Abstract

An optical vortex soliton induces a graded-index waveguide over an extended propagation distance in a self-defocusing nonlinear optical medium. Using numerical techniques, we determine the waveguide dispersion and optimal size of the guided beam.

© 2000 Optical Society of America

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References

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  1. G. A. Askaryan, JETP 42, 1567 (1962); Sov. Phys. JETP 15, 1088 (1962).
  2. See K. Blow and G. Stegeman, eds., feature on nonlinear guided waves: physics and applications, J. Opt. Soc. Am. B 14, 2950–3260 (1997).
  3. G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
    [CrossRef]
  4. G. A. Swartzlander, Opt. Lett. 17, 493 (1992).
    [CrossRef]
  5. A. W. Snyder, L. Poladian, and D. J. Mitchell, Opt. Lett. 17, 789 (1992).
    [CrossRef] [PubMed]
  6. J. Christou, V. Tikhonenko, Y. Kivshar, and B. Luther-Davies, Opt. Lett. 21, 1649 (1995).
    [CrossRef]
  7. M. Morin, G. Duree, and G. Salamo, Opt. Lett. 20, 20 (1995).
    [CrossRef]
  8. R. Y. Chiao, I. H. Deutsch, J. C. Garrison, and E. M. Wright, in Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, London, 1992), p. 156.
  9. C. T. Law and G. A. Swartzlander, Chaos Solitons Fractals 4, 1759 (1994).
    [CrossRef]
  10. D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
    [CrossRef]
  11. D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
    [CrossRef]
  12. D. R. Andersen, D. E. Hooton, G. A. Swartzlander, and A. E. Kaplan, Opt. Lett. 15, 783 (1990); G. A. Swartzlander, Opt. Lett. 17, 493 (1992); B. Luther-Davies and Xiaoping Yang, Opt. Lett. 17, 496 (1992); S. Blair, K. Wagner, and R. McLeod, Opt. Lett. 19, 1943 (1994);
    [CrossRef] [PubMed]
  13. U. Ascher, J. Christiansen, and R. D. Russell, ACM Trans. Math. Software 7, 209 (1981).
    [CrossRef]
  14. J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
    [CrossRef]
  15. G. Arfken, Mathematical Methods for Physicists, 2nd ed. (Academic, New York, 1970), p. 770.

1997 (3)

See K. Blow and G. Stegeman, eds., feature on nonlinear guided waves: physics and applications, J. Opt. Soc. Am. B 14, 2950–3260 (1997).

D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
[CrossRef]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

1995 (2)

1994 (1)

C. T. Law and G. A. Swartzlander, Chaos Solitons Fractals 4, 1759 (1994).
[CrossRef]

1992 (3)

1990 (1)

1981 (1)

U. Ascher, J. Christiansen, and R. D. Russell, ACM Trans. Math. Software 7, 209 (1981).
[CrossRef]

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

1962 (1)

G. A. Askaryan, JETP 42, 1567 (1962); Sov. Phys. JETP 15, 1088 (1962).

Andersen, D. R.

Arfken, G.

G. Arfken, Mathematical Methods for Physicists, 2nd ed. (Academic, New York, 1970), p. 770.

Ascher, U.

U. Ascher, J. Christiansen, and R. D. Russell, ACM Trans. Math. Software 7, 209 (1981).
[CrossRef]

Askaryan, G. A.

G. A. Askaryan, JETP 42, 1567 (1962); Sov. Phys. JETP 15, 1088 (1962).

Chiao, R. Y.

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, and E. M. Wright, in Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, London, 1992), p. 156.

Christiansen, J.

U. Ascher, J. Christiansen, and R. D. Russell, ACM Trans. Math. Software 7, 209 (1981).
[CrossRef]

Christou, J.

Deutsch, I. H.

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, and E. M. Wright, in Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, London, 1992), p. 156.

Duree, G.

M. Morin, G. Duree, and G. Salamo, Opt. Lett. 20, 20 (1995).
[CrossRef]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Garrison, J. C.

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, and E. M. Wright, in Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, London, 1992), p. 156.

Hooton, D. E.

Kaplan, A. E.

