Global optimality for realistic generated-channel responses

Establish global optimality of the stationarity condition in Eq. (8) for real resonant-conversion devices with finite output linewidths, phase-matching windows, and measured modulator responses.

Background

The paper derives a closed-form globally optimal pulse only for an idealized single-mode pump resonator with a spectrally flat or narrowly resonant generated channel. For realistic devices, the generated-side transfer function combines cavity response, phase matching, propagation, collection, and modulator limitations. The authors formulate the optimization through the stationarity condition in Eq. (8), but explicitly state that its global optimality has not been established.

References

What remains open is where the closed form stops. Equation (8) turns real devices—finite output linewidths, phase-matching windows, measured modulators—into a computable problem whose global optimality is un-proven.

— Which pulse maximizes resonant nonlinear conversion?  (2608.19464 - Krasnok, 19 Aug 2026) in Outlook, p. 5

Schematic illustration of the possibility (to be confirmed) that the prompt frequency shift $\omega_0 \rightarrow \omega' = \omega_0 + \delta\omega_0$ associated with (incomplete) auto-optimization studied in the present paper could lead only to the nearest local maximum, like the one on the left-hand side.

— Frequency-inference method for reduced modeling of energetic particle modes (EPM) utilizing resonant auto-optimization remnants of imperfect time-scale separation  (2609.29352 - Bierwage et al., 24 Sep 2026) in Figure 7 caption and surrounding discussion in Section 6, Summary and conclusion