Abstract

We study stimulated mode conversion and dynamics of Rabi-like oscillations of weights of guided modes in deeply subwavelength guiding structures, whose dielectric permittivity changes periodically in the direction of light propagation. We show that despite strong localization of the fields of eigenmodes on the scales below the wavelength of light, even weak longitudinal modulation couples modes of selected parity and causes periodic energy exchange between them, thereby opening the way for controllable transformation of the internal structure of subwavelength beams. The effect is reminiscent of Rabi oscillations in multilevel quantum systems subjected to the action of periodic external fields. By using rigorous numerical solution of the full set of the Maxwell's equations, we show that the effect takes place not only in purely dielectric, but also in metallic-dielectric structures, despite the energy dissipation inherent to the plasmonic waveguides. The stimulated conversion of subwavelength light modes is possible in both linear and nonlinear regimes.

© 2015 Optical Society of America

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References

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    [Crossref]
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2013 (1)

2012 (1)

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

2011 (2)

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett. 106(8), 083902 (2011).
[Crossref] [PubMed]

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

2010 (1)

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

2009 (1)

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

2008 (2)

C. N. Alexeyev and M. A. Yavorsky, “Generation and conversion of optical vortices in long-period helical core optical fibers,” Phys. Rev. A 78(4), 043828 (2008).
[Crossref]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

2007 (2)

V. S. Shchesnovich and S. Chávez-Cerda, “Bragg-resonance-induced Rabi oscillations in photonic lattices,” Opt. Lett. 32(13), 1920–1922 (2007).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Resonant mode oscillations in modulated waveguiding structures,” Phys. Rev. Lett. 99(23), 233903 (2007).
[Crossref] [PubMed]

2004 (2)

2000 (1)

1999 (1)

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

1998 (2)

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58(4), R2648–R2651 (1998).
[Crossref]

D. McGloin, N. B. Simpson, and M. J. Padgett, “Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam,” Appl. Opt. 37(3), 469–472 (1998).
[Crossref] [PubMed]

1997 (1)

1996 (1)

X. G. Zhao, G. A. Georgakis, and Q. Niu, “Rabi oscillations between Bloch bands,” Phys. Rev. B Condens. Matter 54(8), R5235–R5238 (1996).
[Crossref] [PubMed]

1991 (1)

C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9(5), 598–604 (1991).
[Crossref]

1990 (1)

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

1936 (1)

I. I. Rabi, “On the process of space quantization,” Phys. Rev. 49(4), 324–328 (1936).
[Crossref]

Alexeyev, C. N.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

C. N. Alexeyev and M. A. Yavorsky, “Generation and conversion of optical vortices in long-period helical core optical fibers,” Phys. Rev. A 78(4), 043828 (2008).
[Crossref]

Almeida, V. R.

Biancalana, F.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Bilodeau, F.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Chávez-Cerda, S.

Christodoulides, D. N.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Conti, C.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Denz, C.

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett. 106(8), 083902 (2011).
[Crossref] [PubMed]

Desyatnikov, A. S.

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett. 106(8), 083902 (2011).
[Crossref] [PubMed]

Erdogan, T.

Fadeyeva, T. A.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

Fan, S.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

Fischer, M. C.

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58(4), R2648–R2651 (1998).
[Crossref]

Georgakis, G. A.

X. G. Zhao, G. A. Georgakis, and Q. Niu, “Rabi oscillations between Bloch bands,” Phys. Rev. B Condens. Matter 54(8), R5235–R5238 (1996).
[Crossref] [PubMed]

Hill, K. O.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Hu, B.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

Ippen, E. P.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

Joannopoulos, J. D.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

Johnson, D. C.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Kang, M. S.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of topological light states in spiraling structures,” Opt. Lett. 38(17), 3414–3417 (2013).
[PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Resonant mode oscillations in modulated waveguiding structures,” Phys. Rev. Lett. 99(23), 233903 (2007).
[Crossref] [PubMed]

Kip, D.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Kivshar, Y. S.

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett. 106(8), 083902 (2011).
[Crossref] [PubMed]

Kobayashi, T.

Krolikowski, W.

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett. 106(8), 083902 (2011).
[Crossref] [PubMed]

Lapin, B. P.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

Lee, H. W.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Lee, K. S.

Lipson, M.

Madison, K. W.

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58(4), R2648–R2651 (1998).
[Crossref]

Makris, K. G.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Malo, B.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

McGloin, D.

Mihalache, D.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

Morimoto, A.

Nelson, K. T.

C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9(5), 598–604 (1991).
[Crossref]

Neshev, D. N.

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett. 106(8), 083902 (2011).
[Crossref] [PubMed]

Niu, Q.

