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    Non-differentiable angular dispersion enables unique optical field properties. Operating near this frequency is crucial for minimizing errors and spectral uncertainty in realistic systems.

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    Area of Science:

    • Optics and Photonics
    • Wave Packet Dynamics

    Background:

    • Angular dispersion links optical frequencies to propagation angles.
    • Conventional angular dispersion assumes differentiability of angle with respect to frequency.
    • Non-differentiable angular dispersion offers unique optical field characteristics.

    Purpose of the Study:

    • Investigate the impact of spectral proximity to non-differentiable frequencies.
    • Determine the necessity of operating near non-differentiable frequencies for practical applications.
    • Quantify non-differentiable angular dispersion as a resource.

    Main Methods:

    • Theoretical analysis of space-time wave packets.
    • Examination of the role of spectral proximity to non-differentiable frequencies.
    • Quantification using a Schmidt number.

    Main Results:

    • Operating near non-differentiable frequencies is essential to mitigate implementation errors and spectral uncertainty.
    • Non-differentiable angular dispersion is maximized in the vicinity of the non-differentiable frequency.
    • This effect is retained even if the non-differentiable frequency is outside the spectrum.

    Conclusions:

    • Non-differentiable angular dispersion is a valuable resource for optical field manipulation.
    • Proximity to the non-differentiable frequency is critical for practical applications.
    • Findings aid in designing novel phase-matching for nonlinear interactions in dispersive media.