The modulation and enhancement effect of sub-wavelength plasma structures on compact antennas exhibits obvious technological advantage and considerable progress. In order to extend the availability of this technology under complex and actual environment with inhomogeneous plasma structure, a numerical simulation analysis based on finite element method has been conducted in this paper. The modulation function of the antenna radiation with sub-wavelength plasma layer located at different positions was investigated, and the inhomogeneous plasma layer with multiple electron density distribution profiles were employed to explore the effect of plasma density distribution on the antenna radiation. It has been revealed that the optical near-field modulated distance and reduced plasma distribution are more beneficial to enhance the radiation. On the basis above, an application-focused research about communication through the plasma sheath surrounding a hypersonic vehicle has been carried out aiming at exploring an effective communication window. The relevant results devote guiding significance in the field of antenna radiation modulation and enhancement, as well as the development of communication technology in hypersonic flight.

## I. INTRODUCTION

Recently, the investigations on the metamaterial-based electromagnetic modulation has been a hot topic. As to the electrical small antenna loaded by the metamaterial with special properties, the metamaterial not only can offset the large reactance of the small antenna, but also can improve the radiation resistance of the antenna system, thus leading to a significant increase in the overall radiation efficiency of the small electrical antenna. Moreover, the zero or negative index of the meta-materials can focus the electromagnetic energy onto a certain area to accomplish the high radiation gain with narrow beamwidth. This method takes obvious advantages compared to the traditional approaches.^{1–8} Similarly, the plasma can be regarded as a special type of metamaterial with negative permittivity in certain condition. And it has been demonstrated that, when the antenna is covered by a sub-wavelength plasma layer, which means the thickness of plasma layer is comparable to the wavelength of electromagnetic wave, the radiation can be enhanced within a proper match condition. The enhanced phenomenon was firstly discovered by Messiaen and Vandenplas.^{9} And later researches investigated the radiation intensification characteristics of radio frequency signal by sub-wavelength plasma structures theoretically and experimentally mainly from two aspects, including the antenna parameters (i.e. the type, size, working frequency of the antenna) and the plasma parameters (i.e. the temperature, density, thickness, collision frequency, shape).^{10–14} Among which, a rich variety of antenna types have been used, such as single pole antenna, cylindrical antenna, spherical electric diploe antenna, and magnetic dipole antenna. In comparison, a better enhancement effect on antenna radiation can be obtained by applying the antenna with the smaller size. Besides, it has been revealed that the radiation of antenna was sensitive to the plasma parameters. For a certain compact antenna working in some specific frequency bands, the plasma layer which can enhance radiation should be generated by selecting the appropriate couple of plasma thickness and plasma density.^{15} And a relative lower collision frequency and the suitable shape of plasma layer are beneficial to enhance radiation. It is worthwhile to note that, usually, the plasma layer generated by experiments or in reality which can be used to cover the antenna is inhomogeneous. However, the influence of non-uniform plasma to the antenna modulation is less considered, and the effects of density distribution and relative distance of plasma versus antenna on the antenna radiation are still unknown. The investigations on the influence of density distribution and working position of the sub-wavelength plasma layer on the radiation are of great importance to actual applications of the plasma-modulated technology, such as the optimization of plasma enhanced compact antenna,^{15} and the alleviation of communication blackout phenomenon of re-entry and hypersonic vehicle.^{16–20}

In this paper, a numerical simulation investigation based on finite element method has been conducted to study the modulation function of the antenna radiation with sub-wavelength plasma layer located at different positions and the inhomogeneous plasma layer with multiple electron density distribution profiles. On the basis, a practical research on an antenna covered with the plasma layer similar to the RAM flight test data has been conducted, and the effective radiation intensification frequency band for three flight altitude is explored.

## II. NUMERICAL SIMULATION RESEARCH AND RESULTS ANALYSES

### A. Numerical simulation method

In order to explore the near-field modulation effect of sub-wavelength plasma on antenna radiation, a finite element analysis (FEA) based on the software of Comsol Multiphysics is carried out. A spherical dipole antenna is taken as the research object to study the modulation effect by plasma. The dipole antenna covered by air layer and plasma layer can be expressed as a two-dimensional axisymmetric model as shown in figure 1(a). The model includes a spherical antenna with radius of *r*_{1} = 0.8 cm, which is surrounded by a spherical air layer with the outer radius of *r*_{2}. And a spherical plasma layer covers the air layer with a thickness of 3 cm, and the outer radius of the plasma layer is *r*_{3}. The infinite space surrounding the plasma layer is modeled by an air layer with the outer radius of *r*_{4} = 100 cm and a perfect match layer of *d*_{2} = 5 cm. The spherical antenna is assumed to be a perfect electrical conductor and driven by a voltage of *V*_{0} = 10 V, across a narrow gap of *d*_{1} = 0.04 cm between the two poles of the antenna. The frequency of the antenna radiation is *f* = 1 GHz.

