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Upper bounds on focusing efficiency.

Kurt Schab, Lukas Jelinek, Miloslav Capek

    Optics Express
    |December 16, 2022
    PubMed
    Summary

    This study establishes theoretical limits for lens focusing efficiency. It reveals that exit plane fields alone can lead to unbounded efficiency, unlike optimized designs, especially for near-field applications.

    Area of Science:

    • Electromagnetism and Optics
    • Computational Physics
    • Materials Science

    Background:

    • Understanding the fundamental limits of optical focusing is crucial for designing advanced optical systems.
    • Previous work often relied on simplified models or specific design paradigms, lacking comprehensive theoretical bounds.

    Purpose of the Study:

    • To formulate rigorous upper bounds on the focusing efficiency of optical systems, including lenses and aperture fields.
    • To compare these theoretical bounds with existing lens design strategies and inverse design methods.

    Main Methods:

    • Utilized integral equation representations of Maxwell's equations and Lagrangian duality to derive focusing efficiency bounds.
    • Considered two efficiency metrics: lens exit plane fields and optimal polarization currents within defined material and shape constraints.

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  • Analyzed extruded 2D dielectric geometries with out-of-plane electric fields for bound calculations and inverse design.
  • Main Results:

    • Focusing efficiency based solely on lens exit plane fields is unbounded without regularization, analogous to antenna directivity.
    • Time-reversal-based aperture fields do not guarantee optimal lens focusing efficiency.
    • Near-field (high numerical aperture) focusing is particularly sensitive to the limitations of time-reversal approaches.

    Conclusions:

    • Theoretical bounds provide a critical benchmark for evaluating and advancing optical lens design.
    • Optimized polarization currents offer a more robust approach to achieving high focusing efficiency than simple exit plane field considerations.
    • The findings highlight the importance of considering the entire lens volume and material properties for efficient near-field focusing.