26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

The Shortest Optical Pulses in the Complex Short Pulse Equation

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Contributed Oral ANZOS | Photonics and Optics (ANZCOP)

Speaker

Dr Uwe Bandelow (WIAS Berlin)

Description

The propagation of optical pulses approaching the single-cycle limit requires mathematical models that extend beyond the slowly varying envelope approximation. While the Short Pulse Equation (SPE) provides an integrable model for the real-valued electric field of ultra-short pulses, the Complex Short Pulse Equation (CSPE) generalizes this framework to the analytic signal associated with the real field, enabling the simultaneous description of amplitude and phase dynamics. Although the integrability of the CSPE in [1] remains an open question, it admits a rich family of exact solutions [2], making it an attractive model for the theoretical study of few-cycle pulse propagation in nonlinear optical fibers.

In this contribution, we investigate the limiting behavior of bright and dark soliton solutions of the CSPE, with particular emphasis on the shortest physically admissible optical pulses. Using the exact parametric representation of the CSPE solitons, we analyze the transition from smooth localized pulses to cusped and loop-like structures. We discuss how these limiting solutions establish the fundamental lower bound on pulse duration.

Special attention is given to the spectral signatures of the shortest bright and dark CSPE solitons. Their spectra are interpreted in the context of the limiting solitons investigated in [1], where it was shown that the shortest physically realizable optical solitons exhibit characteristic spectral features that differ fundamentally from those predicted by conventional envelope models. We demonstrate that the CSPE provides a natural framework for describing these limiting pulse configurations and discuss the similarities and differences between the shortest bright- and dark-soliton states. These results further establish the CSPE as a canonical model for exploring the mathematical and physical limits of ultra-short pulse propagation beyond the slowly varying envelope approximation.

[1] Sh. Amiranashvili et al, Optics Express 22, 30251–30256 (2014)
[2] H. Mao, Theoretical and Mathematical Physics, 227(1):645–657, (2026)