For the researches on the modulation effect of plasma parameters on the antenna radiation, a macroscopic analysis method based on Drude scattering plasma model is used.

Under the condition without magnetic field, the equation of motion of electrons in the plasma can be written:

Where *m* is electronic mass (kg), *e* is the charge of the electron (C), *r* is electric displacement vector (m), and *v* is electron collision frequency (Hz).

The current density in plasma can be expressed as:

The electric displacement vector can be expressed as:

Thus, the relative intensity of polarization is as follow:

In the Drude model, the plasma is represented as relative permittivity:

And the electrical conductivity is:

Where, *ω*_{p} is plasma frequency, *n*_{0} is the electron number density of plasma.

### B. Mechanism of relative distance to radiation enhancement of antenna

In the previous work, the enhancement effect of the sub-wavelength plasma structure on the radio frequency electromagnetic radiation due to the near-field modulation has been proven, where the plasma layer is located closed to the antenna. However, it is not quite clear the effective range and position of the plasma layer located around the antenna. Therefore, it is crucially significant to reveal the effect of relative distance of the plasma layer covering the antenna on the modulation result.

The effective near-field modulated distance by the sub-wavelength plasma layer will be achieved by controlling the outer surface radius *r*_{2} of the air layer. The modulation effect of plasma is expressed by the normalized radiation gain of dipole antenna, which is obtained at the far-field observation point with *r* = 0.9 m, *z* = 0 m, the collision frequency of plasma is set as 0.2 GHz which is an average value based on the actual experiment.^{15} For different *r*_{2} versus the wavelength λ of antenna radiation that is taken as 0, λ/6, λ/5, λ/4, λ/3, λ/2 separately, the variation of corresponding normalized radiation gain versus the relative plasma frequency (the antenna radiation is *f* = 1 GHz, and the corresponding plasma density regime is 0 - 2×10^{17}m^{-3}) is shown in figure 1(b). It is observed that the normalized radiation gain varies significantly with the increase of relative distance. When the relative distance exceeds the half of wavelength, there is no radiation enhancement, and the attenuation occurs in all regime of relative plasma frequency band. For the plasma layer with the relative distance of λ/6, λ/5, λ/4, λ/3, an intensification of antenna radiation higher than that of the free space can be achieved. It means that a proper space between the antenna and the plasma is beneficial to enhance the radiation. Consequently, the optimal match of plasma density regime corresponding to a target frequency band should be chosen cautiously for a specific distance between the antenna and plasma layer.

### C. Mechanism of density distribution of plasma layer to radiation enhancement of antenna

Aiming at exploring the modulation effect of plasma density distribution on the antenna radiation, four different density distributions of plasma layer are given as shown in figure 2(a). Here, the sub-wavelength plasma layer is covered tightly on the antenna, and the collision frequency of plasma is set as 0.2 GHz. Besides, the other setups of the model parameters are the same as the above definition.

The electric field intensity contour near antenna is illustrated in Figs. 2(c)–(g) based on these four given density distributions of plasma as shown in Fig. 2(a). It is obvious that if the plasma density gradually decreases with the distance to antenna (i.e. Figs. 2(d) and (e)), the radiation enhancement is shown to be more considerable than the opposite case. Correspondingly, it can be observed from Fig. 2(b) that the real part of the relative permittivity of plasma layer with reduced density distribution varies from negative to positive with the distance to antenna. Besides, the location of zero crossing point is farther to antenna than the cases with increasing density distribution, which means the regime of plasma layer adjacent to the antenna with negative permittivity makes more contribution to the radiation intensification. The results are of referential significance for later research on the optimization of plasma layer parameter to acquire a remarkable radiation enhancement.

On the basis above, to further reveal the optimal match of density distribution to radiation enhancement, four representative decreasing density distributions are given, including linear distribution, exponential distribution, parabolic distribution and Boltzmann distribution. The logarithm value of Poynting vector (** S**), which indicates the mean radiation energy density transmitted by plasma added antenna, with radius distance (begin with the outer surface of plasma, i.e. 3.8cm) under different density distribution is illustrated in figure 3. For different density distributions, the plasma layers have similar variation in the modulation effect of Poynting value. However, the radiation energy density with exponential distribution or Boltzmann distribution has the lower average value than those with linear distribution or parabolic distribution. Correspondingly, the far-field (0.9 m) electric fields and relative radiation gains modulated by different density distributions plasma layer are calculated as shown in Table I. It is remarkable that the radiation gain in the far-field is directly determined by the near-field mean radiation energy density, as a result, the radiation gain with linear distribution or parabolic distribution exceed the other two cases.

