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Related Concept Videos

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences01:17

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences

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Related Experiment Video

Updated: Jun 22, 2026

External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures
08:32

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Published on: May 7, 2017

Independent-elementary-pulse representation for non-stationary fields.

Pasi Vahimaa, Jari Turunen

    Optics Express
    |June 12, 2009
    PubMed
    Summary

    We introduce a new model for partially coherent non-stationary wave fields using independent, finite pulses. This model simplifies analysis and yields Gaussian or Lorentzian spectra for specific pulse shapes.

    Area of Science:

    • Optics and Photonics
    • Wave Field Theory
    • Coherence Properties

    Background:

    • Partially coherent and non-stationary wave fields are crucial in various optical applications.
    • Understanding their statistical properties, particularly coherence, is essential for controlling light propagation and interaction.

    Purpose of the Study:

    • To introduce a novel mathematical model for temporally partially coherent non-stationary wave fields.
    • To analyze the spectral coherence properties of these wave fields.
    • To demonstrate the model's ability to recover known cases like fully coherent pulses and stationary fields.

    Main Methods:

    • Representing non-stationary wave fields as a packet of mutually independent, fully temporally coherent pulses of finite length.
    • Determining the spectral coherence properties of these elementary pulses.

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  • Considering Gaussian and exponential elementary pulses with a Gaussian weight function.

    • Main Results:

    • Derived closed-form algebraic expressions for temporal and spectral correlation functions.
    • Showcased that the model can represent fully coherent pulses and stationary fields in limiting cases.
    • Demonstrated that Gaussian and exponential pulses lead to Gaussian and Lorentzian spectra, respectively.

    Conclusions:

    • The proposed model provides a flexible framework for describing partially coherent non-stationary wave fields.
    • The model facilitates the analytical calculation of correlation functions and spectral properties.
    • It offers insights into the relationship between elementary pulse shapes and the resulting spectral characteristics.