Abstract

We investigate strong light confinement in high core-cladding index contrast waveguides with dimensions comparable to and smaller than the wavelength of incident light. We consider oval and rectangular cross sections and demonstrate that an optimal core size exists that maximizes the effective nonlinearity. We also determine that waveguides with asymmetrical cross sections provide the maximum possible nonlinearity, although only a small improvement over the symmetric case. Furthermore, we find that for a specified waveguide shape the largest nonlinearity occurs for nearly the same core area in all cases. Calculations of the dispersion for the optimal-size waveguide at a particular wavelength indicate that the group-velocity dispersion is normal. Ultimately, such designs could be used to develop low-power all-optical devices and to produce waveguides for ultra-low threshold nonlinear frequency generation such as supercontinuum generation.

© 2004 Optical Society of America

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References

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Appl. Phys. B

D. Akimov, M. Schmitt, R. Maksimenka, K. Dukel???skii, Y. Kondrat???ev, A. Khokhlov, V. Shevandin, W. Kiefer, and A. M. Zheltikov, ???Supercontinuum generation in a multiple-submicron-core microstructure fiber: toward limiting waveguide enhancement of nonlinear-optical processes,??? Appl. Phys. B 77, 299???305 (2003).
[CrossRef]

IEEE Photon. Technol. Lett.

V. Finazzi, T. M. Monro, and D. J. Richardson, ???The role of confinement loss in highly nonlinear silica holey fibers,??? IEEE Photon. Technol. Lett. 15, 1246???1248 (2003).
[CrossRef]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St.J. Russell, ???Anomalous dispersion in photonic crystal fiber,??? IEEE Photon. Technol. Lett. 12, 807???809 (2000).
[CrossRef]

J. Lightwave Tech.

M. Artiglia, G. Coppa, P. Divita, M. Potenza, and A. Sharma, ???Mode field diameter measurements in single-mode optical fibers,??? J. Lightwave Tech. 7, 1139???1152 (1989
[CrossRef]

J. Lightwave Technol

T. A. Birks and Y. W. Li, ???The shape of fiber tapers,??? J. Lightwave Technol. 10, 432???438 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Nature

J. C. Knight, ???Photonic crystal fibres,??? Nature 424, 847???851 (2003).
[CrossRef] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, ???Subwavelength-diameter silica wires for low-loss optical wave guiding,??? Nature 426, 816???819 (2003).
[CrossRef] [PubMed]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St.J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, ???Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres,??? Nature 424, 511???515 (2003).
[CrossRef] [PubMed]

Opt. Commun.

D. Ouzounov, D. Homoelle, W. Zipfel, W. W. Webb, A. L. Gaeta, J. A. West, J. C. Fajardo, and K. W. Koch, ???Dispersion measurements of microstructured fibers using femtosecond laser pulses,??? Opt. Commun. 192, 219??? 223 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Optics and Spectroscopy

A. M. Zheltikov, ???The physical limit for the waveguide enhancement of nonlinear-optical processes,??? Optics and Spectroscopy 95, 410???415 (2003).
[CrossRef]

Science

P. St.J. Russell, ???Photonic crystal fibers,??? Science 299, 358???362 (2003).
[CrossRef] [PubMed]

Other

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

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic Publishers, 1983).

C. R. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, 2003).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Power localization and (b) the effective nonlinearity and mode field diameter (MFD) for a circular glass (ncore =1.45) waveguide in air (nclad =1.0).

Fig. 2.
Fig. 2.

Effective nonlinearity of the TE and TM modes of a dielectric planar slab waveguide for core/cladding index contrasts of 3.45/1.45 and 1.45/1.0.

Fig. 3.
Fig. 3.

Effective nonlinearity as a function of core size for the fundamental mode of a circular dielectric waveguide and for rectangular dielectric waveguides with various aspect ratios and core/cladding index contrasts of (a) 1.45/1.0 and (b) 3.45/1.45.

Fig. 4.
Fig. 4.

The optimal effective nonlinearity as a function of core shape for (a) glass (ncore =1.45) in air (nclad =1.0) and for (b) Si (ncore =3.45) in Si02 (nclad =1.45)

Fig. 5.
Fig. 5.

Effective nonlinearity of the lowest order orthogonally polarized modes of a rectangular waveguide with ncore =1.45, nclad =1.0, and an aspect ratio of 1.4 to 1.

Fig. 6.
Fig. 6.

Group-velocity dispersion of a glass rod in air for core diameters of 200 nm, 400 nm, 600 nm, and 800 nm.

Equations (7)

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

S z = ( E × H ) z .
MFD = 2 2 S z r 2 d 2 r S z d 2 r ,
γ = 2 π λ n 2 S z 2 d 2 r ( S z d 2 r ) 2 ,
𝓓 HE 11 = 0.854 λ ( n core + n clad ) 0.6 ( n core n clad ) 0.4 ,
𝓦 TE = 0.422 λ ( n core + n clad ) 0.5 ( n core n clad ) 0.5 ,
𝓦 TM = 0.701 λ ( n core + n clad ) 0.6 ( n core n clad ) 0.4 ,
𝓐 = 0.573 λ ( n core + n clad ) 1.2 ( n core n clad ) 0.8 .

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