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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  1. P. N. Prasad, Nanophotonics, (John Wiley and Sons, New York2004).
    [Crossref]
  2. S. Kawata, M. Ohtsu, and M. Irie, Nano-Optics, (Springer Verlag, Berlin2002).
  3. S. G. Leon-Saval, T. A. Birks, W. J. Wadsworth, P. St. J. Russell, and M. W. Mason, “Supercontinuum generation in submicron fibre waveguides,” Opt. Express 12, 2864–2869 (2004).
    [Crossref] [PubMed]
  4. 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]
  5. M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, “Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires,” Opt. Express 13, 6848–6855 (2005).
    [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.
  8. R. El-Ganainy, S. Mokhov, K. G. Makris, and D. N. Christodoulides, “Solitons in dispersion-inverted AlGaAs nanowires,” Opt. Express 14, 2277–2282 (2006).
    [Crossref] [PubMed]
  9. D. Hondros and P. Debye, “Elektromagnetische Wellen an dielektrischen Drähten,” Ann. Physik 32, 465–476 (1910).
    [Crossref]
  10. S. A. Schelkunoff, Electromagnetic Waves (D. Van Nostrand Inc., New York, 1943).
  11. E. Snitzer, “Cylindrical dielectric waveguide mode,“ J. Opt. Soc. Am. 51, 491–498 (1961).
    [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, London2000).
  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]
  17. S. Kawata and T. Tani, “Optically driven Mie particles in an evanescent field along a channeled waveguide,” Opt. Lett. 21, 1768–1770 (1996).
    [Crossref] [PubMed]
  18. A. Askin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159, (1970).
    [Crossref]
  19. J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
    [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]

Aitchison, J. S.

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.

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.

R. El-Ganainy, S. Mokhov, K. G. Makris, and D. N. Christodoulides, “Solitons in dispersion-inverted AlGaAs nanowires,” Opt. Express 14, 2277–2282 (2006).
[Crossref] [PubMed]

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.

De Angelis, C.

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.

Debye, P.

D. Hondros and P. Debye, “Elektromagnetische Wellen an dielektrischen Drähten,” Ann. Physik 32, 465–476 (1910).
[Crossref]

El-Ganainy, R.

Fan, S.

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.

Fejer, M. M.

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.

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]

Harris, J. S.

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.

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]

Irie, M.

S. Kawata, M. Ohtsu, and M. Irie, Nano-Optics, (Springer Verlag, Berlin2002).

Iwanow, R.

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.

Jackson, J. D.

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

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.

Locatelli, A.

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.

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]

Modotto, D.

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.

Mokhov, S.

Morandotti, R.

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.

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]

Ohtsu, M.

S. Kawata, M. Ohtsu, and M. Irie, Nano-Optics, (Springer Verlag, Berlin2002).

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, London2000).

Povinelli, M. L.

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.

Prasad, P. N.

P. N. Prasad, Nanophotonics, (John Wiley and Sons, New York2004).
[Crossref]

Russell, P. St. J.

Scaccabarozzi, L.

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.

Schelkunoff, S. A.

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

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.

Sorel, M.

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.

Stanley, C. R.

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.

Stegeman, G. I.

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.

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.

Yu, X.

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.

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, London2000).

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

P. N. Prasad, Nanophotonics, (John Wiley and Sons, New York2004).
[Crossref]

S. Kawata, M. Ohtsu, and M. Irie, Nano-Optics, (Springer Verlag, Berlin2002).

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.

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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.

Download Full Size | PPT Slide | PDF

Fig. 2.
Fig. 2.

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

Download Full Size | PPT Slide | PDF

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

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

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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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