Abstract

We show that energy circulation within a pulse is possible when it propagates in a high-contrast dielectric nanowire. This process is accomplished through electromagnetic “wormhole” regions, in which the Poynting vector associated with the guided mode is negative with respect to the direction of propagation. For demonstration purposes this mechanism is elucidated in AlGaAs and silicon nanowaveguides. The effect of dispersion on the power circulation is also considered.

© 2006 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. L. Scaccabarozzi, X. Yu, M. L. Povinelli, S. Fan, M. M. Fejer and J. S. Harris, "Highly efficient birefringent second harmonic generation in submicron AlGaAs/AlxOy waveguides," CLEO 2005 Techncial Digest, paper CPDA10.
  7. R. Iwanow, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, D. Modotto, A. Locatelli, C. De Angelis, C. R. Stanley, M. Sorel and J. S. Aitchison, "Enhanced third order nonlinear effects in AlGaAs nano-wire waveguides," post-deadline paper PDP7, Nonlinear guided waves and their applications, OSA Topical Meeting, Dresden, Germany, Sept. 6-9, 2005.
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    [CrossRef] [PubMed]
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    [CrossRef]
  10. S. A. Schelkunoff, Electromagnetic Waves (D. Van Nostrand Inc., New York, 1943).
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    [CrossRef]
  12. E. F. F. Gillespie, Proc. Inst. Elect. Eng. 107c, 198-201 (1960).
  13. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  14. K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, London 2000).
  15. Y. N. Noskov, "Method for measuring properties of high relative dielectric constant materials in a cutoff waveguide cavity," IEEE Trans. Microwave Theory Tech,  MTT-48, 329-333 (2000).
    [CrossRef]
  16. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67,0576021-0576024 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (1)

2005 (1)

2004 (1)

2003 (2)

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

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67,0576021-0576024 (2003).
[CrossRef]

2000 (1)

Y. N. Noskov, "Method for measuring properties of high relative dielectric constant materials in a cutoff waveguide cavity," IEEE Trans. Microwave Theory Tech,  MTT-48, 329-333 (2000).
[CrossRef]

1996 (1)

1973 (1)

J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

1970 (1)

A. Askin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159, (1970).
[CrossRef]

1961 (1)

1960 (1)

E. F. F. Gillespie, Proc. Inst. Elect. Eng. 107c, 198-201 (1960).

1910 (1)

D. Hondros and P. Debye, "Elektromagnetische Wellen an dielektrischen Drähten," Ann. Physik 32, 465-476 (1910).
[CrossRef]

Ashcom, J. B.

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

Askin, A.

A. Askin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159, (1970).
[CrossRef]

Birks, T. A.

Cao, Q.

Christodoulides, D. N.

Debye, P.

D. Hondros and P. Debye, "Elektromagnetische Wellen an dielektrischen Drähten," Ann. Physik 32, 465-476 (1910).
[CrossRef]

El-Ganainy, R.

Foster, M. A.

Gaeta, A. L.

Gattass, R. R.

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

Gillespie, E. F. F.

E. F. F. Gillespie, Proc. Inst. Elect. Eng. 107c, 198-201 (1960).

Gordon, J. P.

J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

He, S.

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

Hondros, D.

D. Hondros and P. Debye, "Elektromagnetische Wellen an dielektrischen Drähten," Ann. Physik 32, 465-476 (1910).
[CrossRef]

Kawata, S.

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67,0576021-0576024 (2003).
[CrossRef]

Leon-Saval, S. G.

Lou, J.

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

Makris, K. G.

Mason, M. W.

Maxwell, I.

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

Mokhov, S.

Noskov, Y. N.

Y. N. Noskov, "Method for measuring properties of high relative dielectric constant materials in a cutoff waveguide cavity," IEEE Trans. Microwave Theory Tech,  MTT-48, 329-333 (2000).
[CrossRef]

Russell, P. St. J.

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67,0576021-0576024 (2003).
[CrossRef]

Shen, M.

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

Snitzer, E.

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67,0576021-0576024 (2003).
[CrossRef]

Tani, T.

Tong, L.

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

Trebino, R.

Wadsworth, W. J.

