Abstract

We expose a mechanism for the dynamical generation and control of light states with diverse topologies in spiraling guiding structures. Specifically, we show that spiraling shallow refractive index landscapes induce coupling and periodic energy exchange between states with different topological charges. Such a resonant effect enables excitation of optical vortices by vortex-free inputs and allows the output topological charge of the beam to be controlled. The presence of nonlinearity results in a strong asymmetrization of the resonant curves and a shift of the resonant frequencies. Resonant vortex dynamic generation, including revivals, is shown to be possible not only in waveguides mediated by total internal reflection but also in Bragg-guiding hollow-core geometries.

© 2013 Optical Society of America

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  1. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
    [CrossRef]
  2. J. Leach, M. R. Dennis, J. Courtial, and J. Padgett, Nature 432, 165 (2004).
    [CrossRef]
  3. A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, Sci. Rep. 2, 771 (2012).
    [CrossRef]
  4. J. P. Torres and L. Torner, eds., Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).
  5. A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).
  6. I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
    [CrossRef]
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    [CrossRef]
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  9. K. S. Lee and T. Erdogan, Appl. Opt. 39, 1394 (2000).
    [CrossRef]
  10. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 99, 233903 (2007).
    [CrossRef]
  11. K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
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    [CrossRef]
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    [CrossRef]
  17. C. N. Alexeyev, Appl. Opt. 51, 6125 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
    [CrossRef]
  21. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
    [CrossRef]

2013

H. Xu and L. Yang, Opt. Lett. 38, 1978 (2013).
[CrossRef]

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[CrossRef]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

2012

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, Science 337, 446 (2012).
[CrossRef]

C. N. Alexeyev, Appl. Opt. 51, 6125 (2012).
[CrossRef]

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, Sci. Rep. 2, 771 (2012).
[CrossRef]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
[CrossRef]

2011

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 83, 063820 (2011).
[CrossRef]

2009

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

2008

C. N. Alexeyev and M. A. Yavorsky, Phys. Rev. A 78, 043828 (2008).
[CrossRef]

2007

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 99, 233903 (2007).
[CrossRef]

2004

J. Leach, M. R. Dennis, J. Courtial, and J. Padgett, Nature 432, 165 (2004).
[CrossRef]

2001

2000

1998

1991

C. D. Poole, C. D. Townsend, and K. T. Nelson, J. Lightwave Technol. 9, 598 (1991).
[CrossRef]

1990

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, Electron. Lett. 26, 1270 (1990).
[CrossRef]

1974

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

1936

I. Rabi, Phys. Rev. 49, 324 (1936).
[CrossRef]

Alexeyev, C. N.

C. N. Alexeyev, Appl. Opt. 51, 6125 (2012).
[CrossRef]

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 83, 063820 (2011).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, Phys. Rev. A 78, 043828 (2008).
[CrossRef]

Barnett, S. M.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[CrossRef]

Bekshaev, A.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Biancalana, F.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[CrossRef]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, Science 337, 446 (2012).
[CrossRef]

Bilodeau, F.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, Electron. Lett. 26, 1270 (1990).
[CrossRef]

Buccoliero, D.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, Sci. Rep. 2, 771 (2012).
[CrossRef]

Christodoulides, D. N.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Conti, C.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, Science 337, 446 (2012).
[CrossRef]

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial, and J. Padgett, Nature 432, 165 (2004).
[CrossRef]

Dennis, M. R.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, Sci. Rep. 2, 771 (2012).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and J. Padgett, Nature 432, 165 (2004).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, Sci. Rep. 2, 771 (2012).
[CrossRef]

Dreisow, F.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Erdogan, T.

Fadeyeva, T. A.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 83, 063820 (2011).
[CrossRef]

Garanovich, I. L.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
[CrossRef]

Hill, K. O.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, Electron. Lett. 26, 1270 (1990).
[CrossRef]

Johnson, D. C.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, Electron. Lett. 26, 1270 (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, Science 337, 446 (2012).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 99, 233903 (2007).
[CrossRef]

Kip, D.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Kivshar, Y. S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
[CrossRef]

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, Sci. Rep. 2, 771 (2012).
[CrossRef]

Lapin, B. P.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 83, 063820 (2011).
[CrossRef]

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, and J. Padgett, Nature 432, 165 (2004).
[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, Science 337, 446 (2012).
[CrossRef]

Lee, K. S.

Longhi, S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
[CrossRef]

Lumer, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Makris, K. G.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Malo, B.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, Electron. Lett. 26, 1270 (1990).
[CrossRef]

McGloin, D.

Nelson, K. T.

C. D. Poole, C. D. Townsend, and K. T. Nelson, J. Lightwave Technol. 9, 598 (1991).
[CrossRef]

Nolte, S.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Padgett, J.

J. Leach, M. R. Dennis, J. Courtial, and J. Padgett, Nature 432, 165 (2004).
[CrossRef]

Padgett, M. J.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[CrossRef]

D. McGloin, N. B. Simpson, and M. J. Padgett, Appl. Opt. 37, 469 (1998).
[CrossRef]

Peleg, O.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Plotnik, Y.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Podolsky, D.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Poole, C. D.

C. D. Poole, C. D. Townsend, and K. T. Nelson, J. Lightwave Technol. 9, 598 (1991).
[CrossRef]

Rabi, I.

