Existence of guided cylindrical TM-modes in a homogeneous self-focusing dielectric

Charles A. Stuart; Huan-Song Zhou

Annales de l'I.H.P. Analyse non linéaire (2001)

  • Volume: 18, Issue: 1, page 69-96
  • ISSN: 0294-1449

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Stuart, Charles A., and Zhou, Huan-Song. "Existence of guided cylindrical TM-modes in a homogeneous self-focusing dielectric." Annales de l'I.H.P. Analyse non linéaire 18.1 (2001): 69-96. <http://eudml.org/doc/78513>.

@article{Stuart2001,
author = {Stuart, Charles A., Zhou, Huan-Song},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {self-trapped beam of light; guided waves; energy integral; focusing dielectric material; nonlinear eigenvalue problem; self-trapped transverse magnetic field modes; cylindrical optical filter; Mountain Pass Theorem},
language = {eng},
number = {1},
pages = {69-96},
publisher = {Elsevier},
title = {Existence of guided cylindrical TM-modes in a homogeneous self-focusing dielectric},
url = {http://eudml.org/doc/78513},
volume = {18},
year = {2001},
}

TY - JOUR
AU - Stuart, Charles A.
AU - Zhou, Huan-Song
TI - Existence of guided cylindrical TM-modes in a homogeneous self-focusing dielectric
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 1
SP - 69
EP - 96
LA - eng
KW - self-trapped beam of light; guided waves; energy integral; focusing dielectric material; nonlinear eigenvalue problem; self-trapped transverse magnetic field modes; cylindrical optical filter; Mountain Pass Theorem
UR - http://eudml.org/doc/78513
ER -

References

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  2. 2 Chen Y, TE and TM families of self-trapped beams, IEEE J. Quantum ElectronicsVol. 27 (1991) 1236-1241. 
  3. 3 Chen Y, Snyder A.W, TM-type self-guided beams with circular cross-section, Electr. Lett.Vol. 27 (1991) 564-566. 
  4. 4 Jeanjean L, On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer type problem, Proc. Royal Soc. Edinburgh, Ser. AVol. 129A (1999) 787-809. Zbl0935.35044
  5. 5 John O, Stuart C.A, Guidance properties of a cylindrical defocusing waveguide, Comm. Math. Univ. CarolinaeVol. 35 (1994) 653-673. Zbl0819.35137MR1321236
  6. 6 Lebedev N.N, Special Functions and their Applications, Dover, 1972. Zbl0271.33001MR350075
  7. 7 Rabinowitz P.H, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. in Math., No. 65, Amer. Math. Soc, Providence, RI, 1986. Zbl0609.58002MR845785
  8. 8 Ruppen H.-J, Multiple cylindrical TE-Modes for a homogeneous self-focusing dielectric, Nonlinear WorldVol. 2 (1995) 387-418. Zbl0833.34038MR1360868
  9. 9 Ruppen H.-J, Multiple cylindrical TM-Modes in a homogeneous self-focusing dielectric, J. Differential EquationsVol. 201 (1997) 112-123. Zbl0898.34017
  10. 10 Showalter R.E, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, Mathematical Surveys and Monographs (AMS), Vol. 49, 1997. Zbl0870.35004MR1422252
  11. 11 Stuart C.A, Self-trapping of an electromagnetic field and bifurcation from the essential spectrum, Arch. Rat. Mech. Anal.Vol. 113 (1991) 65-96. Zbl0745.35044MR1079182
  12. 12 Stuart C.A, Cylindrical TM-modes in a homogeneous self-focusing dielectric, Math. Models Methods Appl. Sci.Vol. 6 (1996) 977-1008. Zbl0934.35190MR1419240
  13. 13 Stuart C.A, Magnetic field wave equations for TM-modes in nonlinear optical waveguides, in: Caristi, Mitidieri (Eds.), Reaction Diffusion Systems, Marcel Dekker, 1997. Zbl0894.35111MR1472530
  14. 14 Stuart C.A, Zhou H.S, A variational problem related to self-trapping of an electromagnetic field, Math. Methods Appl. Sci.Vol. 19 (1996) 1397-1407. Zbl0862.35123MR1414401

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