A sea foam layer produced by wave breaking consists of seawater-coated air bubbles, fluid water, and air. The non-uniformity and microstructure of the air–water mixture in a foam layer can cause some important effects on microwave or optical properties. Considering the vertical non-uniformity of the air–water volume, the air-volume fraction is derived as a function of the foam depth variable, coated air bubble velocity, and foam temperature using the gas convection–diffusion equation. For a vertical graded profile of the air volume fraction, we discuss the effects of the coated air bubble velocity parameter and the air–sea temperature difference on the air volume fraction. The results show that the coated air bubble velocity is a key parameter that widely modulates the air volume fraction. Furthermore, an effective medium approximation (EMA) of spherical shell microstructures is proposed to investigate the graded foam effective permittivity and the emissivity of the sea surface covered with the foam layer of the graded air volume fraction in a vertical profile, and good agreement is obtained on comparing the EMA results with the experimental data of foam layer microwave emissivities at frequencies 1.4, 10.8, and 36.5 GHz. In our EMA model, the depth average of graded foam permittivity is adopted. This model can produce reasonable results by only tuning the air bubble velocity. It indicates that the EMA model can combine the effects of graded foam permittivity and foam microstructures into the coated air bubble velocity parameter. Meanwhile, we have qualitatively discussed the influence of air–sea temperature difference on the brightness temperature of the foam layer. It is shown that a negative (or positive) air–sea temperature difference enhances (or reduces) the sea surface brightness temperature, and the brightness temperature difference increases with an increase in microwave frequency.

For a foam-covered sea surface, it is difficult to retrieve sea surface salinity (SSS) with L-band brightness temperature (1.4 GHz) because of the effect of a foam layer with wind speeds stronger than 7 m/s, especially at low sea surface temperature (SST). With foam-controlled experiments, emissivities of a foam-covered water surface at low SST (−1.4 °C to 1.7 °C) are measured for varying SSS, foam thickness, incidence angle, and polarization. Furthermore, a theoretical model of emissivity is introduced by combining wave approach theory with the effective medium approximation method. Good agreement is obtained upon comparing theoretical emissivities with those of experiments. The results indicate that foam parameters have a strong influence on increasing emissivity of a foam-covered water surface. Increments of experimental emissivities caused by foam thickness of 1 cm increase from about 0.014 to 0.131 for horizontal polarization and 0.022 to 0.150 for vertical polarization with SSS increase and SST decrease. Contributions of the interface between the foam layer and water surface to the foam layer emissivity increments are discussed for frequencies between 1 and 37 GHz.

This paper investigates analytically the electric field distribution of graded spherical core-shell metamaterials, whose permittivity is given by the graded Drude model. Under the illumination of a uniform incident optical field, the obtained results show that the electrical field distribution in the shell region is controllable and the electric field peak's position inside the spherical shell can be confined in a desired position by varying the frequency of the optical field as well as the parameters of the graded dielectric profiles. It has also offered an intuitive explanation for controlling the local electric field by graded metamaterials.

The air volume fraction (AVF) of a sea foam layer is a key parameter that affects the microwave emissivity and brightness temperature of the sea surface. To extract AVF of a sea foam layer from the measured emissivity data at microwave frequencies, a novel retrieval method is developed based on the spectral representation of effective dielectric constant of sea foam composites media, with the volume fraction of constituents and the geometry of foam microstructure included in the spectral function. In the retrieval method, the cost function of emissivity is constructed with two constraints: one is the first two moments of the spectral function and the other is derived from the spectral representation of coated spherical composites. We tested the inverse method using the simulation data of a known emissivity model with Gaussian noise. Good agreement is obtained between the inverse results and the known AVF of sea foam from the simulated emissivity data with varying sea surface temperature, salinity, and incident angle. Finally, the proposed method was used to estimate the AVF of the sea foam layer from the measured emissivity data at frequencies 1.4, 6.8, 10.8, 35, and 36.5 GHz. Generally, the retrieved values of the AVF fall in the range of 0.85–0.98. This study implies that our method can be extended to retrieve the volume fraction of constituents of other composites media from the passive microwave remote-sensing data.