WIAS Preprint No. 1391, (2009)

Padé approximant for refractive index and nonlocal envelope equations


  • Amiranashvili, Shalva
    ORCID: 0000-0002-8132-882X
  • Bandelow, Uwe
    ORCID: 0000-0003-3677-2347
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 78A60

2008 Physics and Astronomy Classification Scheme

  • 42.65.-k, 42.65.Re, 31.15.-p, 02.30.Mv


  • Short optical pulses, Envelope equation, Padé approximant




Padé approximant is superior to Taylor expansion when functions contain poles. This is especially important for response functions in complex frequency domain, where singularities are present and intimately related to resonances and absorption. Therefore we introduce a diagonal Padé approximant for the complex refractive index and apply it to the description of short optical pulses. This yields a new nonlocal envelope equation for pulse propagation. The model offers a global representation of arbitrary medium dispersion and absorption, e.g., the fulfillment of the Kramers-Kronig relation can be established. In practice, the model yields an adequate description of spectrally broad pulses for which the polynomial dispersion operator diverges and can induce huge errors.

Appeared in

  • Opt. Commun., 283 (2010) pp. 480--485.

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