https://doi.org/10.1140/epjp/s13360-025-06491-x
Regular Article
Perturbation-based classical and quantum field theoretic approach for parameter estimation of Kerr nonlinear medium
1
Department of Electronics and Communication Engineering, Bhagwan Parshuram Institute of Technology, PSP-4, Dr. K. N. Katju Marg, Sector-17, 110089, Rohini, Delhi, India
2
Department of Electronics and Communication Engineering, Netaji Subhash University of Technology, Azad Hind Fauj Marg, Sector-3, Dwarka-110078, Delhi, India
Received:
12
March
2025
Accepted:
28
May
2025
Published online:
5
July
2025
Perturbation theoretic formulas for the electric field scattered by a Kerr nonlinear medium are proposed when an incident field interacts with the medium. From these formulas, a linear least squares-based algorithm for estimating the parameters of the Kerr medium using measurements of the scattered field is discussed. Finally, using the formalism of quantum field theory methods for computing scattering, absorption and emission probabilities of a finite number of photons are discussed. Generalizations to higher-degree polynomial nonlinearities in the medium are also presented. These formulae can be applied to estimate the nonlinear medium parameters at the quantum level from measuring of photon scattering cross sections. We point out the fact that although the Kerr parameter estimation problem is highly nonlinear, by replacing by the problem of estimating the statistical moments of the parameters, it can be transformed into a linear least squares problem. This can be regarded as new contribution to the development of mathematical statistics especially when parameter estimation is a highly nonlinear optimization problem. This piece of work can be used as a tool to enhance the process of parameter estimation in mathematical statistics.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
