Abstract

It is proposed that the direct calculation of the dispersion for a waveguide using the effective power-dependent permittivity is a rigorous way to determine its nonlinear Kerr coefficient. The tensor permittivity accounts fully for the vectorial nature of the electric field. The calculated Kerr coefficients for the lowest transverse-magnetic modes of a nonlinear slab and wire are compared with the results of several formulas existing in the literature. The proposed approach can conveniently be implemented using standard mode solvers.

© 2014 Optical Society of America

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References

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    [CrossRef]

2013 (1)

2010 (3)

N. C. Panoiu, J. F. McMillan, and C. W. Wong, IEEE J. Sel. Top. Quantum Electron. 16, 257 (2010).
[CrossRef]

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

A. V. Maslov and M. Miyawaki, J. Appl. Phys. 108, 083105 (2010).
[CrossRef]

2009 (3)

2008 (1)

2007 (1)

2005 (1)

2004 (2)

M. A. Foster, K. D. Moll, and A. L. Gaeta, Opt. Express 12, 2880 (2004).
[CrossRef]

A. V. Maslov and C. Z. Ning, IEEE J. Quantum Electron. 40, 1389 (2004).
[CrossRef]

2001 (1)

Y. Z. Huang, IEE Proc. Optoelectron. 148, 131 (2001).
[CrossRef]

1997 (1)

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, IEEE J. Quantum Electron. 33, 1763 (1997).
[CrossRef]

Afshar, S. V.

Afshar V., S.

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 5th ed. (Elsevier, 2013), Sect. 2.3.1, pp. 34–39.

Blok, H.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, IEEE J. Quantum Electron. 33, 1763 (1997).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 3rd. ed. (Academic, 2008).

Chen, X.

Corcoran, B.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Dadap, J. I.

de Sterke, C. M.

Demeulenaere, B.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, IEEE J. Quantum Electron. 33, 1763 (1997).
[CrossRef]

Dulkeith, E.

Ebendorff-Heidepriem, H.

Ebnali-Heidari, M.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Eggleton, B. J.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Foster, M. A.

Freude, W.

Gaeta, A. L.

Green, W. M.

Grillet, C.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Hsieh, I.-W.

Huang, Y. Z.

Y. Z. Huang, IEE Proc. Optoelectron. 148, 131 (2001).
[CrossRef]

Jacome, L.

Koos, C.

Krauss, T. F.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Lenstra, D.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, IEEE J. Quantum Electron. 33, 1763 (1997).
[CrossRef]

Leuthold, J.

Lipson, M.

Liu, X.

Maslov, A. V.

A. V. Maslov and M. Miyawaki, J. Appl. Phys. 108, 083105 (2010).
[CrossRef]

A. V. Maslov and C. Z. Ning, IEEE J. Quantum Electron. 40, 1389 (2004).
[CrossRef]

A. V. Maslov and C. Z. Ning, in Nitride Semiconductor Devices: Principles and Simulation, J. Piprek, ed. (Wiley-VCH Verlag, 2007), Chap. 21, pp. 467–491.

McMillan, J. F.

N. C. Panoiu, J. F. McMillan, and C. W. Wong, IEEE J. Sel. Top. Quantum Electron. 16, 257 (2010).
[CrossRef]

Miyawaki, M.

A. V. Maslov and M. Miyawaki, J. Appl. Phys. 108, 083105 (2010).
[CrossRef]

Moll, K. D.

Monat, C.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Monro, T. M.

Moss, D. J.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Ning, C. Z.

A. V. Maslov and C. Z. Ning, IEEE J. Quantum Electron. 40, 1389 (2004).
[CrossRef]

A. V. Maslov and C. Z. Ning, in Nitride Semiconductor Devices: Principles and Simulation, J. Piprek, ed. (Wiley-VCH Verlag, 2007), Chap. 21, pp. 467–491.

O’Faolain, L.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Osgood, R. M.

Panoiu, N. C.

Pelusi, M. D.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Poulton, C.

Pudo, D.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Turner, A. C.

Visser, T. D.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, IEEE J. Quantum Electron. 33, 1763 (1997).
[CrossRef]

Vlasov, Y. A.

White, T. P.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

Wong, C. W.

