Abstract

We revisit the problem of the optimization of a silicon-nanocrystal (Si-NC) waveguide, aiming to attain the maximum field confinement inside its nonlinear core and to ensure optimal waveguide performance for a given mode power. Using a Si-NC/SiO2 slot waveguide as an example, we show that the common definition of the effective mode area may lead to significant errors in estimation of optical intensity governing the nonlinear optical response and, as a result, to poor strength evaluation of the associated nonlinear effects. A simple and physically meaningful definition of the effective mode area is given to relate the total mode power to the average field intensity inside the nonlinear region and is employed to study the optimal parameters of Si-NC slot waveguides.

© 2012 Optical Society of America

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References

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2011

F. De Leonardis and V. M. N. Passaro, Adv. Optoelectron. 2011, 1 (2011).
[CrossRef]

2010

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

2009

2008

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, IEEE J. Quantum Electron. 44, 692 (2008).
[CrossRef]

2007

2004

Afshar V, S.

Agrawal, G. P.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, Opt. Express 17, 22124 (2009).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Blasco, J.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, J. Lightwave Technol. 25, 1298 (2007).
[CrossRef]

Brinkmeyer, E.

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, IEEE J. Quantum Electron. 44, 692 (2008).
[CrossRef]

Daldosso, N.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

De Leonardis, F.

F. De Leonardis and V. M. N. Passaro, Adv. Optoelectron. 2011, 1 (2011).
[CrossRef]

Fathpour, S.

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, IEEE J. Quantum Electron. 44, 692 (2008).
[CrossRef]

Fedeli, J. M.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Foster, M. A.

Freude, W.

Gaeta, A. L.

Galan, J. V.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Garcia-Ruperez, J.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Garrido, B.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Gautier, P.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Guider, R.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Hernandez, S.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Jacome, L.

Jalali, B.

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, IEEE J. Quantum Electron. 44, 692 (2008).
[CrossRef]

Jordana, E.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Koos, C.

Krause, M.

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, IEEE J. Quantum Electron. 44, 692 (2008).
[CrossRef]

Lebour, Y.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Leuthold, J.

Marti, J.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, J. Lightwave Technol. 25, 1298 (2007).
[CrossRef]

Martinez, A.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, J. Lightwave Technol. 25, 1298 (2007).
[CrossRef]

Moll, K. D.

Monro, T. M.

Passaro, V. M. N.

F. De Leonardis and V. M. N. Passaro, Adv. Optoelectron. 2011, 1 (2011).
[CrossRef]

Pavesi, L.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Poulton, C.

Premaratne, M.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, Opt. Express 17, 22124 (2009).
[CrossRef]

Renner, H.

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, IEEE J. Quantum Electron. 44, 692 (2008).
[CrossRef]

Rukhlenko, I. D.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, Opt. Express 17, 22124 (2009).
[CrossRef]

Sanchis, P.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

P. Sanchis, J. Blasco, A. Martinez, and J. Marti, J. Lightwave Technol. 25, 1298 (2007).
[CrossRef]

Spano, R.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Adv. Optoelectron.

F. De Leonardis and V. M. N. Passaro, Adv. Optoelectron. 2011, 1 (2011).
[CrossRef]

IEEE J. Quantum Electron.

M. Krause, H. Renner, S. Fathpour, B. Jalali, and E. Brinkmeyer, IEEE J. Quantum Electron. 44, 692 (2008).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, IEEE J. Sel. Top. Quantum Electron. 16, 200 (2010).
[CrossRef]

J. Lightwave Technol.

Nano Lett.

A. Martinez, J. Blasco, P. Sanchis, J. V. Galan, J. Garcia-Ruperez, E. Jordana, P. Gautier, Y. Lebour, S. Hernandez, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Marti, Nano Lett. 10, 1506 (2010).
[CrossRef]

Opt. Express

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Si-NC/SiO2 slot waveguide, (b) three types of EMAs, and (c) effective index and transversality of the fundamental quasi-TM mode as functions of waveguide width for 500 and 700 nm thick waveguides. Density plots of Poynting vector in (d)–(h) correspond to locations marked in (b). In all cases, f=0.1 and t=100nm. For other parameters, refer to the text.

Fig. 2.
Fig. 2.

(a) Effective mode area, (b) effective mode index and transversality as functions of Si-NC fraction f in the slot region for three waveguides corresponding to points (d), (e), and (f) in Fig. 1(b). Upper scales show the effective refractive index of Si-NC/SiO2 composite. Material parameters are the same as in Fig. 1.

Fig. 3.
Fig. 3.

Effective mode area versus (a) thickness of Si-NC/SiO2 layer and (b) scaling factor q for f=0.1. Legends above the panels show waveguide dimensions and equations employed. Two sets of curves in (b) correspond to optimum waveguide parameters in Fig. 1(e): h0=500nm, w0=200nm, t0=100nm; and in Fig. 1(g): h0=700nm, w0=130nm, t0=100nm. For other parameters, refer to the text.

Equations (5)

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

Aeff=(Szdxdy)2/Sz2dxdy,
Aeff=(|F(x,y)|2dxdy)2/|F(x,y)|4dxdy,
aeff=aNLSzdxdy/NLSzdxdy,
Aeff=πSz(x2+y2)dxdy/Szdxdy,
τ=(|Ex|2+|Ey|2)dxdy/|E|2dxdy,

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