Ultra-Focused Optical Pulses as Analogous Quantum Gravitational Systems

Journal Article

• المجلة \ الصحيفة: Submitted to Physical Review Letters

مستخلص المنشور

The generalized uncertainty principle describes the existence of a minimal measurable length scale, which is a postulate in almost all approaches to quantum gravity.  Recently, the application of its formalism to different fields, as nonlinear optics, furnished powerful mathematical tools and offered the opportunity to increase the knowledge in these fields. Here, we apply the Feynman path integral method, rarely used in optics, to the generalized Schr\"odinger equation describing ultra-short pulses and ultra-focused beams propagation. Thanks to this approach, we find that a minimal length in the system gives rise to an upper limitation in the momentum. This result open the way to the investigation of path integral approach in optics and gives a further proof that the generalized uncertainty principle is a powerful formalism to analyze physical systems with a minimal length scale. We demonstrate that new theoretical and experimental investigations are essential in physical analogues.