. | electric field intensity (V) . | relative radiation gain (dB) . |
---|---|---|

Linear distribution | 1.41 | 10.89 |

Exponential distribution | 0.636 | 3.85 |

Parabolic distribution | 1.53 | 11.58 |

Boltzmann distribution | 1.02 | 8.05 |

. | electric field intensity (V) . | relative radiation gain (dB) . |
---|---|---|

Linear distribution | 1.41 | 10.89 |

Exponential distribution | 0.636 | 3.85 |

Parabolic distribution | 1.53 | 11.58 |

Boltzmann distribution | 1.02 | 8.05 |

In order to explore the mechanism of plasma density distribution on radiation characteristics of antenna, the contour of electric field intensity for above four different hypothetic density distributions are shown in figure 4. With exponential distribution (Fig. 4(c)) or Boltzmann distribution (Fig. 4(e)) plasma layer, a relative stronger radiation regime is formed inside the body of plasma, moreover, it seems a novel radiation source as same as the dipole emitter, but its relative smaller radiation surface leads to the unsatisfied capacity of electromagnetic radiation. In comparison, with a new radiating surface that is reconstructed at the interface of plasma and air, the case with linear distribution (Fig. 4(b)) or parabolic distribution (Fig. 4(d)) possesses larger emitting area, and thus their radiation gains are relative considerable, which conforms to the antenna theory and benefits the antenna radiation.

### D. A applicable study of modulation and enhancement to antenna radiation for the plasma density distribution similar to re-entry and hypersonic vehicle

The mechanism of plasma density distribution to radiation enhancement of antenna has been generally achieved. However, the plasma density distribution assumed in the previous simulation is far from the actual situation, and there is of necessity to extend this technology to the cases where the antenna is probably covered by the plasma generated in reality. Here, an application-focused research about communication through the plasma sheath surrounding a hypersonic vehicle has been studied preliminarily to explore an effective communication window. A blackout plasma layer based on the RAM flight test data^{21} is applied to cover the dipole antenna tightly, and the structure of the dipole antenna is the same as that described in Section II A, the plasma density, thickness and density distribution is same as shown in figure 5(a). The collision frequency of plasma is set as 0.2 GHz for all cases. The effective frequency band of antenna radiation intensification for three typical flight altitudes is explored as showed in figure 5(b).

Under such conditions, the results have shown that, at 71 km altitude, the average plasma density is relative low, when the working frequency is less than 3.4 GHz, the relative radiation power decrease below zero. In the band of 3.4 GHz < f < 4.0 GHz, the antenna radiation has a certain enhancement effect, there is hardly attenuation for the frequency higher than 4 GHz, relative radiation gain remains near zero, which is similar to the case without plasma. Under 48 km altitude, the radiation attenuation also occur in the low frequency band that is less than 8.8 GHz. Afterwards, an enhancement appears from 8.8 GHz to 9.3 GHz and 9.9 GHz to 13.7 GHz. At 25 km altitude, the average plasma density is highest in three cases, the radiation power attenuates largely in frequency band as list in this paper. Comparatively speaking, the effective communication frequency band is directly determined by the plasma density as well as its distribution profile.

## III. CONCLUSION

In summary, an antenna radiation model covered by plasma layer has been structured based on Drude scattering plasma analysis method.

The research on relative distance between antenna and plasma layer to radiation enhancement exhibits that the plasma layer with suitable distance is more beneficial to radiation enhancement. Accordingly, the intensification of plasma on antenna radiation should be built on a near-field modulated condition.

Then the effect of different density distributions on antenna radiation was investigated. The results showed that the reduced distribution, especially the parabolic reduced distribution and linear reduced distribution are better for radiation enhancement, the corresponding mechanism analysis based on novel radiation surface which is reconstructed by plasma layer is achieved.

Finally, a practical research to known distribution based on the RAM flight test data has been conducted, and the effective radiation intensification frequency band for three flight altitudes was explored.

The work in this paper has guiding significance for the follow-up study, and the results based on flight data are worthy of reference for effectively alleviating the problem of blackout.

## ACKNOWLEDGMENTS

This work has been supported by the National Natural Science Foundation of China (No. 51577044). And the authors wish to express their gratitude to C. S. Wang for his great help.