Nonlinear guided waves in saturable nonlinear media

Langbein, U.; Lederer, F.; Peschel, Thomas; Ponath, H. E.

doi:10.1364/ol.10.000571

Cited by 73 publications

(12 citation statements)

References 6 publications

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“…Conditions (11), (12) correspond to the situation that the maximum of the solution u moves from the interior system to the exterior. This situation occurs indeed, in example 2.1 for λ = α 1 > α 2 , i.e.…”

Section: Remark 37mentioning

confidence: 99%

“…The nonlinear eigenvalue problem has been treated for special choices of . Typical nonlinearities with an appropriate choice of parameters include: (i) (x, s) = 0 + as Akhmediev [1], Etrich, Moloney, Jones [5] (ii) (x, s) = 0 + as + bs 2 Bolshinskii [4], Etrich, Moloney, Jones [5] (iii) (x, s) = 0 + as 1+bs (b > 0) Langbein, Lederer, Peschel, Ponath [11] (iv) (x, s) = 0 + a(1 − exp(−bs)) Langbein, Lederer, Peschel, Ponath [11] A systematic bifurcation analysis for (1) has been carried out by Stuart [16] giving general results concerning the existence of nontrivial solutions for various intensities. The general approach however did not include information about symmetry properties of the nontrivial solutions.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation of asymmetric solutions in nonlinear optical media

Jones

Küpper

Schaffner

2001

Z. angew. Math. Phys.

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We study the propagation of monochromatic fields in a layered medium. The mathematical model is derived from Maxwell's equations. It consists of a nonlinear eigenvalue problem on the real axis with coefficients depending on the various layers. A systematic analysis is carried out to uncover the various mechanisms leading to the bifurcation of asymmetric solutions even in a completely symmetric setting. We derive two particular simple conditions for the occurence of asymmetric bifurcation from the symmetric branch. One of these conditions occurs at a matching of the refractive indices across the interface while the other corresponds to a switching of the peak from the core to the cladding. The rich bifurcation structure is illustrated by numerical calculations. Further stability considerations are included. ZusammenfassungDie Arbeit befaßt sich mit der Ausbreitung monochromatischer Wellen in einem geschichteten Medium. Die zugrundeliegende nichtlineare Eigenwertaufgabe wird von den Maxwell-Gleichungen hergeleitet; die Koeffizienten sind unterschiedlich in den einzelnen Schichten definiert. In einer systematischen Analyse werden zwei Mechanismen aufgedeckt, die zur Verzweigung asymmetrischer Lösungen selbst in einer vollkommen symmetrischen Konstellation führen. Während das eine Kriterium auf der bereinstimmung der Refraktionsindizes beruht, entspricht das andere dem Wechsel der maximalen Intensität von der inneren zuräußeren Schicht. Die reichhaltige Verzweigungsstruktur wird anhand von numerischen Beispielen illustriert. Außer-dem werden Stabilitätsbetrachtungen einbezogen; mit Hilfe geometrischerÜberlegungen kann die Instabilität einiger Konstellationen erkannt werden. Mathematics Subject Classification (2000). 34B15, 58E07, 78A60.

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Section: Remark 37mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcation of asymmetric solutions in nonlinear optical media

Jones

Küpper

Schaffner

2001

Z. angew. Math. Phys.

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“…wi th I s pl ayi ng the sam e ro le as in (2 ) (the exponenti al m odel of satura ti on [18]) or appl y the p ol yno mia l functi on (qubi c-qui nti c model ) [20] " N L ( I ) =˜I À˜I 2 = I s :…”

Section: T H E Sol U T Io N O F G N L S Ementioning

confidence: 99%

“…By no w the tw o-level m odel [17], the exp onenti al mo del [18 ], \ square two-level" [19], and pol yno m ial m odel s (qubi c-qui nti c) [20{ 2 2] ha ve been used most frequentl y. Since al l these m odel s gi ve very simi la r results for sm all Ùelds (f ar fro m satura ti on), appl icati o n of any of them i s the matter of conveni ence.…”

