Abstract

We propose and study slot waveguide geometries where both quasi-TE and quasi-TM modes may propagate highly confined within the same low-index slot region. Conventional horizontal and vertical slot waveguides can only provide high slot confinement for either the quasi-TM or quasi-TE modes, respectively. Different two-dimensional slot waveguide structures are analyzed in terms of their mode characteristics, such as the effective index, the confinement factor, and the overlap of quasi-TE and -TM modes within the slot. Attention is also paid to practical manufacturability. Various waveguide structures can be tailored to have zero birefringence or equal confinement at both polarizations. Values for the confinement factors and the overlap of the two polarizations, in the slot region, can reach 0.4 to 0.5.

© 2010 Optical Society of America

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2010 (1)

2009 (6)

2008 (1)

A. Khanna, M. Mulot, S. Arpiainen, A. Saynatjoki, J. Ahopelto, S. Honkanen, and H. Lipsanen, “Amorphous silicon optical waveguides and Bragg mirrors,” Proc. SPIE 6996, 699605(2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (2)

H. Dötsch, N. Bahlmann, O. Zhuromskyy, M. Hammer, L. Wilkens, R. Gerhardt, P. Hertel, and A. F. Popkov, “Applications of magneto-optical waveguides in integrated optics: review,” J. Opt. Soc. Am. B 22, 240–253 (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]

2004 (1)

1993 (1)

A. Sv. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculation in dielectric waveguides,” Pure Appl. Opt. 2, 211–233 (1993).
[CrossRef]

Ahopelto, J.

A. Khanna, M. Mulot, S. Arpiainen, A. Saynatjoki, J. Ahopelto, S. Honkanen, and H. Lipsanen, “Amorphous silicon optical waveguides and Bragg mirrors,” Proc. SPIE 6996, 699605(2008).
[CrossRef]

Alasaarela, T.

Almeida, V. R.

Arpiainen, S.

A. Khanna, M. Mulot, S. Arpiainen, A. Saynatjoki, J. Ahopelto, S. Honkanen, and H. Lipsanen, “Amorphous silicon optical waveguides and Bragg mirrors,” Proc. SPIE 6996, 699605(2008).
[CrossRef]

Baehr-Jones, T.

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]

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Bahlmann, N.

Barrios, C. A.

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Blasco, J.

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Dong, P.

Dötsch, H.

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Feng, N.

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Fujisawa, T.

Galan, J. V.

Gangopadhyay, P.

A. Lopez-Santiago, P. Gangopadhyay, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, “Faraday rotation in magnetite-polymethylmethacrylate core-shell nanocomposites with high optical quality,” Appl. Phys. Lett. 95, 143302 (2009).
[CrossRef]

Garcia, J.

Gerhardt, R.

Hainberger, R.

Hammer, M.

Hertel, P.

Hochberg, M.

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]

Hong, C.

Honkanen, S.

Karvonen, L.

Khanna, A.

Kimerling, L.

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Koshiba, M.

Kuittinen, M.

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Lipsanen, H.

A. Khanna, M. Mulot, S. Arpiainen, A. Saynatjoki, J. Ahopelto, S. Honkanen, and H. Lipsanen, “Amorphous silicon optical waveguides and Bragg mirrors,” Proc. SPIE 6996, 699605(2008).
[CrossRef]

Lipson, M.

Lopez-Santiago, A.

A. Lopez-Santiago, P. Gangopadhyay, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, “Faraday rotation in magnetite-polymethylmethacrylate core-shell nanocomposites with high optical quality,” Appl. Phys. Lett. 95, 143302 (2009).
[CrossRef]

Martí, J.

Martinez, A.

Michel, J.

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Muellner, P.

Mulot, M.

A. Khanna, M. Mulot, S. Arpiainen, A. Saynatjoki, J. Ahopelto, S. Honkanen, and H. Lipsanen, “Amorphous silicon optical waveguides and Bragg mirrors,” Proc. SPIE 6996, 699605(2008).
[CrossRef]

Norwood, R. A.

A. Lopez-Santiago, P. Gangopadhyay, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, “Faraday rotation in magnetite-polymethylmethacrylate core-shell nanocomposites with high optical quality,” Appl. Phys. Lett. 95, 143302 (2009).
[CrossRef]

Persoons, A.

A. Lopez-Santiago, P. Gangopadhyay, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, “Faraday rotation in magnetite-polymethylmethacrylate core-shell nanocomposites with high optical quality,” Appl. Phys. Lett. 95, 143302 (2009).
[CrossRef]

Peyghambarian, N.

