The parameters of the 7 × 7 hole coherent acoustic source in Figure 9 .

## Abstract

The physical mechanism of generating the lasting tropospheric refractivity fluctuation with a stable array-distributed structure by coherent acoustic waves is investigated. An example of the quantitative calculation of atmospheric refractive index is given and analyzed. Based on the theory of electromagnetic wave propagation and scattering in the troposphere, the feasibility to purposefully affect radio wave propagation is qualitatively demonstrated by the experiment of the coherent acoustic source-induced laser interference fringe change. The potential application aspects of synthetically controlling the radio wave propagation by the artificial refractivity fluctuation structure are preliminarily proposed. This chapter will promote the development of the coherent acoustic wave-induced tropospheric refractivity fluctuation, and it has the important theoretical significance and potential application value to purposely apply the positive or negative effects on radio wave propagation.

### Keywords

- troposphere
- atmospheric refractive index
- coherent acoustic waves
- radio wave propagation
- positive or negative effects

## 1. Introduction

Radio wave propagation is an important part of wireless systems. The investigations into various environment channel media with different physical properties, different dielectric properties, and spatiotemporal structures are inevitable to research radio wave propagation. There are two types of influences induced by the environment media on the radio wave propagation: the one is to realize particular propagation mode and advanced wireless technology, such as to realize the over-the-horizon communication or detection by atmospheric turbulence scattering and the multiple-input multiple-output wireless system by multipath propagation, which is seen as the positive influence; the other is to restrict radio signal propagation to be received or detected. For instance, the propagation effects of attenuation, depolarization, scintillation, and atmospheric noise are restrictive effects on communication systems, which are seen as the negative influence. It is the goal of the research on radio wave propagation to investigate the propagation environment media-caused positive influence and negative one and to apply them to the two aspects, based on the precondition of sufficiently mastering and controlling the physical and dielectric properties of propagation environment media. On the one hand, it makes the performances of an expected wireless electronic system perfectly match with its wireless channel, by forecasting, modifying, and applying the positive effects. On the other hand, it destroys the original perfect match between the hostile wireless electronic system and its wireless channel during wireless system countermeasures, by forecasting, creating, and controlling the negative effects.

The idea of coherent acoustic wave-induced atmospheric refractivity fluctuation is to control the characteristic parameters of radio wave, such as amplitude, phase, propagation direction, and polarization, by the propagation effects caused by the artificial atmospheric refractivity fluctuation. And, the final aim is to purposefully apply the positive effects or the negative effects. Note that the idea of coherent acoustic wave-induced atmospheric refractivity fluctuation and its application is a new field and is in its infant stage.

The idea of changing the tropospheric refractivity by the disturbance of acoustic wave is first proposed in [1], in which A. Tonning pointed out the viewpoint that an acoustic wave propagating in the troposphere can cause the atmospheric refractivity fluctuation and theoretically analyzed the rationality of the viewpoint. In the next 50 years, radio acoustic sounding system (RASS) began to be established to detect atmospheric temperature, wind profile, and turbulence in the lower troposphere [2–4]. The first RASS system to measure atmospheric temperature profile was born at Stanford University [5]. By the 1990s, this technique was adopted to solve the problems of measuring the temperature in indoor environment [6–9], also employed to detect the wake vortex of aircrafts [10, 11], and even explored to track and detect the taggant for the soldier identification friend-or-foe application [12]. Currently, RASS can detect the atmospheric parameters below 20 km [13]. The RASS history was summarized, and the applications of RASS in the detection of turbulence were analyzed in [14]. The applications and limitations of RASS system are analyzed in [15]. Afterward, the broadband acoustic pulse technology [16] and imaging techniques [17] are applied to RASS system.

The idea of coherent acoustic wave-induced tropospheric refractivity fluctuation mentioned in this chapter is fundamentally different from RASS. The main idea of RASS is to obtain the parameters of atmospheric physical properties based on the relationship between acoustic propagation velocity and atmospheric physical property parameters by tracking the velocity of acoustic wave front which can be seen as an artificial refractivity irregularity. However, the main idea, in this chapter, is to purposely apply the positive influences and negative ones induced by artificial array-distributed refractivity irregularity, which is stable, lasting, and controllable because the coherent acoustic source is used. The viewpoint to purposely affect radio wave propagation by a coherent acoustic source is proposed for the first time in [18]. In this chapter, the physical mechanism of generating the lasting tropospheric refractivity fluctuation with stable array-distributed structure by coherent acoustic waves is elaborated in Section 2, the distribution of the artificial atmospheric refractive index is quantitatively calculated, and the feasibility to purposefully affect radio wave propagation is qualitatively demonstrated by the experiment of the coherent acoustic source-induced laser interference fringe change in Section 3. The potential application aspects of synthetically controlling the radio wave propagation by the artificial refractivity fluctuation structure are preliminarily proposed in Section 4; further investigations in the future are listed in Section 5. This chapter will promote the development of the coherent acoustic wave-induced tropospheric refractivity fluctuation.

