Abstract

We investigate the nonlinearity of ultra-low loss Si3N4-core and SiO2-cladding rectangular waveguides. The nonlinearity is modeled using Maxwell’s wave equation with a small amount of refractive index perturbation. Effective n2 is used to describe the third-order nonlinearity, which is linearly proportional to the optical intensity. The effective n2 measured using continuous-wave self-phase modulation shows agreement with the theoretical calculation. The waveguide with 2.8-μm wide and 80-nm thick Si3N4 core has low loss and high power handling capability, with an effective n2 of about 9×1016cm2/W.

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References

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  1. A. Boskovic, S. V. Chernikov, J. R. Taylor, L. Gruner-Nielsen, and O. A. Levring, “Direct continuous-wave measurement of n_2 in various types of telecommunication fiber at 155 µm,” Opt. Lett. 21(24), 1966–1968 (1996).
    [CrossRef] [PubMed]
  2. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
    [CrossRef] [PubMed]
  3. J. F. Bauters, M. J. R. Heck, D. John, M.-C. Tien, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. Bowers, “Ultra-low loss silica-based waveguides with millimeter bend radius,” in ECOC(Torino, Italy, 2010).
  4. R. S. Grant, “Effective non-linear coefficients of optical waveguides,” Opt. Quantum Electron. 28(9), 1161–1173 (1996).
    [CrossRef]
  5. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15(10), 5976–5990 (2007).
    [CrossRef] [PubMed]
  6. K. Okamoto, Fundamentals of optical waveguides (Academic Press, 2006).
  7. A. B. Fallahkhair, K. S. Li, and T. E. Murphy, “Vector finite difference modesolver for anisotropic dielectric waveguides,” J. Lightwave Technol. 26(11), 1423–1431 (2008).
    [CrossRef]
  8. S. V. Chernikov and J. R. Taylor, “Measurement of normalization factor of n(2) for random polarization in optical fibers,” Opt. Lett. 21(19), 1559–1561 (1996).
    [CrossRef] [PubMed]
  9. A. Lamminpaa, T. Niemi, E. Ikonen, P. Marttila, and H. Ludvigsen, ““Effects of dispersion on nonlinearity measurement of optical fibers,” Opt. Fiber Technol,” Mater. Devices Syst. 11, 278–285 (2005).
  10. K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/ silicon dioxide waveguides,” Opt. Express 16(17), 12987–12994 (2008).
    [CrossRef] [PubMed]
  11. H. Schmidt, M. Gupta, and M. Bruns, “Nitrogen diffusion in amorphous silicon nitride isotope multilayers probed by neutron reflectometry,” Phys. Rev. Lett. 96(5), 055901 (2006).
    [CrossRef] [PubMed]

2008 (2)

2007 (2)

2006 (1)

H. Schmidt, M. Gupta, and M. Bruns, “Nitrogen diffusion in amorphous silicon nitride isotope multilayers probed by neutron reflectometry,” Phys. Rev. Lett. 96(5), 055901 (2006).
[CrossRef] [PubMed]

2005 (1)

A. Lamminpaa, T. Niemi, E. Ikonen, P. Marttila, and H. Ludvigsen, ““Effects of dispersion on nonlinearity measurement of optical fibers,” Opt. Fiber Technol,” Mater. Devices Syst. 11, 278–285 (2005).

1996 (3)

Agrawal, G. P.

Alic, N.

Boskovic, A.

Bruns, M.

H. Schmidt, M. Gupta, and M. Bruns, “Nitrogen diffusion in amorphous silicon nitride isotope multilayers probed by neutron reflectometry,” Phys. Rev. Lett. 96(5), 055901 (2006).
[CrossRef] [PubMed]

Chernikov, S. V.

Fainman, Y.

Fallahkhair, A. B.

Freude, W.

Grant, R. S.

R. S. Grant, “Effective non-linear coefficients of optical waveguides,” Opt. Quantum Electron. 28(9), 1161–1173 (1996).
[CrossRef]

Gruner-Nielsen, L.

Gupta, M.

H. Schmidt, M. Gupta, and M. Bruns, “Nitrogen diffusion in amorphous silicon nitride isotope multilayers probed by neutron reflectometry,” Phys. Rev. Lett. 96(5), 055901 (2006).
[CrossRef] [PubMed]

Ikeda, K.

Ikonen, E.

A. Lamminpaa, T. Niemi, E. Ikonen, P. Marttila, and H. Ludvigsen, ““Effects of dispersion on nonlinearity measurement of optical fibers,” Opt. Fiber Technol,” Mater. Devices Syst. 11, 278–285 (2005).

Jacome, L.

Koos, C.

Lamminpaa, A.

A. Lamminpaa, T. Niemi, E. Ikonen, P. Marttila, and H. Ludvigsen, ““Effects of dispersion on nonlinearity measurement of optical fibers,” Opt. Fiber Technol,” Mater. Devices Syst. 11, 278–285 (2005).

Leuthold, J.

Levring, O. A.

Li, K. S.

Lin, Q.

Ludvigsen, H.

A. Lamminpaa, T. Niemi, E. Ikonen, P. Marttila, and H. Ludvigsen, ““Effects of dispersion on nonlinearity measurement of optical fibers,” Opt. Fiber Technol,” Mater. Devices Syst. 11, 278–285 (2005).

