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# Modelling of Energy Storage Photonic Medium by WavelengthBased Multivariable Second-Order Differential Equation

T. Binesh1, *
1 Government Model Engineering College, Ernakulam, 682021, India.
* Corresponding Author: T Binesh. Email: .
(This article belongs to this Special Issue: Numerical Methods for Differential and Integral Equations)

Computer Modeling in Engineering & Sciences 2020, 123(1), 333-351. https://doi.org/10.32604/cmes.2020.08097

Received 26 July 2019; Accepted 04 November 2019; Issue published 01 April 2020

### Abstract

Wavelength-dependent mathematical modelling of the differential energy change of a photon has been performed inside a proposed hypothetical optical medium. The existence of this medium demands certain mathematical constraints, which have been derived in detail. Using reverse modelling, a medium satisfying the derived conditions is proven to store energy as the photon propagates from the entry to exit point. A single photon with a given intensity is considered in the analysis and hypothesized to possess a definite non-zero probability of maintaining its energy and velocity functions analytic inside the proposed optical medium, despite scattering, absorption, fluorescence, heat generation, and other nonlinear mechanisms. The energy and velocity functions are thus singly and doubly differentiable with respect to wavelength. The solution of the resulting second-order differential equation in two variables proves that energy storage or energy flotation occurs inside a medium with a refractive index satisfying the described mathematical constraints. The minimum-value-normalized refractive index profiles of the modelled optical medium for transformed wavelengths both inside the medium and for vacuum have been derived. Mathematical proofs, design equations, and detailed numerical analyses are presented in the paper.

### Keywords

Optical medium modelling, energy storage, multivariable second order differential equation, numerical analysis, minimum value-normalized refractive index profile.

Binesh, T. (2020). Modelling of Energy Storage Photonic Medium by WavelengthBased Multivariable Second-Order Differential Equation. CMES-Computer Modeling in Engineering & Sciences, 123(1), 333–351. This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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