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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  1. T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Technol. 10, 432–438 (1992).
    [CrossRef]
  2. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000).
    [CrossRef]
  3. W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St.J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
    [CrossRef]
  4. J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
    [CrossRef] [PubMed]
  5. P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
    [CrossRef] [PubMed]
  6. 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]
  7. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28, 1302–1304 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. S. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  19. 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]
  20. 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]
  21. W. H. Reeves, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-6095.
    [CrossRef] [PubMed]
  22. 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]

2004 (1)

2003 (8)

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]

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]

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

P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (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]

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28, 1302–1304 (2003).
[CrossRef] [PubMed]

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]

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

2002 (2)

2001 (2)

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]

S. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173.
[CrossRef] [PubMed]

2000 (3)

1993 (1)

1992 (1)

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

1989 (1)

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]

Agrawal, G. P.

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

Akimov, D.

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]

Almeida, V. R.

Arriaga, J.

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]

Artiglia, M.

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]

Ashcom, J. B.

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]

Biancalana, F.

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]

Birks, T. A.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St.J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[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]

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

Coppa, G.

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]

Divita, P.

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]

Dukel’skii, K.

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]

Dumais, P.

Efimov, A.

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]

Fajardo, J. C.

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]

Finazzi, V.

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]

Gaeta, A. L.

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]

Gattass, R. R.

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]

Gonthier, F.

He, S. L.

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]

Homoelle, D.

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]

Joannopoulos, J. D.

Johnson, S.

Khokhlov, A.

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]

Kiefer, W.

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]

Knight, J. C.

J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (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]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St.J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[CrossRef]

W. H. Reeves, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-6095.
[CrossRef] [PubMed]

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]

Koch, K. W.

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]

Kondrat’ev, Y.

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]

Lacroix, S.

Li, Y. W.

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

Lipson, M.

Lou, J. Y.

L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode properties of sub-wavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1025.
[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]

Love, J. D.

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

Maksimenka, R.

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]

Man, T. P. M.

Maxwell, I.

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]

Mazur, E.

L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode properties of sub-wavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1025.
[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]

Monro, T. M.

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]

Omenetto, F. G.

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]

Ortigosa-Blanch, A.

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St.J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[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]

Ouzounov, D.

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]

Panepucci, R. R.

Pollock, C. R.

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

Potenza, M.

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]

Ranka, J. K.

Reeves, W. H.

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]

W. H. Reeves, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-6095.
[CrossRef] [PubMed]

Richardson, D. J.

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]

Roberts, P. J.

Russell, P. St.J.

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]

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

W. H. Reeves, J. C. Knight, P. St.J. Russell, and P. J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-6095.
[CrossRef] [PubMed]

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Man, and P. St.J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[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]

Schmitt, M.

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]

Sharma, A.

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]

Shen, M. Y.

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]

Shevandin, V.

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]

Skryabin, D. V.

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]

Snyder, A. W.

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

Stegeman, G. I.

Stentz, A. J.

Taylor, A. J.

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]

Tong, L. M.

L. M. Tong, J. Y. Lou, and E. Mazur, “Single-mode properties of sub-wavelength-diameter silica and silicon wire waveguides,” Opt. Express 12, 1025–1035 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1025.
[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]

Villeneuve, A.

Wadsworth, W. J.

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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).
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Webb, W. W.

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]

West, J. A.

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).
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Zheltikov, A. M.

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

Appl. Phys. B (1)

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).
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J. C. Knight, “Photonic crystal fibres,” Nature 424, 847–851 (2003).
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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).
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Opt. Express (3)

Opt. Lett. (4)

Optics and Spectroscopy (1)

A. M. Zheltikov, “The physical limit for the waveguide enhancement of nonlinear-optical processes,” Optics and Spectroscopy 95, 410–415 (2003).
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P. St.J. Russell, “Photonic crystal fibers,” Science 299, 358–362 (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)

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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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