A. Lopez-Santiago, P. Gangopadhyay, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, “Faraday rotation in magnetite-polymethylmethacrylate core-shell nanocomposites with high optical quality,” Appl. Phys. Lett. 95, 143302 (2009).
[CrossRef]

Popkov, A. F.

Sanchis, P.

Saynatjoki, A.

A. Khanna, M. Mulot, S. Arpiainen, A. Saynatjoki, J. Ahopelto, S. Honkanen, and H. Lipsanen, “Amorphous silicon optical waveguides and Bragg mirrors,” Proc. SPIE 6996, 699605(2008).
[CrossRef]

Säynätjoki, A.

Scherer, A.

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]

Stenberg, P.

Sudbo, A. Sv.

A. Sv. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculation in dielectric waveguides,” Pure Appl. Opt. 2, 211–233 (1993).
[CrossRef]

Sun, R.

Tervonen, A.

Thomas, J.

A. Lopez-Santiago, P. Gangopadhyay, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, “Faraday rotation in magnetite-polymethylmethacrylate core-shell nanocomposites with high optical quality,” Appl. Phys. Lett. 95, 143302 (2009).
[CrossRef]

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Walker, C.

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]

Wellenzohn, M.

Wilkens, L.

Xiao-Li, Y.

Xu, Q.

Zhuromskyy, O.

Appl. Opt. (2)

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]

A. Lopez-Santiago, P. Gangopadhyay, J. Thomas, R. A. Norwood, A. Persoons, and N. Peyghambarian, “Faraday rotation in magnetite-polymethylmethacrylate core-shell nanocomposites with high optical quality,” Appl. Phys. Lett. 95, 143302 (2009).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nat. Photon. (1)

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photon. 3, 216–219 (2009).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (1)

A. Khanna, M. Mulot, S. Arpiainen, A. Saynatjoki, J. Ahopelto, S. Honkanen, and H. Lipsanen, “Amorphous silicon optical waveguides and Bragg mirrors,” Proc. SPIE 6996, 699605(2008).
[CrossRef]

Pure Appl. Opt. (1)

A. Sv. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculation in dielectric waveguides,” Pure Appl. Opt. 2, 211–233 (1993).
[CrossRef]

Other (1)

FIMMWAVE Ver 5.0.2, Photon Design, www.photond.com.

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Figures (24)

Fig. 1
Fig. 1

Schematic of the ideal closed 2-D slot waveguide and its main parameters.

Fig. 2
Fig. 2

Distribution of E y field component of quasi-TM mode of the ideal closed 2-D slot waveguide with w = h = 500 nm and c = 60 nm . (a) Contour plot. (b) Distribution at the vertical symmetry line, and (c) distribution at the horizontal symmetry line.

Fig. 3
Fig. 3

For a square slot cross section with w = h , variation of (a) effective index n eff , (b) confinement Γ, and (c) overlap coefficient κ / θ F , versus width w of the ideal closed 2-D slot waveguide.

Fig. 4
Fig. 4

Variation of (a) effective index n eff , (b) confinement Γ, and (c) overlap coefficient κ / θ F , versus height h in an ideal closed 2-D slot waveguide.

Fig. 5
Fig. 5

Schematic of a practical geometry for a closed 2-D slot waveguide.

Fig. 6
Fig. 6

(a) Contour plot of the E x component of the electric field of the quasi-TE mode and (b) E x component of the electric field distribution for the quasi-TE mode along the horizontal section at y = 7.7 μm in Fig. 6a for a practical closed 2-D slot waveguide. Parameters used for simulation are c top = 45 nm , c low = 30 nm , w = h = 500 nm , and L = 800 nm .

Fig. 7
Fig. 7

(a) Contour plot of the E y component of electric field of quasi-TM mode and (b) E y component of the electric field distribution for the quasi-TM mode across a vertical section at x = 7.5 μm in Fig. 7a for a practical closed 2-D slot waveguide. Parameters used for simulation are c top = 45 nm , c low = 30 nm , w = h = 500 nm , and L = 800 nm .

Fig. 8
Fig. 8

Variation in (a) n eff , (b) Γ, and (c) κ / θ F for change in aspect ratio in a practical closed 2-D slot waveguide when w = 300 , 500 nm , c low = 30 nm , and c top = 60 nm . L = 600 nm for w = 300 nm , and L = 800 nm for w = 500 nm .