I. Rabi, Phys. Rev. 49, 324 (1936).
[CrossRef]

Rechtsman, M. C.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Russell, J.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[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, Science 337, 446 (2012).
[CrossRef]

Rüter, C. E.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Segev, M.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Shandarova, K.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

Simpson, N. B.

Skinner, I.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, Electron. Lett. 26, 1270 (1990).
[CrossRef]

Soskin, M.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

St, P.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[CrossRef]

Sukhorukov, A. A.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
[CrossRef]

Szameit, A.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 99, 233903 (2007).
[CrossRef]

Townsend, C. D.

C. D. Poole, C. D. Townsend, and K. T. Nelson, J. Lightwave Technol. 9, 598 (1991).
[CrossRef]

Vasnetsov, M.

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

Vineberg, K. A.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, Electron. Lett. 26, 1270 (1990).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 99, 233903 (2007).
[CrossRef]

Weiss, T.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[CrossRef]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, Science 337, 446 (2012).
[CrossRef]

Wong, G. K. L.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[CrossRef]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, Science 337, 446 (2012).
[CrossRef]

Xi, X. M.

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[CrossRef]

Xu, H.

Yang, L.

Yavorsky, M. A.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 83, 063820 (2011).
[CrossRef]

C. N. Alexeyev and M. A. Yavorsky, Phys. Rev. A 78, 043828 (2008).
[CrossRef]

Zeuner, J. M.

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Appl. Opt.

Electron. Lett.

K. O. Hill, B. Malo, K. A. Vineberg, F. Bilodeau, D. C. Johnson, and I. Skinner, Electron. Lett. 26, 1270 (1990).
[CrossRef]

J. Lightwave Technol.

C. D. Poole, C. D. Townsend, and K. T. Nelson, J. Lightwave Technol. 9, 598 (1991).
[CrossRef]

J. Opt. Soc. Am. A

Nature

J. Leach, M. R. Dennis, J. Courtial, and J. Padgett, Nature 432, 165 (2004).
[CrossRef]

M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Nature 496, 196 (2013).
[CrossRef]

Opt. Lett.

Phys. Rep.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rep. 518, 1 (2012).
[CrossRef]

Phys. Rev.

I. Rabi, Phys. Rev. 49, 324 (1936).
[CrossRef]

Phys. Rev. A

C. N. Alexeyev and M. A. Yavorsky, Phys. Rev. A 78, 043828 (2008).
[CrossRef]

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, Phys. Rev. A 83, 063820 (2011).
[CrossRef]

Phys. Rev. Lett.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 99, 233903 (2007).
[CrossRef]

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef]

X. M. Xi, T. Weiss, G. K. L. Wong, F. Biancalana, S. M. Barnett, M. J. Padgett, P. St, and J. Russell, Phys. Rev. Lett. 110, 143903 (2013).
[CrossRef]

Proc. R. Soc. London Ser. A

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Sci. Rep.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, Sci. Rep. 2, 771 (2012).
[CrossRef]

Science

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, Science 337, 446 (2012).
[CrossRef]

Other

J. P. Torres and L. Torner, eds., Twisted Photons: Applications of Light with Orbital Angular Momentum (Wiley, 2011).

A. Bekshaev, M. Soskin, and M. Vasnetsov, Paraxial Light Beams with Angular Momentum (Nova Science, 2008).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Eigenmodes of a Gaussian waveguide with different topological charges, for p=10. The mode weights νm with m=0, 1, 2 versus ξ for (b) ωξ=ωr01 and (c) ωξ=ωr12. In (b) only the m=0 mode was launched into the waveguide at ξ=0, while in (c) only the m=1 mode was launched. Circles in (b) and (c) correspond to distributions from Figs. 2(a) and 2(b), respectively. (d) Dependence of the maximal weight of the m=1 mode on ωξ. In all cases μ=0.01.

Fig. 2.
Fig. 2.

Intensity and phase distributions at different distances, illustrating the dynamics of resonant conversion of (a) the m=0 mode into the m=1 mode for ωξ=ωr01, and of (b) the m=1 mode into the m=2 mode for ωξ=ωr12. In all cases μ=0.01.

Fig. 3.
Fig. 3.

Intensity and phase distributions at different propagation lengths, illustrating the dynamics of conversion of the m=0 mode into the m=2 mode at ωξ=ωr02/2 and μ=0.006.

Fig. 4.
Fig. 4.

(a) Width of the resonance for 01 and 12 transitions versus μ at σ=0. (b) Distance of energy exchange for the 01 transition versus μ at σ=0. (c) Maximal weight of the mode with m=1 versus ωξ for the 01 transition at σ=+1.1 (curve 1) and σ=1.1 (curve 2) at μ=0.01. The dashed line indicates the resonance frequency for a linear medium. (d) Resonance frequency ωr01 as a function of σ for μ=0.01.

Fig. 5.
Fig. 5.

(a) Eigenmodes of a Bragg waveguide with various charges. (b) Resonance curve for 01 transition at μ=0.01.

Fig. 6.
Fig. 6.

Intensity and phase distributions at different propagation lengths, illustrating the dynamics of resonant conversion of the m=0 mode into the m=1 mode for ωξ=ωr01 and μ=0.01 in a Bragg waveguide.

Equations (1)

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iqξ=12(2qη2+2qζ2)+σq|q|2pR(η,ζ,ξ)q.

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