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Abstract

The present work develops a rigorous framework for collective dipole oscillations in dense dielectric media by extending the Lorentz oscillator model to include both quadratic (second order) and cubic (third order) nonlinear restoring forces. Dipole-dipole interactions are incorporated via the dyadic Greens function, leading to a nonlocal description of the medium. Starting from the generalised oscillator equation, the system is expressed in matrix form with an effective stiffness matrix. Using a harmonic steady state ansatz, nonlinear terms are approximated in the frequency domain. Diagonalisation provides collective normal modes, which serve as a basis for perturbative expansion zeroth order captures the linear response, while higher orders describe nonlinear corrections. The polarisation is expressed through corrected mode amplitudes, yielding an effective nonlinear nonlocal susceptibility kernel. Finally, the scalar Greens function formalism is applied to derive the structured output field. These approaches bridge microscopic dipole dynamics with macroscopic optical propagation, offering key insights into nonlinear light matter interaction and turbulence influenced field evolution.