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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
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Geodesic lenses for guided optical waves.

G C Righini, V Russo, S Sottini

    Applied Optics
    |February 4, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Researchers developed novel two-dimensional geodesic lenses for integrated optics. This method extends microwave antenna principles to thin film optics, enabling precise light manipulation in planar circuits.

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    Area of Science:

    • Optics
    • Integrated Optics
    • Materials Science

    Background:

    • Two-dimensional lenses are crucial for integrated optical systems.
    • Existing methods for fabricating these lenses have limitations.
    • The principle of configuration lenses, successful in microwave antennas, offers a potential alternative.

    Purpose of the Study:

    • To introduce a novel method for creating two-dimensional geodesic lenses for integrated optics.
    • To adapt the configuration lens principle from microwave antennas to thin film optics.
    • To demonstrate the practical application and advantages of these geodesic lenses.

    Main Methods:

    • Extending the principle of configuration lenses to thin film optics.
    • Utilizing the concept of propagation along a curved surface in a two-dimensional Riemann space, where rays follow geodesics.
    • Constructing and testing two optical geodesic lenses with planar input and output.

    Main Results:

    • Successfully constructed and tested two optical geodesic lenses.
    • Demonstrated that these lenses can be easily integrated into planar film circuits.
    • Highlighted the advantage of pre-fabricating the substrate with high accuracy, similar to glass optics.

    Conclusions:

    • The developed method offers a viable alternative for fabricating two-dimensional geodesic lenses.
    • These lenses are suitable for integration into planar optical circuits.
    • The technique allows for precise substrate preparation and subsequent dielectric film deposition using established methods.