Kivshar, Y.

Law, C. T.

D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
[CrossRef]

C. T. Law and G. A. Swartzlander, Chaos Solitons Fractals 4, 1759 (1994).
[CrossRef]

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

Luther-Davies, B.

Mitchell, D. J.

Morin, M.

M. Morin, G. Duree, and G. Salamo, Opt. Lett. 20, 20 (1995).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Poladian, L.

Rozas, D.

D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
[CrossRef]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Russell, R. D.

U. Ascher, J. Christiansen, and R. D. Russell, ACM Trans. Math. Software 7, 209 (1981).
[CrossRef]

Sacks, Z. S.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Salamo, G.

M. Morin, G. Duree, and G. Salamo, Opt. Lett. 20, 20 (1995).
[CrossRef]

Snyder, A. W.

Swartzlander, G. A.

Tikhonenko, V.

Wright, E. M.

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, and E. M. Wright, in Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, London, 1992), p. 156.

ACM Trans. Math. Software (1)

U. Ascher, J. Christiansen, and R. D. Russell, ACM Trans. Math. Software 7, 209 (1981).
[CrossRef]

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, Appl. Phys. 10, 129 (1976).
[CrossRef]

Chaos Solitons Fractals (1)

C. T. Law and G. A. Swartzlander, Chaos Solitons Fractals 4, 1759 (1994).
[CrossRef]

J. Opt. Soc. Am. B (2)

D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997).
[CrossRef]

See K. Blow and G. Stegeman, eds., feature on nonlinear guided waves: physics and applications, J. Opt. Soc. Am. B 14, 2950–3260 (1997).

JETP (1)

G. A. Askaryan, JETP 42, 1567 (1962); Sov. Phys. JETP 15, 1088 (1962).

Opt. Lett. (5)

Phys. Rev. Lett. (2)

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Other (2)

R. Y. Chiao, I. H. Deutsch, J. C. Garrison, and E. M. Wright, in Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, London, 1992), p. 156.

G. Arfken, Mathematical Methods for Physicists, 2nd ed. (Academic, New York, 1970), p. 770.

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Figures (3)

Fig. 1
Fig. 1

Transverse profiles of exact (Exact) and trial (sech and Gaussian) eigenmodes within a vortex soliton waveguide have an induced index, Δnmax=1.5×10-6. The transverse normalization factor is wNL=78 µm. The exact eigenmode is determined from Eqs. (4), whereas the trial functions are arbitrary analytical expressions whose size parameters have been optimized to minimize Eq. (6). Inset, experimental setup with a beam splitter to introduce collinear vortex and signal beams within a self-defocusing medium.

Fig. 2
Fig. 2

Variation of signal beam parameters for the profiles in Fig. 1: normalized signal beam peak intensity upeak2 and percentage change in normalized power P% (inset) over an area where the initial signal beam is greater than 1/e2 of its peak intensity versus normalized propagation distance Z. The longitudinal normalization factor is zNL=127 mm.

Fig. 3
Fig. 3

Normalized optimal width w1/e/wNL and waveguide dispersion Dw (inset) of the sech beam versus its wavelength λu. Each curve corresponds to a different guiding beam wavelength λv with wNL=4 µm, which can be achieved by adjustment of the background intensity.

Tables (1)

Tables Icon

Table 1 Trial Functions for the Nonlinear Guided Wave and the Corresponding Normalized Size w, Normalized Effective Width w1/e, and Normalized Propagation Constant βesta

Equations (9)

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Ev=Ar,zexpimθ,
-ivZ+2v-Cν2+κηu2v=0,
-ikukvuZ+2u-ΛCηu2+κv2u=0,
vR,θ,Z=v¯Rexpimθexpi2Z,
uR,Z=u¯Rexpi2βZ,
2v¯+1RRRv¯R-m2R2v¯-2v¯2v¯=0,
2βu¯+1RRRv¯R-2v¯2u¯=0.
P%=100×1-0W1/eur,z2rdr0W1/eur,z=02rdr.
βestw=0Ru¯w/R2+2Λv¯2Ru¯2wdR×02u¯2wRdR-1,

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