## 2. The mechanism of controlling the atmospheric refractivity fluctuation by coherent acoustic waves

The real part *N* of the atmospheric refraction index in the radio band is nearly independent of frequency. *N* depends on the atmospheric pressure *P* in hPa, the absolute temperature *T* in K, and the water vapor pressure *e* in hPa, and the relation among them is [19]

Operating the difference algorithm on Eq. (1), the relation among *ΔN*, *ΔT*, *ΔP*, and *Δe* is given as

Eq. (2) shows that *ΔN* is closely related to *ΔT*, *ΔP*, and *Δe*. The refractivity fluctuation *ΔN* can be steered by controlling one or more parameters among *ΔT*, *ΔP*, and *Δe* according to Eq. (2).

Acoustic wave movement follows the three basic laws: Newton’s second law of motion, law of conservation of mass, and thermodynamic equation of state [20]. The wave function of an acoustic wave can be derived from the three basic laws and is written as [21]

where *p* is the instantaneous acoustic pressure and *c* _{0} denotes the acoustic propagation velocity in the atmosphere. *p* and *c* _{0} can be expressed as

In Eq. (4), *P* _{0} and *P* are the atmospheric pressure in Pa before and after the disturbance by an acoustic wave, respectively. And *tt *in Eq. (5) is the atmospheric temperature in °C. Eq. (3) shows that when an acoustic wave passes through the atmospheric medium, the additional periodical variational pressure, that is, acoustic pressure *p* = *ΔP*, will be exerted upon the medium based on the original atmospheric pressure. It is rational to neglect the temperature change induced by the additional periodical variational pressure; therefore *ΔT* = 0. According to [18], *ΔP* and *Δe* satisfy the formula *Δe*/*e* = *ΔP*/*P*. Therefore, Eq. (2) can be deduced as

It is shown in Eq. (6) that the refractivity fluctuation *ΔN* will present a specific spatial and temporal distributions along with the acoustic pressure *p*.

The solutions to Eq. (3) for the cases of the plane wave, the cylindrical wave, and the spherical wave can be, respectively, formulated as

In Eqs. (7) and (9), *p* denotes the instantaneous value of the acoustic pressure at a point in their acoustic pressure field, *rp *represents the distance between a planar acoustic source to a point in the acoustic pressure field, *rs *represents the distance between the center axis of a cylinder-surface acoustic source to a point in the acoustic pressure field, *r* _{0} represents the distance between the center of a spherical-surface acoustic source and a point in the acoustic pressure field, *rc *is the diameter of the spherical-surface acoustic source, *l* _{0} is the length of the cylindrical-surface acoustic source, and *pA *is the acoustic pressure on the surface of the above acoustic sources. *ω* and *k* denote the angular frequency and wave number of the acoustic waves, respectively.

*pA *for the three types of acoustic sources mentioned above can be, respectively, expressed as

where *W* is the acoustic wave power radiated by the acoustic sources, *S* is the area of the plane acoustic source, and *ρ* _{0} is the density of air.

In other words, when a spherical-surface acoustic wave passes through the homogeneous atmosphere medium, the distribution of acoustic pressure *p* or atmospheric refractivity fluctuation *ΔN* at a certain moment in a plane including the point acoustic source shown in Figure 1 is similar to the waveform of a mechanical wave in water surface shown in Figure 2 . Correspondingly, the refractivity fluctuation *ΔN* will present a similar spatial distribution following Eq. (6). It is by means of the reflection effect of the acoustic wave front with *ΔN* that the purpose of tracking the propagation speed of acoustic wave is realized in RASS.

The principle of independent propagation and superposition of waves indicates that if two coherent waves meet, the interference phenomenon can be formed. Figure 3 shows the waveform when two coherent water surface waves meet. Figure 4 shows the simulation of the distribution of *p* or *ΔN* when two coherent acoustic waves meet.