Fig. 9
Fig. 9

Variation in (a) n eff , (b) Γ, and (c) κ / θ F for change in thickness of undercladding c low in a practical closed 2-D slot waveguide when w = h = 300 , 500 nm , and c top = 60 nm . L = 600 nm for w = 300 nm , and L = 800 nm for w = 500 nm .

Fig. 10
Fig. 10

Variation in (a) n eff , (b) Γ, and (c) κ / θ F versus overcladding thickness c top in a practical closed 2-D slot waveguide when w = 300 , 500 nm , and c low = 30 nm . L = 600 nm for w = 300 nm , and L = 800 nm for w = 500 nm .

Fig. 11
Fig. 11

Variation in (a) n eff , (b) Γ, and (c) κ / θ F versus undercladding width L in a practical closed 2-D slot waveguide when w = 300 , 500 nm , c low = 30 nm , and c top = 60 nm . L = 600 nm for w = 300 nm , and L = 800 nm for w = 500 nm .

Fig. 12
Fig. 12

Schematic of an open 2-D slot waveguide with overcladding thickness c, width w, and height h.

Fig. 13
Fig. 13

(a) Contour plot of the E x field component of the quasi-TE mode and (b) E x field component of the quasi-TE mode across a horizontal section in Fig. 13a at y = 7.9 μm for an open 2-D slot waveguide where w = h = 300 nm and c = 60 nm .

Fig. 14
Fig. 14

(a) Contour plot of the E y field component of the quasi-TM mode and (b) E y field component of the quasi-TM mode across a vertical section in Fig. 14a at x = 7.5 μm for an open 2-D slot waveguide where w = h = 300 nm and c = 60 nm .

Fig. 15
Fig. 15

Variation in (a) effective index n eff , (b) confinement Γ, and (c) overlap coefficient κ / θ F , versus w = h and c = 60 nm for an open 2-D slot waveguide.

Fig. 16
Fig. 16

Variation in (a) effective index n eff , (b) confinement Γ, and (c) overlap coefficient κ / θ F , versus c for an open 2-D slot waveguide, where w = h .

Fig. 17
Fig. 17

Variation in (a) effective index n eff , (b) confinement Γ, and (c) overlap coefficient κ / θ F , versus height h for an open 2-D slot waveguide where w = 500 nm and c = 60 nm .

Fig. 18
Fig. 18

(a) Schematic of the O-slot waveguide with annular slot thickness s, outer frame thickness c, and inner rail cross-section width w and height h. (b) Schematic of a practical U-slot waveguide.

Fig. 19
Fig. 19

(a) Contour plot of the E x field of the quasi-TE mode, (b) section plot at y = 2.4 μm , and (c) section plot at y = 2.05 μm for a U-slot waveguide where w = h = 250 nm , s = 300 nm , and c = 50 nm .

Fig. 20
Fig. 20

(a) Contour plot of the E y field of the quasi-TM mode and (b) section plot at x = 3 μm for a U-slot waveguide where w = h = 250 nm , s = 300 nm , and c = 50 nm .

Fig. 21
Fig. 21

Contour plots of the E y component of the electric field of the fundamental quasi-TM mode in a U-slot waveguide with (a) w = h = 250 nm , s = 300 nm , and c = 0 nm ; (b) w = h = 250 nm , s = 300 nm , and c = 50 nm ; and (c) w = h = 200 nm , s = 300 nm , and c = 50 nm .

Fig. 22
Fig. 22

(a) Effective index n eff , (b) confinement Γ, and (c) overlap coefficient κ / θ F in a U-slot waveguide with s = 300 nm as a function of c with three inner rail sizes: w = h = 250 , 200, and 150 nm .

Fig. 23
Fig. 23

(a) Effective index n eff , (b) confinement Γ, and (c) overlap coefficient κ / θ F in a U-slot waveguide with c = 50 nm as a function of s with w = h = 250 , 200, and 150 nm .

Fig. 24
Fig. 24

(a) Effective index n eff , (b) confinement Γ, and (c) overlap coefficient κ / θ F in a U-slot waveguide with c = 50 nm and s = 300 nm as a function of w with h = 240 and 200 nm .

Equations (4)

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

Γ = n 0 2 Z 0 slot | E ¯ | 2 d x d y .
κ = ω ε 0 4 slot E TE , x * E TM , y d x d y .
ε x y = 2 n o k o Θ F .
κ / Θ F = 2 n 0 ω ε 0 4 k 0 slot E TE , x * E TM , y d x d y = n 0 2 Z 0 slot E TE , x * E TM , y d x d y .

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