png, C. E.

Psaltis, D.

D. Psaltis, S. R. Quake, and C. H. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

D. Erickson, T. Rockwood, T. Emery, A. Scherer, and D. Psaltis, “Nanofluidic tuning of photonic crystal circuits,” Opt. Lett. 31, 59–61 (2006).
[CrossRef] [PubMed]

Quake, S. R.

D. Psaltis, S. R. Quake, and C. H. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

Reed, G. T.

Risk, W. P.

Robinson, J. T.

Rockwood, T.

Scherer, A.

Schmidt, B. S.

Schmidt, H.

D. Yin, J. P. Barber, A. R. Hawkins, D. W. Dreamer, and H. Schmidt, “Integrated optical waveguides with liquid cores,” Appl. Phys. Lett. 85, 3477–3479 (2004).
[CrossRef]

Temkin, H.

Xu, Q. F.

Yang, C. H.

D. Psaltis, S. R. Quake, and C. H. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

Yin, D.

D. Yin, J. P. Barber, A. R. Hawkins, D. W. Dreamer, and H. Schmidt, “Integrated optical waveguides with liquid cores,” Appl. Phys. Lett. 85, 3477–3479 (2004).
[CrossRef]

Appl. Phys. Lett.

D. Yin, J. P. Barber, A. R. Hawkins, D. W. Dreamer, and H. Schmidt, “Integrated optical waveguides with liquid cores,” Appl. Phys. Lett. 85, 3477–3479 (2004).
[CrossRef]

U. Levy, K. Campbell, A. Groisman, S. Mookherjea, and Y. Fainman, “On-chip microfluidic tuning of an optical microring resonator,” Appl. Phys. Lett. 88, 111107 (2006).
[CrossRef]

Bell Syst. Tech. J.

E. A. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48, 2071–2102 (1969).

Electron. Lett.

C. A. Barrios, “High-performance all optical silicon microswitch,” Electron. Lett. 40, 862–863 (2004).
[CrossRef]

J. Lightwave Technol.

Nature

D. Psaltis, S. R. Quake, and C. H. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

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Figures (5)

Fig. 1
Fig. 1

Marcatili’s method provides solutions in the numbered regions as shown in this cross section. The inner slot (Region 1) that has index n s is surrounded by a high index region of index n h , which is further surrounded by a cladding of index n c .

Fig. 2
Fig. 2

Normalized transverse electric field of an embedded air core surrounded by a high index material (Si) n h = 3.477 , n c = 1.444 , and n s = 1 with w and t = 50   nm and w Si and t Si = 650   nm in the quasi-TE mode.

Fig. 3
Fig. 3

Core optical power P core , normalized average core intensity I core (it is a cross-sectional area average), and normalized silicon substrate average intensity I Si for both quasi-TE and quasi-TM polarizations.

Fig. 4
Fig. 4

Core optical power P core , normalized average core intensity I core per μ m 2 , and normalized silicon substrate average intensity I Si for different waveguide widths ( w = 50 , 70, and 90 nm). (a) quasi-TE polarization and (b) quasi-TM polarization.

Fig. 5
Fig. 5

Effective index of the propagating mode for both polarizations and various core widths as a function of core height.

Equations (9)

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Region   1 :     E x = E 0   cosh ( γ s x x ) cosh ( γ s y y ) ,
Region   2 :     E x = E 0   cosh ( γ s y b ) cosh ( γ s x x ) cos [ k h y ( | y | b ) ] + E 0 γ s y k h y sinh ( γ s y b ) cosh ( γ s x x ) sin [ k h y ( | y | b ) ] ,
Region   3 :     E x = E 0 β 2 γ s x 2 β 2 + k h x 2 cosh ( γ s x a ) cosh ( γ s y y ) cos [ k h x ( | x | a ) ] + E 0 γ s x k h x sinh ( γ s x a ) cosh ( γ s y y ) sin [ k h x ( | x | a ) ] ,
Region   4 :     E x = E 0 [ cosh ( γ s y b ) cos [ k h y ( d b ) ] + γ s y k h y sinh ( γ s y b ) sin [ k h y ( d b ) ] ] cosh ( γ s x x ) e γ ( | y | d ) ,
Region   5 :     E x = E 0 [ k h x γ c x ( β 2 γ s x 2 β 2 + k h x 2 ) cosh ( γ s x a ) sin [ k h x ( c a ) ] γ s x γ c x sinh ( γ s x a ) cos [ k h x ( c a ) ] ] cosh ( γ s y y ) e γ ( | x | c ) .
β 2 = k 0 2 n s 2 + γ s x 2 + γ s y 2 = k 0 2 n h 2 + γ s y 2 k h x 2 = k 0 2 n h 2 + γ s x 2 k h y 2 = k 0 2 n c 2 + γ c x 2 + γ s y 2 = k 0 2 n c 2 + γ c y 2 + γ s x 2 ,
k h y γ c y sin   ϕ 1 cos   ϕ 1 = γ s y k h y tanh ( γ s y b ) [ k h y γ c y cos   ϕ 1 + sin   ϕ 1 ] ,
β 2 γ s x 2 β 2 + k h x 2 [ k h x γ c x sin   ϕ 2 ( β 2 + k h x 2 β 2 γ c x 2 ) cos   ϕ 2 ] = γ s x k h x tanh ( γ s x a ) [ ( β 2 + k h x 2 β 2 γ c x 2 ) sin   ϕ 2 + k h x γ c x cos   ϕ 2 ] .
S h = | n eff n s | n c = n c 0 ,

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