Ann. Physik (1)

D. Hondros and P. Debye, "Elektromagnetische Wellen an dielektrischen Drähten," Ann. Physik 32, 465-476 (1910).
[CrossRef]

IEEE Trans. Microwave Theory Tech (1)

Y. N. Noskov, "Method for measuring properties of high relative dielectric constant materials in a cutoff waveguide cavity," IEEE Trans. Microwave Theory Tech,  MTT-48, 329-333 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (1)

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

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (1)

J. P. Gordon, "Radiation forces and momenta in dielectric media," Phys. Rev. A 8, 14-21 (1973).
[CrossRef]

Phys. Rev. E (1)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67,0576021-0576024 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

A. Askin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159, (1970).
[CrossRef]

Proc. Inst. Elect. Eng. (1)

E. F. F. Gillespie, Proc. Inst. Elect. Eng. 107c, 198-201 (1960).

Other (7)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, London 2000).

S. A. Schelkunoff, Electromagnetic Waves (D. Van Nostrand Inc., New York, 1943).

L. Scaccabarozzi, X. Yu, M. L. Povinelli, S. Fan, M. M. Fejer and J. S. Harris, "Highly efficient birefringent second harmonic generation in submicron AlGaAs/AlxOy waveguides," CLEO 2005 Techncial Digest, paper CPDA10.

R. Iwanow, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, D. Modotto, A. Locatelli, C. De Angelis, C. R. Stanley, M. Sorel and J. S. Aitchison, "Enhanced third order nonlinear effects in AlGaAs nano-wire waveguides," post-deadline paper PDP7, Nonlinear guided waves and their applications, OSA Topical Meeting, Dresden, Germany, Sept. 6-9, 2005.

P. N. Prasad, Nanophotonics, (John Wiley and Sons, New York 2004).
[CrossRef]

S. Kawata, M. Ohtsu and M. Irie, Nano-Optics, (Springer Verlag, Berlin 2002).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Distribution of the HE11x Poynting vector Sz associated with an Al 0.2 Ga 0.8 As nanowire of core radius a = 170 nm . (b) Top view shows the ellipticity of the sz distribution. (c) Negative sz regions with the positive part removed for illustration purposes.

Fig. 2.
Fig. 2.

Iso-contour lines |Szmax / Szmax+| associated with the HE 11 mode in an air-clad nanowire, as a function of index contrast and the V number.

Fig. 3.
Fig. 3.

Electric field and negative Poynting vector distributions in an (a) elliptical waveguide with aspect ratio 400×350nm 2 (b) square waveguide 350×350nm 2 and (c) “pyramid” waveguide of approximate dimensions 300×350nm 2

Fig. 4.
Fig. 4.

(a) Transverse Poynting vector distribution at the leading edge of a pulse (b) An expanded view of the power-flow density around the wormhole area.

Fig. 5.
Fig. 5.

Schematic demonstration of the space-time Poynting vector field (in T and x). Power circulation within the pulse (traveling from right to left) is evident.

Equations (8)

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

A S d a = W t
E = e ( r , θ ) exp [ i ( ω t β z ) ]
H = h ( r , θ ) exp [ i ( ω t β z ) ]
{ E H } = e i ( ω 0 t β 0 z ) 2 π d Ω Φ 0 ( Ω ) e i ( Ω T F ( Ω ) z ) { e ( r , ω 0 + Ω ) h ( r , ω 0 + Ω ) }
[ E H ] = [ e 0 i e 1 h 0 i h 1 ] [ ϕ ϕ T ] exp [ i ( ω 0 t β 0 z ) ]
S = 1 2 Re { A 2 ( e 0 × h 0 * ) + A 2 ψ T ( e 1 × h 0 * + e 0 × h 1 * ) + i 2 A 2 T ( e 0 × h 1 * e 1 × h 0 * ) } ,
S = E 0 2 2 1 + ( z z d ) 2 exp ( 2 τ 2 1 + ( z z d ) 2 )
Re { ( e 0 × h 0 * ) + 2 ( τ τ 0 ) ( z z d ) 1 + ( z z d ) 2 ( e 1 × h 0 * + e 0 × h 1 * ) 2 i ( τ τ 0 ) 1 + ( z z d ) 2 ( e 0 × h 1 * e 1 × h 0 * ) }

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