According to the wave interference theory, interference pattern is closely related to coherent wave frequency, phase, acoustic source structure, and so on. For any type of coherent acoustic source with array structure, the acoustic pressure at point

where *S*| is the array factor, which presents the interference process. The array factor of the uniform spherical-surface acoustic source planar array shown in Figure 5 and the uniform cylindrical-surface acoustic source linear array shown in Figure 6 are, respectively, given as [18]

In Eq. (12), *Nx *and *Ny *are, respectively, the number of array elements along the x-axis and y-axis, and *bx *and *by *are, respectively, the inter-element spacing along the x- and y-axes in Figure 5 . In Eq. (13), *N* and *b* denote, respectively, the element number and the interval in Figure 6 . *λ* is the acoustic wavelength. *βx *and *βy *are the harmonic vibration phase differences between the adjacent elements along x-axis and y-axis in Figure 5 , respectively. *β* is the harmonic vibration phase difference between the adjacent elements in Figure 6 . Figures 7 and 8 are the simulating examples according to Eq. (12) and Eq. (13).

Therefore, the lasting artificial atmospheric refractivity irregularities with a stable, controllable, and subtle array structure in a specific space can be generated by setting the geometric structure of acoustic source and adjusting the frequency, amplitude, and phrase of acoustic waves. In [18], the coherent acoustic source shown in Figure 9 and the short scattering communication link shown in Figure 10 are used in the experiment. The experimental results as shown in Figures 11 – 18 are observed, which further verify the feasibility of perturbation in the tropospheric atmospheric refractivity by coherent acoustic wave.

## 3. The interaction between a radio wave and the artificial refractivity fluctuation

According to [18], the spatial distribution of the acoustic pressure caused by the uniform spherical-surface acoustic source planar array shown in Figure 5 is

where *α* denotes the attenuation coefficient of acoustic wave and |*S*(*θ*, *φ*)| is the array factor of Eq. (12). The instantaneous *ΔN* _{C_I }and the effective *ΔN* _{C_E }of the atmospheric refractivity fluctuation *ΔN* at a space point are given by

where *p* is the instantaneous acoustic pressure in Pa and |*p*| denotes the amplitude of the acoustic pressure harmonically changing over time in Pa. The effective acoustic pressure can be given as 0.707|*p*|.

Figures 19 and 20 show the spatial distributions of atmospheric refractivity fluctuation caused by the 49 × 49 hole acoustic source. In the calculation, the attenuation coefficient of acoustic wave *α* and the diameter of array element are ignored. The atmospheric pressure *P* is 1013.25 hPa, the temperature *T* is 288.15 K, the water vapor pressure *e*is 10.02 hPa, and the power of each acoustic source element is 10 W.

As can be seen from Figures 19 and 20 , when the coherent acoustic wave travels through the tropospheric medium, there will be a periodical atmospheric refractivity fluctuation. The mechanism the artificial dielectric irregularities impacting the radio wave propagation is similar to that the atmospheric turbulence impacting the radio wave propagation. The atmospheric refractivity fluctuation caused by the atmospheric turbulence is stochastic distributed, and that caused by acoustic wave shows spatial periodic distribution. Therefore, the influences of atmospheric turbulence on radio wave propagation need to be analyzed by the wave propagation theory in the random medium [22], and the effects of the artificial dielectric irregularities on the radio wave propagation need to be studied using the theory of electromagnetic scattering, reflection, and refraction by the periodic structure medium. Bragg volume scattering theory and Fresnel volume scattering theory are mainly used to analyze the impacts of artificial irregularities on radio wave propagation [23–26].

Our research group is devoted to quantitatively analyzing the influences of the artificial irregularities on the amplitude, phase, propagation direction, polarization, and other parameters of an electromagnetic wave. The related exploration is possible to implement leap-forward development in the fields of electronic countermeasure, communications, radar detection, and other wireless technologies.

