Single-device independent control of propagation angle and angular dispersion

Determine whether a single optical device can provide independent control over the central propagation angle \(\varphi_{\mathrm{o}}\) and the first-order angular-dispersion coefficient \(\varphi_{\mathrm{o}}^{(1)}\), thereby enabling tuning of the group velocity over the entire \((\varphi_{\mathrm{o}},\omega_{\mathrm{o}}\varphi_{\mathrm{o}}^{(1)})\) plane.

Background

Conventional optical components such as diffraction gratings and prisms allow adjustment of the first-order angular-dispersion coefficient but do not independently control the central propagation angle and angular dispersion. Consequently, they cannot access the full range of group velocities predicted by the theoretical map in Fig. 5(a).

The paper describes universal angular-dispersion synthesizers that can generate arbitrary angular-dispersion profiles, but asks whether a single optical device can directly provide independent control of the central propagation angle and first-order angular dispersion. Resolving this issue would enable complete experimental access to the predicted luminal, subluminal, superluminal, and negative-group-velocity regimes for conventionally differentiable angular dispersion.

References

It remains an open question whether a single optical device can provide access to independent control over \varphi_{\mathrm{o} and \varphi_{\mathrm{o}{(1)} and thus tune the group velocity over the entire plane in Fig.~\ref{fig:GroupVelocity}(a).

— Limits on the free-space group velocity of optical wave packets incorporating angular dispersion. Part~I, conventional angular dispersion: tutorial  (2609.19576 - Hall et al., 17 Sep 2026) in Section “Practical limitations”

Because of the rapid variation in \varphi with \omega, it is not clear how to choose the new \varphi_{\mathrm{o}} (by contrast to conventional AD that is typically dominated by the linear AD term, thus making identifying \varphi_{\mathrm{o}} more straightforward ).

— Limits on the free-space group velocity of optical wave packets incorporating angular dispersion. Part~II, non-differentiable angular dispersion: tutorial  (2609.19580 - Hall et al., 17 Sep 2026) in Section 2.2, “Non-differentiable AD for on-axis propagation”