Path integral for non-paraxial optics

¹ Department of Physical and Chemical Sciences, University of L'Aquila - Via Vetoio 10, I-67010 L'Aquila, Italy
² Institute for Complex Systems, National Research Council (ISC-CNR) - Via dei Taurini 19, I-00185 Rome, Italy
³ Department of Physics, University Sapienza - Piazzale Aldo Moro 5, I-00185 Rome, Italy
⁴ Irving K. Barber School of Arts and Sciences, University of British Columbia-Okanagan - 3333 University Way, Kelowna, British Columbia V1V 1V7, Canada
⁵ Department of Physics and Astronomy, University of Lethbridge - Lethbridge, Alberta, T1K 3M4, Canada
⁶ Department of Physical Sciences, Indian Institute of Science Education and Research Mohali Sector 81, SAS Nagar, Manauli 140306, India
⁷ Université Clermont Auvergne - 4, Avenue Blaise Pascal, F-63178 Aubire Cedex, France
⁸ Department of Physics and Astronomy, College of Science, King Saud Universty - Riyadh 11451, Saudi Arabia
⁹ Mathematics Department, Faculty of Science, Damascus University - Damascus, Syria

Received: 3 August 2018
Accepted: 5 November 2018

Abstract

In this paper, we have constructed the Feynman path integral method for non-paraxial optics. This is done by using the mathematical analogy between a non-paraxial optical system and the generalized Schrödinger equation deformed by the existence a minimal measurable length. Using this analogy, we investigated the consequences of a minimal length in this optical system. This path integral has been used to obtain instanton solution for such an optical system. Moreover, the Berry phase of this optical system has been investigated. These results may disclose a new way to use the path integral approach in optics. Furthermore, as such systems with an intrinsic minimal length have been studied in quantum gravity, the ultra-focused optical pulses can be used as an optical analog of quantum gravity.