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58(4), R2648–R2651 (1998).
[Crossref]

X. G. Zhao, G. A. Georgakis, and Q. Niu, “Rabi oscillations between Bloch bands,” Phys. Rev. B Condens. Matter 54(8), R5235–R5238 (1996).
[Crossref] [PubMed]

Padgett, M. J.

Panepucci, R. R.

Panoiu, N. C.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

Peleg, O.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Poole, C. D.

C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9(5), 598–604 (1991).
[Crossref]

Rabi, I. I.

I. I. Rabi, “On the process of space quantization,” Phys. Rev. 49(4), 324–328 (1936).
[Crossref]

Raizen, M. G.

M. C. Fischer, K. W. Madison, Q. Niu, and M. G. Raizen, “Observation of Rabi oscillations between Bloch bands in an optical potential,” Phys. Rev. A 58(4), R2648–R2651 (1998).
[Crossref]

Robinett, R. W.

R. W. Robinett, “Quantum wave packet revivals,” Phys. Rep. 392(1-2), 1–119 (2004).
[Crossref]

Russell, P. St. J.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Rüter, C. E.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

Segev, M.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Shandarova, K.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

Shchesnovich, V. S.

Simpson, N. B.

Skinner, I.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Takahara, J.

Taki, H.

Terhalle, B.

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett. 106(8), 083902 (2011).
[Crossref] [PubMed]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of topological light states in spiraling structures,” Opt. Lett. 38(17), 3414–3417 (2013).
[PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Resonant mode oscillations in modulated waveguiding structures,” Phys. Rev. Lett. 99(23), 233903 (2007).
[Crossref] [PubMed]

Townsend, C. D.

C. D. Poole, C. D. Townsend, and K. T. Nelson, “Helical-grating two-mode fiber spatial-mode coupler,” J. Lightwave Technol. 9(5), 598–604 (1991).
[Crossref]

Vineberg, K. A.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, “Efficient mode conversion in telecommunication fiber using externally written gratings,” Electron. Lett. 26(16), 1270–1272 (1990).
[Crossref]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of topological light states in spiraling structures,” Opt. Lett. 38(17), 3414–3417 (2013).
[PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Resonant mode oscillations in modulated waveguiding structures,” Phys. Rev. Lett. 99(23), 233903 (2007).
[Crossref] [PubMed]

Weiss, T.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Winn, J. N.

J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Phys. Rev. B 59(3), 1551–1554 (1999).
[Crossref]

Wong, G. K. L.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Xu, Q.

Yamagishi, S.

Yavorsky, M. A.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Transverse (a) and longitudinal (b) electric field distributions in three linear eigenmodes of Gaussian waveguide with p=2 and a=250nm . Transverse (c) and longitudinal (b) electric field distributions in three eigenmodes supported by the dielectric slab with a=600nm and p=2 surrounded by metal with Re ε m =20 .
Fig. 2
Fig. 2 (a),(b) Dynamic of resonant nonparaxial mode conversion at δ=0.1 in dielectric structure at ω z = ω r 0.389 k 0 , when only first or third mode is provided at the input. The propagation distance and transverse window size are 130μm and 4μm , respectively. (c),(d) Dynamics of mode conversion at δ=0.1 and ω z = ω r 0.232 k 0 in metal-dielectric-metal structure. The propagation distance and transverse window size are 75μm and 2μm , respectively. Only | E x | 2 distribution is shown.
Fig. 3
Fig. 3 Mode weights ν k = | c k | 2 versus propagation distance for 13 and 31 resonant transitions. The dependencies ν k (z) in (a),(b) correspond to evolution dynamics shown in Fig. 2.
Fig. 4
Fig. 4 (a) Maximal weight of the third mode versus modulation frequency at δ=0.1 in the linear medium. Resonance width (b) and effective coupling distance at ω z = ω r (c) versus refractive index modulation depth δ in the linear medium. (d) Maximal weight of the third mode versus modulation frequency in focusing medium for peak nonlinear contribution to the refractive index n nl =0.02 and δ=0.1 .

Equations (6)

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i E x z = 1 ε 0 ω x [ 1 ε(x,z) H y x ] μ 0 ω H y , i H y z = ε 0 ε(x,z)ω E x ,
ε(x,z)= ε bg +p[1+δsin( ω z z)]exp( x 2 / a 2 ),
{ E m , H m }= n a n (z) e i β n z { E n , H n }
i d a n dz = m ω K nm a m exp[i( β n β m )z] ,
2 K nm = δ ε lin ( E x n E x m + E z n E z m )dx / Re( E x n H y n )dx ,
c n (z)= E x (x,z) H y n dx / E x n H y n dx ,

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