Power circulation via negative energy-flux wormholes in optical nanowaveguides

Sergiy Mokhov; Ramy El-Ganainy; Demetrios N. Christodoulides

doi:10.1364/OE.14.003255

Power circulation via negative energy-flux wormholes in optical nanowaveguides

Sergiy Mokhov, Ramy El-Ganainy, and Demetrios N. Christodoulides

Optics Express
Vol. 14,
Issue 8,
pp. 3255-3262
(2006)
•https://doi.org/10.1364/OE.14.003255

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Sergiy Mokhov, Ramy El-Ganainy, and Demetrios N. Christodoulides, "Power circulation via negative energy-flux wormholes in optical nanowaveguides," Opt. Express 14, 3255-3262 (2006)

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Related Topics
Table of Contents Category
- Integrated Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Pulse propagation and temporal solitons (060.5530)
- Guided waves (130.2790)

About this Article
History
- Original Manuscript: February 21, 2006
- Revised Manuscript: April 4, 2006
- Manuscript Accepted: April 8, 2006
- Published: April 17, 2006

Accessible

Open Access

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.

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References

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Year
|
Author
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Publication

P. N. Prasad, Nanophotonics, (John Wiley and Sons, New York2004).
[Crossref]
S. Kawata, M. Ohtsu, and M. Irie, Nano-Optics, (Springer Verlag, Berlin2002).
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]
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]
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]
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.
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]
D. Hondros and P. Debye, “Elektromagnetische Wellen an dielektrischen Drähten,” Ann. Physik 32, 465–476 (1910).
[Crossref]
S. A. Schelkunoff, Electromagnetic Waves (D. Van Nostrand Inc., New York, 1943).
E. Snitzer, “Cylindrical dielectric waveguide mode,“ J. Opt. Soc. Am. 51, 491–498 (1961).
[Crossref]
E. F. F. Gillespie, Proc. Inst. Elect. Eng. 107c, 198–201 (1960).
J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, London2000).
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]
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]
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]
A. Askin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159, (1970).
[Crossref]
J. P. Gordon, “Radiation forces and momenta in dielectric media,” Phys. Rev. A 8, 14–21 (1973).
[Crossref]

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)

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]

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)

E. Snitzer, “Cylindrical dielectric waveguide mode,“ J. Opt. Soc. Am. 51, 491–498 (1961).
[Crossref]

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.

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]

De Angelis, C.

Debye, P.

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

El-Ganainy, R.

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]

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.

Foster, M. A.

Gaeta, A. L.

Gattass, R. R.

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.

He, S.

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.

Jackson, J. D.

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

Kawata, S.

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]

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

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.

Lou, J.

Makris, K. G.

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]

Mason, M. W.

Maxwell, I.

Mazur, E.

Modotto, D.

Mokhov, S.

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]

Morandotti, R.

Noskov, Y. N.

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.

Prasad, P. N.

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

Russell, P. St. J.

Scaccabarozzi, L.

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.

Snitzer, E.

E. Snitzer, “Cylindrical dielectric waveguide mode,“ J. Opt. Soc. Am. 51, 491–498 (1961).
[Crossref]

Sorel, M.

Stanley, C. R.

Stegeman, G. I.

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.

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]

Tong, L.

Trebino, R.

Wadsworth, W. J.

Yu, X.

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)

J. Opt. Soc. Am. (1)

E. Snitzer, “Cylindrical dielectric waveguide mode,“ J. Opt. Soc. Am. 51, 491–498 (1961).
[Crossref]

Nature (1)

Opt. Express (3)

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]

Opt. Lett. (1)

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]

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).

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Fig. 1.

(a) Distribution of the ${HE}_{11}^{x}$ Poynting vector S_z 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 s_z distribution. (c) Negative s_z regions with the positive part removed for illustration purposes.

Download Full Size | PPT Slide | PDF

Fig. 2.

Iso-contour lines | $S_{z - max}^{-}$ / $S_{z - max}^{+}$ | 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.

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.

(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.