N. C. Panoiu, J. F. McMillan, and C. W. Wong, IEEE J. Sel. Top. Quantum Electron. 16, 257 (2010).
[CrossRef]

Zhang, W. Q.

Zheltikov, A.

Adv. Opt. Photon. (1)

IEE Proc. Optoelectron. (1)

Y. Z. Huang, IEE Proc. Optoelectron. 148, 131 (2001).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. V. Maslov and C. Z. Ning, IEEE J. Quantum Electron. 40, 1389 (2004).
[CrossRef]

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, IEEE J. Quantum Electron. 33, 1763 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

N. C. Panoiu, J. F. McMillan, and C. W. Wong, IEEE J. Sel. Top. Quantum Electron. 16, 257 (2010).
[CrossRef]

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, IEEE J. Sel. Top. Quantum Electron. 16, 344 (2010).
[CrossRef]

J. Appl. Phys. (1)

A. V. Maslov and M. Miyawaki, J. Appl. Phys. 108, 083105 (2010).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (5)

Opt. Lett. (1)

Other (3)

A. V. Maslov and C. Z. Ning, in Nitride Semiconductor Devices: Principles and Simulation, J. Piprek, ed. (Wiley-VCH Verlag, 2007), Chap. 21, pp. 467–491.

R. W. Boyd, Nonlinear Optics, 3rd. ed. (Academic, 2008).

G. Agrawal, Nonlinear Fiber Optics, 5th ed. (Elsevier, 2013), Sect. 2.3.1, pp. 34–39.

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Figures (2)

Fig. 1.
Fig. 1.

(a) Dispersion for the TM0 mode guided by a slab with n0=1.5. (b) L/Leff based on Eqs. (20a)–(20d). The inset in (a) shows the slab geometry.

Fig. 2.
Fig. 2.

(a) Dispersion for the TM01 mode guided by a wire with n0=1.5 and (b) A/Aeff based on Eqs. (20a)–(20d) for the wire with A=πR2. The inset in (a) shows the wire geometry.

Equations (31)

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n=n0+n¯2E2,
n=n0+n2I=n0+n2P/A,
β=β0+γP,
γ=ωcn2Aeff.
Aeff=(dA|et|2)2nldA|et|4,
Aeff=μ0ε03|dA(e×h*)·z^|2ncore2nldA(2|e|4+|e2|2).
Pnl=ε0A[(E·E*)E+12(E·E)E*],
Pinl=ε0jχijeffEj
χijeff=A2[(E·E*)δij+(EiEj*+Ei*Ej)].
χxxeff=A2[3|Ex|2+|Ez|2],
χzzeff=A2[3|Ez|2+|Ex|2],
χxzeff=χzxeff=A2[ExEz*+Ex*Ez].
iβExEzx=iωμ0Hy,
βωHy=εEx+Pxnl,
iωHyx=εEz+Pznl,
Pxnl=ε0χxxeffEx+ε0χxzeffEz,
Pznl=ε0χzxeffEx+ε0χzzeffEz.
Ex,z(x)=E0fx,z(x),Hy(x)=ε0/μ0E0gy(x),
P=ε0μ0|E0|2Lη,η=1Ldx[fxgy*+fx*gy].
χxxeff(x)=ξ2η[3|fx(x)|2+|fz(x)|2],
χzzeff(x)=ξ2η[3|fz(x)|2+|fx(x)|2)],
χxzeff(x)=ξ2η[fx(x)fz*(x)+fx*(x)fz(x)]
ξ=(AP/L)μ0/ε0.
[c2ω2ε˜xx1ε˜zx+ε˜x]Hy=(cβω)2Hy,
ε˜x,z(x)=ε(x)/ε0+χxx,zzeff(x).
γ=ΔβP=μ0ε0AωLc·cΔβωξ=Aωε0Lc2·cΔβωξ,
1Leff(a)=8n023L·cΔβωξ,
1Leff(b)=n023S22L/2L/2dx2(|fx|2+|fz|2)2+|fx2+fz2|2,
1Leff(c)=1S12L/2L/2dx|fx|4,
1Leff(d)=1S22L/2L/2dx(fxgy*)2,
S1=dx|fx|2,S2=dxfxgy*.

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