Section: Introductionmentioning

confidence: 99%

Bright and Dark Solitons in Generalized Kerr-Like Media

Jasiński

2001

Acta Phys. Pol. A

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w U ni versity of T echnolo gy K oszy kowa 75, 00-662 W arszawaIn the pap er the propagation of short pulses in nonli near K err-like me dium is considered . Pulses are describ ed by the nonlinear Schr odinger equation in w hich the generalizati on of nonlinear disp ersion term and the self-frequency shif t are taken into account. T he solution of the equation in the form of quadrature is derived. Both the phase and pro Ùle of the pulse intensity are obtained. T he cases of propagating bright and dark solitons in saturable K err-like medium are analyzed. T w o mo dels of saturation are considered. T he explic it analytical expressions describing the K err limit are rep orted. T he relations b etw een the medium and propagatio n parameters are thoroughly discussed .PACS numb ers: 42. 65. T g, 42. 82. Et 1. I n t r o d u ct io n I n no nl i near Kerr di electri c stro ng l i ght p ul ses of specia l shap e (sol i to ns) pro pagate wi tho ut changi ng i ts for m due to the com p ensati on of two e˜ects | the l i near gro up vel ocit y di spersion ( G V D ) and nonl i near p ol ari zati on of the medi um (self-pha se m odul atio n, SP M) [1{ 3]. Pro pagati on of these pul ses i s descri b ed by no nl i near Schr odi nger equa ti on (N LSE).The stro ng electri c Ùeld of sol i to n can cause ma ny other e˜ects in the Kerr di electri c. One of these e˜ects | the thi rd or hi gher order di spersion | i s l i near [4{ 6]; the others are no nl i near. In the pap er two of such e˜ects are considered | nonl i near di spersio n (ND ) [6{ 9] and self-frequency shif t (SFS) [10,11]. The NLSE equati on general i zed by these (G NLSE) term s al so p ossesse s sol uti ons i n the form of sol i to ns, but special requi rem ents b etween para m eters of the medi um and sol i to n are needed i n order to preserve the ori gina l pro Ùle fro m the pure Kerr di electri c [6, 12{ 16].In the presence of stro ng soli to n Ùeld the nonl i near perm i tti vi ty of the m edi um can devi ate fro m the sim pl e Kerr dep endence reveal ing satura ti o n. The wa y we shoul d m odi fy i t depends on m odel of satura ti on. By no w the tw o-level m odel [17], the exp onenti al mo del [18 ], \ square two-level" [19], and pol yno m ial (7 7)

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“…Thi s m odel enabl es anal yti cal sol uti ons of man y pro bl ems i nv olvi ng non-Kerr m edia, but i n fa ct does not predi ct any satura ti on for l arge i ntensi ty . The other model s of satura ti on | tw o-l evel [1 7] and exp onenti al [18] | gua ra ntee the pro p er b eha vi or of p ermi tti vi t y for l arg e i ntensi ty , but pra cti cal l y no ne of the pro bl ems i n such m edi a canno t b e sol ved ana l yti cal l y. The m ost pro mi sing i s the square-two -level m odel [19] wi th a pro per l arg e i ntensi ty l i m it and many anal yti cal sol uti ons.…”

Section: Introductionmentioning

confidence: 99%

Grey Solitons in Saturable Media with Nonlinear Dispersion and Self-Frequency Shift

Jasiński

2003

Acta Phys. Pol. A

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In t he paper a special for m of the generali zed nonline ar Schr odinger equation in satura ble medium w ith nonlinear disp ersion and the self-frequenc y shif t terms is considered . T he solutions describin g both the intensity and phase pro Ùles of grey soliton s propagating in this medium are obtained . F our cases of medium w ith or w ithout saturation and w ith or without higher order terms are considered. F or a square-tw o-level mo del of saturation analytical explici t solutions are derived. T he relations b etw een the medium and propagation parameters of solitons are discussed . PACS numb ers: 42.65.T g, 42. 82. Et

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Nonlinear guided waves in saturable nonlinear media

Cited by 73 publications

References 6 publications

Bifurcation of asymmetric solutions in nonlinear optical media

Bifurcation of asymmetric solutions in nonlinear optical media

Bright and Dark Solitons in Generalized Kerr-Like Media

Grey Solitons in Saturable Media with Nonlinear Dispersion and Self-Frequency Shift

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