Abstract

Nonlinear optical devices based on third-order nonlinear effects are optimized when the optically induced phase shift is maximum. This phase shift can be expressed in terms of two quantities that depend on waveguide geometry and composition: the effective area and the effective nonlinear index. The coupling coefficient into the waveguide must also be considered when optimal device efficiency is sought. A combination of these three factors yields a quantity to optimize without loss of physical insight into the problem. This method of analysis is applied to a ridge waveguide made of chalcogenide glass, which exhibits nonlinear indices as much as 400 times higher than that of silica glass.

© 2000 Optical Society of America

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References

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  1. P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wigley, and G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett. 18, 1996–1998 (1993).
    [CrossRef] [PubMed]
  2. R. H. Stolen and J. F. Bjorkholm, “Parametric amplification and frequency-conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1995).
    [CrossRef]
  3. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1989).
  4. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983). See Eq. (18–5) therein.
  5. T. Kato, Y. Suetsugu, and M. Nishimura, “Estimation of nonlinear refractive index of various silica-based glasses for optical fibers,” Opt. Lett. 20, 2279–2281 (1995).
    [CrossRef]
  6. T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
    [CrossRef]

1999 (1)

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

1995 (2)

R. H. Stolen and J. F. Bjorkholm, “Parametric amplification and frequency-conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1995).
[CrossRef]

T. Kato, Y. Suetsugu, and M. Nishimura, “Estimation of nonlinear refractive index of various silica-based glasses for optical fibers,” Opt. Lett. 20, 2279–2281 (1995).
[CrossRef]

1993 (1)

Beatty, R.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

Bjorkholm, J. F.

R. H. Stolen and J. F. Bjorkholm, “Parametric amplification and frequency-conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1995).
[CrossRef]

Bures, J.

Cardinal, T.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

Dumais, P.

Gonthier, F.

Kato, T.

Lacroix, S.

Le Foulgoc, K.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

Meneghini, C.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

Nishimura, M.

Richardson, K. A.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

Schulte, A.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

Shim, H.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

Stegeman, G. I.

Stolen, R. H.

R. H. Stolen and J. F. Bjorkholm, “Parametric amplification and frequency-conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1995).
[CrossRef]

Suetsugu, Y.

Viens, J. F.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

Villeneuve, A.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

P. Dumais, F. Gonthier, S. Lacroix, J. Bures, A. Villeneuve, P. G. J. Wigley, and G. I. Stegeman, “Enhanced self-phase modulation in tapered fibers,” Opt. Lett. 18, 1996–1998 (1993).
[CrossRef] [PubMed]

Wigley, P. G. J.

IEEE J. Quantum Electron. (1)

R. H. Stolen and J. F. Bjorkholm, “Parametric amplification and frequency-conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1995).
[CrossRef]

J. Non-Cryst. Solids (1)

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Nonlinear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256, 353–360 (1999).
[CrossRef]

Opt. Lett. (2)

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1989).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983). See Eq. (18–5) therein.

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Figures (8)

Fig. 1
Fig. 1

Model of the ridge waveguide. W designates the width of the ridge and T the thickness of the core layer. The figure is to scale with the result for optimal γ.

Fig. 2
Fig. 2

Ternary diagram of chalcogenide glass compositions for which experimental data are available. Data are given in Table 1.

Fig. 3
Fig. 3

Experimentally determined linear (circles) and nonlinear (squares) indices of the chalcogenide glasses. Open symbols, glasses number 1–5; filled symbols, glass number 6. The line and the curve represent empirical polynomial fits to the data along the 1–5 line.

Fig. 4
Fig. 4

Effective area (in µm2) of the ridge waveguide as a function of ridge width W and core thickness T.

Fig. 5
Fig. 5

Effective n2 (in m2/W) of the ridge waveguide as a function of ridge width W and core thickness T. It is almost independent of lateral mode confinement.

Fig. 6
Fig. 6

Nonlinearity coefficient γ (in m-1 W-1) of the ridge waveguide as a function of ridge width W and core thickness T.

Fig. 7
Fig. 7

Coupling coefficient of the ridge waveguide (normalized to 1) with a standard SMF-28 fiber at λ=1.6 µm. The two axes are reversed compared with those in Figs. 4, 5, 6, and 8 for greater clarity.

Fig. 8
Fig. 8

Product γC (in W-1 m-1) of the nonlinearity coefficient and the coupling efficiency.

Tables (1)

Tables Icon

Table 1 Experimentally Measured Linear and Nonlinear Index of Chalcogenide Glasses of Different Compositions at λ=1.6 µm

Equations (8)

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ϕNL=k0An2ψ4d AAψ2d A2PL,
Aeff=Aψ2d A2Aψ4d A.
n2eff=An2ψ4d AAψ4d A.
ϕNL=γ PL,
γ=k0n2effAeff.
Pw=CPin,
C=Aψ1ψ2d Aψ12d Aψ22d A1/2,
ϕNL=γ CPinL.

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