Universality and non-differentiability: A new perspective on angular dispersion in optics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916807558823936 |
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| author | Hall, Layton A. Yessenov, Murat Schepler, Kenneth L. Abouraddy, Ayman F. |
| author_facet | Hall, Layton A. Yessenov, Murat Schepler, Kenneth L. Abouraddy, Ayman F. |
| contents | Angular dispersion (AD) is a ubiquitous phenomenon in optics after light traverses a diffractive or dispersive device, whereby each wavelength propagates at a different angle. AD is useful in a variety of applications; for example, modifying the group velocity or group-velocity dispersion of pulsed lasers in free space or optical materials, which are essential ingredients in group-velocity matching and dispersion compensation. Conventional optical components introduce `differentiable' AD, so that the propagation angle can be expanded perturbatively around a fixed frequency, in which only a few low AD-orders are typically relevant. However, this model does not encompass newly emerging classes of propagation-invariant pulsed optical fields, such as `space-time wave packets', which incorporate a new form of AD that we call `non-differentiable AD'. This is a surprising feature: there exists a frequency at which the derivative of the propagation angle with respect to frequency is not defined. Consequently, the propagation angle cannot be expanded perturbatively at this frequency, and a large number of independently controllable AD orders are needed to approximate this condition. Synthesizing these new AD-induced field configurations requires constructing a `universal AD synthesizer' capable of accessing the magnitude and sign of any AD order, a capability missing from any single optical component to date. This Perspective article provides a unified schema for studying differentiable and non-differentiable AD, shows that non-differentiable AD enables circumventing many well-established constraints in optics -- thereby giving rise to new applications, and outlines the requirements for a universal AD synthesizer capable of producing both forms of AD. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_18858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality and non-differentiability: A new perspective on angular dispersion in optics Hall, Layton A. Yessenov, Murat Schepler, Kenneth L. Abouraddy, Ayman F. Optics Angular dispersion (AD) is a ubiquitous phenomenon in optics after light traverses a diffractive or dispersive device, whereby each wavelength propagates at a different angle. AD is useful in a variety of applications; for example, modifying the group velocity or group-velocity dispersion of pulsed lasers in free space or optical materials, which are essential ingredients in group-velocity matching and dispersion compensation. Conventional optical components introduce `differentiable' AD, so that the propagation angle can be expanded perturbatively around a fixed frequency, in which only a few low AD-orders are typically relevant. However, this model does not encompass newly emerging classes of propagation-invariant pulsed optical fields, such as `space-time wave packets', which incorporate a new form of AD that we call `non-differentiable AD'. This is a surprising feature: there exists a frequency at which the derivative of the propagation angle with respect to frequency is not defined. Consequently, the propagation angle cannot be expanded perturbatively at this frequency, and a large number of independently controllable AD orders are needed to approximate this condition. Synthesizing these new AD-induced field configurations requires constructing a `universal AD synthesizer' capable of accessing the magnitude and sign of any AD order, a capability missing from any single optical component to date. This Perspective article provides a unified schema for studying differentiable and non-differentiable AD, shows that non-differentiable AD enables circumventing many well-established constraints in optics -- thereby giving rise to new applications, and outlines the requirements for a universal AD synthesizer capable of producing both forms of AD. |
| title | Universality and non-differentiability: A new perspective on angular dispersion in optics |
| topic | Optics |
| url | https://arxiv.org/abs/2506.18858 |