Marttila, P.

A. Lamminpaa, T. Niemi, E. Ikonen, P. Marttila, and H. Ludvigsen, ““Effects of dispersion on nonlinearity measurement of optical fibers,” Opt. Fiber Technol,” Mater. Devices Syst. 11, 278–285 (2005).

Murphy, T. E.

Niemi, T.

A. Lamminpaa, T. Niemi, E. Ikonen, P. Marttila, and H. Ludvigsen, ““Effects of dispersion on nonlinearity measurement of optical fibers,” Opt. Fiber Technol,” Mater. Devices Syst. 11, 278–285 (2005).

Painter, O. J.

Poulton, C.

Saperstein, R. E.

Schmidt, H.

H. Schmidt, M. Gupta, and M. Bruns, “Nitrogen diffusion in amorphous silicon nitride isotope multilayers probed by neutron reflectometry,” Phys. Rev. Lett. 96(5), 055901 (2006).
[CrossRef] [PubMed]

Taylor, J. R.

J. Lightwave Technol. (1)

Mater. Devices Syst. (1)

A. Lamminpaa, T. Niemi, E. Ikonen, P. Marttila, and H. Ludvigsen, ““Effects of dispersion on nonlinearity measurement of optical fibers,” Opt. Fiber Technol,” Mater. Devices Syst. 11, 278–285 (2005).

Opt. Express (3)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

R. S. Grant, “Effective non-linear coefficients of optical waveguides,” Opt. Quantum Electron. 28(9), 1161–1173 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

H. Schmidt, M. Gupta, and M. Bruns, “Nitrogen diffusion in amorphous silicon nitride isotope multilayers probed by neutron reflectometry,” Phys. Rev. Lett. 96(5), 055901 (2006).
[CrossRef] [PubMed]

Other (2)

K. Okamoto, Fundamentals of optical waveguides (Academic Press, 2006).

J. F. Bauters, M. J. R. Heck, D. John, M.-C. Tien, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. Bowers, “Ultra-low loss silica-based waveguides with millimeter bend radius,” in ECOC(Torino, Italy, 2010).

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of a channel waveguide with Si3N4 core and SiO2 cladding. (b) Calculated TE fundamental mode profile of the channel waveguide. The dimension of the Si3N4 core is 2.8 μm by 80 nm.

Fig. 2
Fig. 2

Calculated nonlinear coefficient γ of channel waveguides with various Si3N4 core thicknesses using different methods. The measured nonlinearity is also included for comparison.

Fig. 3
Fig. 3

Nonlinearity measurement setup using CW SPM method.

Fig. 4
Fig. 4

SPM spectrum through a 6-m long spiral waveguide with 2.8 μm of core width and 80 nm of core thickness. The input light is TE-polarized with optical power of 29 dBm.

Fig. 5
Fig. 5

Measured nonlinear phase shifts at various input powers for different Si3N4 core thicknesses. The solid lines are linear fitting of the measurements.

Fig. 6
Fig. 6

Effective n2 for different core thicknesses. The solid lines represent the theoretical calculation using the perturbation theory while the squares represent the measured data points.

Equations (15)

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Δ n = n 2 , e f f I e f f = n 2 , e f f P t o t A e f f ,
where A e f f = ( I ( x , y ) d x d y ) 2 I ( x , y ) 2 d x d y .
n ( x , y ) 2 = ( n 0 ( x , y ) + n 2 ( x , y ) I ( x , y ) ) 2 n 0 ( x , y ) 2 + 2 n 0 ( x , y ) n 2 ( x , y ) I ( x , y ) ,
2 H y + ( k 2 n ( x , y ) 2 β 2 ) H y = 0 ,
H y = H y 0 + Δ H y 1
β 2 = β 0 2 + Δ β 1 2 .
Δ β 1 2 = k 2 2 n 0 ( x , y ) n 2 ( x , y ) I ( x , y ) 2 d x d y I ( x , y ) d x d y .
β 2 = ( n 0 , e f f + n 2 , e f f I e f f ) 2 k 2 β 0 2 + 2 n 0 , e f f n 2 , e f f I e f f k 2 ,
I e f f = P t o t A e f f = I ( x , y ) 2 d x d y I ( x , y ) d x d y .
n 2 , e f f = n 0 ( x , y ) n 2 ( x , y ) I ( x , y ) 2 d x d y n 0 , e f f I ( x , y ) 2 d x d y .
Γ c o r e = c o r e I ( x , y ) 2 d x d y I ( x , y ) 2 d x d y Γ c l a d = c l a d I ( x , y ) 2 d x d y I ( x , y ) 2 d x d y .
n 2 , e f f = n 0 , c o r e n 2 , c o r e Γ c o r e + n 0 , c l a d n 2 , c l a d Γ c l a d n 0 , e f f .
I 0 I 1 = J 0 2 ( φ S P M / 2 ) + J 1 2 ( φ S P M / 2 ) J 1 2 ( φ S P M / 2 ) + J 2 2 ( φ S P M / 2 ) ,
φ S P M = 2 π λ n 2 , e f f A e f f L e f f P i n = γ L e f f P i n ,
L e f f = ( 1 e α L ) α ,

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