Nonpolynomial Schroedinger equation for resonantly absorbing gratings

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.023807· OSTI ID:21537217

Shabtay, Lior; Malomed, Boris A ^[1]

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1. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

We derive a nonlinear Schroedinger equation with a radical term, {approx}{radical}(1-|V|{sup 2}), as an asymptotic model of the resonantly absorbing Bragg reflector (RABR), i.e., a periodic set of thin layers of two-level atoms, resonantly interacting with the electromagnetic field and inducing the Bragg reflection. A family of bright solitons is found, which splits into stable and unstable parts, exactly obeying the Vakhitov-Kolokolov criterion. The soliton with the largest amplitude, (|V|){sub max}=1, is a ''quasipeakon,'' i.e., a solution with a discontinuity of the third derivative at the center. Families of exact cnoidal waves, built as periodic chains of quasipeakons, are found too. The ultimate solution belonging to the family of dark solitons, with the background level V=1, is a dark compacton. Those bright solitons that are unstable destroy themselves (if perturbed) attaining the critical amplitude, |V|=1. The dynamics of the wave field around this critical point is studied analytically, revealing a switch of the system into an unstable phase, in terms of the RABR model. Collisions between bright solitons are investigated too. The collisions between fast solitons are quasielastic, while slowly moving ones merge into breathers, which may persist or perish (in the latter case, also by attaining |V|=1).

• OSTI ID: 21537217
• Journal Information: Physical Review. A, Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevA.83.023807; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
AMPLITUDES
ASYMPTOTIC SOLUTIONS
ATOMS
BRAGG REFLECTION
COLLISIONS
ELECTROMAGNETIC FIELDS
GRATINGS
NONLINEAR PROBLEMS
PERIODICITY
RESONANCE ABSORPTION
SCHROEDINGER EQUATION
SOLITONS
THIN FILMS
ABSORPTION
DIFFERENTIAL EQUATIONS
EQUATIONS
FILMS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
REFLECTION
SORPTION
VARIATIONS
WAVE EQUATIONS