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Optimal waveguide dimensions for nonlinear interactions

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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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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)

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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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