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Related Concept Videos

Properties of Fourier Transform II01:24

Properties of Fourier Transform II

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The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
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Scaling01:26

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In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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Related Experiment Video

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Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
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Multi-element, multi-frequency lens transformations enabled by optical wavefront matching.

Sawyer D Campbell, Jogender Nagar, Douglas H Werner

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    |August 10, 2017
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    Summary
    This summary is machine-generated.

    Transformation optics (TO) enables gradient-index (GRIN) optics for arbitrary geometries. A new wavefront-matching (WFM) method overcomes single-frequency limitations for multi-component, multi-frequency optical designs.

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    Area of Science:

    • Optics and Photonics
    • Electromagnetism
    • Materials Science

    Background:

    • Transformation optics (TO) utilizes gradient-index (GRIN) materials to mimic conventional optical structures.
    • Quasi-conformal TO (qTO) is effective at microwave/RF frequencies but limited to single frequencies.
    • qTO faces challenges in multi-element and multi-frequency optical design.

    Purpose of the Study:

    • To present a novel multi-component, multi-frequency lens transformation procedure.
    • To overcome the inherent single-frequency limitation of qTO for optical applications.
    • To demonstrate a more general transformation method for optical systems.

    Main Methods:

    • Development of a multi-component lens transformation procedure.
    • Application of the wavefront-matching (WFM) design methodology.
    • Testing the procedure on various optical systems.

    Main Results:

    • A successful multi-component, multi-frequency transformation procedure was developed.
    • The WFM-based method addresses limitations of qTO in optical regimes.
    • The procedure proved effective for diverse optical system designs.

    Conclusions:

    • The presented WFM-based procedure offers a generalizable approach for multi-frequency GRIN optical design.
    • This method expands the applicability of transformation optics beyond single-frequency constraints.
    • The technique shows promise for advanced optical system development.