## 1 Introduction  
When a vehicle flies in near space at hypersonic speed, a shock layer will be formed at the head of the vehicle. Due to the shock layer's extremely high temperature, air passing through it undergoes a dissociation and ionization process, resulting in the formation of plasma in the head region of the vehicle. As the vehicle continues to move forward, the plasma in the head region continuously gathers and flows towards the middle and tail of the vehicle, forming a layer of plasma that envelops the vehicle. This plasma sheath is generated by the high-temperature real gas effect [1] and belongs to the quasi-neutral plasma sheath [2]. According to the EM properties of the plasma, EM waves below this frequency can be reflected, absorbed, and scattered by the plasma sheath, causing the attenuation or even interruption of the communication signal, forming a so-called communication \"blackout\" [3; 4; 5]. During the flight of hypersonic vehicles, due to the change of speed and the difference of altitude, the air around the vehicle will be in a thermodynamic equilibrium and chemical non-equilibrium state, or a thermodynamic and chemical non-equilibrium state [1; 6; 7]. Because of the existence of these two thermodynamic states, the fluid distribution around the vehicle is different. For example, the high-temperature air model and the hybrid structure based on the graphic processing unit are used to simulate the flow field around the hypersonic vehicle as studied in [8]. The computational fluid dynamics (CFD) benchmark problem is used to verify the mathematical model and the calculation algorithm, and the results of hypersonic fluid flow efficiency on the graphic processing unit are given. The thermal and chemical non-equilibrium effects on the flow structure and the performance of the hypersonic internal turning inlet passage of the air-breathing scramjet at Mach 12 were studied by the numerical method in ref. [9]. The results show that the thermochemical non-equilibrium effect of the Mach 12 inlet is significant under the condition of an adiabatic wall. Reference [10] developed a domestic parallel solver for hypersonic thermochemical non-equilibrium flow with the Reynolds-averaged Navier-Stokes (N-S) turbulence model. Using this solver, it is found that the combined effect of turbulence and thermochemical non-equilibrium has a significant impact on the flow field organization, wall data, and separation length of the shock/boundary layer interaction. The influence of the high-temperature effect on the motion characteristics of hypersonic vehicles was studied in ref. [11]. Using numerical methods, hypersonic fluids were numerically simulated under the consideration of the high-temperature effect and non-equilibrium chemical reaction. The numerical results of flow momentum distribution and separation distance in the shock layer at different free-flow Mach numbers are given in the literature. The communication problem of the hypersonic vehicle during flight is essentially the interaction between EM waves and plasma. In particular, the plasma produced by hypersonic vehicles is also in these two thermodynamic states, which have a very direct impact on the propagation between plasma and EM waves. The interaction between them, including the flow field, thermal field, and EM field, is a comprehensive problem of multi-physical field coupling. However, there are few works about how the thermodynamic state affects the propagation of EM waves in the plasma. Moreover, for multi-physics field coupled numerical computation, the huge numerical simulation computation is a difficult problem for daily solutions. In electromagnetic numerical computation, meta-structures can be utilized to bring a new twist to the computation of electromagnetic waves in the spatial domain [12]. Refer to [13] for computational complexity. The material structure of surface coatings for hypersonic vehicles is also one of the issues that need to be addressed. Metamaterials present an extremely advantageous side as currently focused materials [14; 15].