Metamaterials Based on a Gaseous Mixture: Analytical Modeling of Electrostriction Effect and Corresponding Brillouin Frequency Shift

Electrostriction properties of a dilute gas mixture are analytically calculated and derived herein for the first time. Electrostriction in a gaseous mixture is expressed in a standard process based on the energy conservation law using the Lorentz-Lorentz model and a model for calculating the electrostriction is introduced. The internal interactions of the gaseous environment follow the ideal gas law. These relationships show that electrostriction can be controlled by changing the volume ratio of gases. Since, electrostriction is an essential parameter in determining the Brillouin scattering, the proposed modeling is a key theoretical method to control the Brillouin scattering in gases. According to the numerical results, it was found that the electrostriction coefficient is almost independent of the wavelength range. More importantly, the frequency shift induced in an N₂-He gas mixture is independent of the volume fraction. E.g., in volume fraction of 0.3 and wavelength of 300 nm, if the volume fraction is increased by 20%, the electrostriction of the gas mixture (\({\gamma }_{mix}\)) will change by 4.3%, but the frequency shift almost does not change. On the other hand, if the frequency varies by 20%, the frequency shift will change by 16%, but in practice \({\gamma }_{mix}\) almost remains constant.