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} \vec{S} ∙ d \vec{a} = - \frac{\partial W}{\partial t}

\vec{E} = \vec{e} (r, θ) \exp [i (ω t - β z)]

\vec{H} = \vec{h} (r, θ) \exp [i (ω t - β z)]

{\begin{matrix} \vec{E} \\ \vec{H} \end{matrix}} = \frac{e^{i (ω_{0} t - β_{0} z)}}{2 π} \int_{- \infty}^{\infty} d Ω Φ_{0} (Ω) e^{i (Ω T - F (Ω) z)} {\begin{matrix} \vec{e} ({\vec{r}}_{⊥}, ω_{0} + Ω) \\ \vec{h} ({\vec{r}}_{⊥}, ω_{0} + Ω) \end{matrix}}

[\begin{matrix} \vec{E} \\ \vec{H} \end{matrix}] = [\begin{matrix} {\vec{e}}_{0} & - i {\vec{e}}_{1} \\ {\vec{h}}_{0} & - i {\vec{h}}_{1} \end{matrix}] [\begin{matrix} ϕ \\ \frac{\partial ϕ}{\partial T} \end{matrix}] \exp [i (ω_{0} t - β_{0} z)]

\vec{S} = \frac{1}{2} Re {A^{2} ({\vec{e}}_{0} \times {\vec{h}}_{0}^{*}) + A^{2} \frac{\partial ψ}{\partial T} ({\vec{e}}_{1} \times {\vec{h}}_{0}^{*} + {\vec{e}}_{0} \times {\vec{h}}_{1}^{*}) + \frac{i}{2} \frac{{\partial A}^{2}}{\partial T} ({\vec{e}}_{0} \times {\vec{h}}_{1}^{*} - {\vec{e}}_{1} \times {\vec{h}}_{0}^{*})},

\vec{S} = \frac{{∣ E_{0} ∣}^{2}}{2 \sqrt{1 + {(\frac{z}{z_{d}})}^{2}}} \exp (- \frac{2 τ^{2}}{1 + {(\frac{z}{z_{d}})}^{2}}) ∙

Re {({\vec{e}}_{0} \times {\vec{h}}_{0}^{*}) + \frac{2 (\frac{τ}{τ_{0}}) (\frac{z}{z_{d}})}{1 + {(\frac{z}{z_{d}})}^{2}} ({\vec{e}}_{1} \times {\vec{h}}_{0}^{*} + {\vec{e}}_{0} \times {\vec{h}}_{1}^{*}) - \frac{2 i (\frac{τ}{τ_{0}})}{1 + {(\frac{z}{z_{d}})}^{2}} ({\vec{e}}_{0} \times {\vec{h}}_{1}^{*} - {\vec{e}}_{1} \times {\vec{h}}_{0}^{*})}

Abstract

References

2006 (1)

2005 (1)

2004 (1)

2003 (2)

2000 (1)

1996 (1)

1973 (1)

1970 (1)

1961 (1)

1960 (1)

1910 (1)

Aitchison, J. S.

Ashcom, J. B.

Askin, A.

Birks, T. A.

Cao, Q.

Christodoulides, D. N.

De Angelis, C.

Debye, P.

El-Ganainy, R.

Fan, S.

Fejer, M. M.

Foster, M. A.

Gaeta, A. L.

Gattass, R. R.

Gillespie, E. F. F.

Gordon, J. P.

Harris, J. S.

He, S.

Hondros, D.

Irie, M.

Iwanow, R.

Jackson, J. D.

Kawata, S.

Kivshar, Y. S.

Leon-Saval, S. G.

Locatelli, A.

Lou, J.

Makris, K. G.

Mason, M. W.

Maxwell, I.

Mazur, E.

Modotto, D.

Mokhov, S.

Morandotti, R.

Noskov, Y. N.

Ohtsu, M.

Okamoto, K.

Povinelli, M. L.

Prasad, P. N.

Russell, P. St. J.

Scaccabarozzi, L.

Schelkunoff, S. A.

Shadrivov, I. V.

Shen, M.

Snitzer, E.

Sorel, M.

Stanley, C. R.

Stegeman, G. I.

Sukhorukov, A. A.

Tani, T.

Tong, L.

Trebino, R.

Wadsworth, W. J.

Yu, X.

Ann. Physik (1)

IEEE Trans. Microwave Theory Tech (1)

J. Opt. Soc. Am. (1)

Nature (1)

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (1)

Phys. Rev. E (1)

Phys. Rev. Lett. (1)

Proc. Inst. Elect. Eng. (1)

Other (7)

Cited By

Figures (5)