TY - EJOU
AU - Binesh, T.
TI - Modelling of Energy Storage Photonic Medium by WavelengthBased Multivariable Second-Order Differential Equation
T2 - Computer Modeling in Engineering \& Sciences
PY - 2020
VL - 123
IS - 1
SN - 1526-1506
AB - 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.
KW - Optical medium modelling
KW - energy storage
KW - multivariable second order differential equation
KW - numerical analysis
KW - minimum value-normalized refractive index profile
DO - 10.32604/cmes.2020.08097