An experiment aims to influence Michelson interference fringes by the coherent acoustic wave-induced atmospheric refractivity fluctuation was carried out, and it qualitatively verifies the feasibility to purposefully change the phase of the electromagnetic wave by the artificial refractivity fluctuation. As shown in Figure 21 , a light emitted by laser emits hits the beam splitter G1, which is partially reflective. One part of the light denoted by 1 is reflected, while another part of the light denoted by 2 is transmitted through G1. The path of light 1 passes through the region disturbed by the artificial refractivity fluctuation, while the light 2 travels through the normal air. Both beams meet at a receiving screen to produce an interference pattern. Comparing the interference fringes when the acoustic source is on and off, the feasibility of artificially changing the phase of the electromagnetic wave is demonstrated.

As shown in Figure 9 , the 7 × 7 hole acoustic excitation system working at 300 Hz is adopted in the testing experiment; its parameters are shown in Table 1 . Before the acoustic source is on, a dark fringe is in the center of the interference fringes as shown in Figure 22 . After the acoustic source is on, the variation of the interference fringes is captured by a high-resolution vidicon. The typical frame pictures are extracted by a video processing software, which are shown in Figures 23 – 26 . Figures 23 – 26 obviously show that the central fringe is gradually changing. So the experimental results qualitatively verify the feasibility to purposefully change the phase of the electromagnetic wave by the artificial refractivity fluctuation.

Parameter | Total power of the horn speaker | Diameter of the horn speaker | Diameter of the inner cavity hole | Diameter of the external cavity holes |
---|---|---|---|---|

Value | 5 W | 0.10 m | 5 mm | 2 mm |

Parameter | Structure | Distance between the front panels of the inner and external cavities | Interval of the external cavity holes | |

Value | 7 × 7 | 1.2 m | 30 mm |

## 4. The potential application aspects of the artificial refractivity fluctuation

This chapter proposes a new way to purposely affect radio wave propagation by controlling and adjusting the artificial atmospheric refractivity irregularity distribution. Based on the accurate calculation of the electromagnetic wave scattering, reflection, and refraction in the areas with the artificial atmospheric refractivity irregularities, the amplitude, phase, propagation direction, polarization, and other parameters of an electromagnetic wave can be controlled artificially, so that we can purposely exert the environment media-caused positive or negative effects on radio wave propagation. The method of altering the properties of electromagnetic waves by a coherent acoustic wave-induced tropospheric refractivity fluctuation is possible to realize leap-forward development in the fields of emergency troposcatter communication, the over-the-horizon radar stealth in evaporation duct environments, electromagnetic countermeasure of coherent imaging technique, and so on. The more applications need to be explored and discovered by researchers harnessing their clever and wisdom.

The artificial dielectric irregularities are more stable and lasting than the atmospheric turbulence, and its distribution construction can be steered artificially. It is obvious that the artificial dielectric irregularities can be used to effectively improve the stability of the troposcatter communication channel. Based on the experiment shown in Figures 23 , 24 , 25 , and 26 , if the amount of phase shift caused by the coherent acoustic waves is quantitatively calculated, the interference fringes on the receiving screen can be artificially controlled. In a similar way, the artificial dielectric irregularities can be used to disturb the coherent optical imaging radar. In what follows, the mechanism of the application to the over-the-horizon radar stealth in evaporation duct environments is briefly discussed.

Because of some natural phenomena, such as the evaporation of sea water, heat exchange between air, and sea surface, as the height increases, the water vapor pressure rapidly decreases, and the temperature increases, which causes a steep fall in *N*. If the refractivity gradient meets the condition of d*N*/d*h* < − 0.157 N ‐ unit/m, the evaporation duct will arise in the specific region. If the wavelength of a radio wave is short enough and its angle of elevation is small enough, the super-refraction of radar wave over the sea surface will occur. In other words, the evaporation duct can be regarded as a natural waveguide which steers the radio signal from the transmitter to a receiver that may be situated well beyond the radio horizon.

If coherent acoustic sources are set around the target to be protected, the evaporation duct environment will be destroyed when the acoustic wave-induced refractivity fluctuation makes the refractivity gradient not accord with d*N*/d*h* < − 0.157 N ‐ unit/m, so that the target will not be detected by the over-the-horizon radar in evaporation duct environment. Figure 27 shows the simulation of the refractive index profile of evaporation duct environment. Figure 28 shows the simulation of the refractive index profile of evaporation duct when coherent acoustic waves are applied. Comparing the results in Figures 27 and 28 , it can be concluded that the refractive index profile of evaporation duct is easily destroyed by coherent acoustic waves.

The potential applications proposed in this section based on the mechanism altering the properties of an electromagnetic wave by coherent acoustic wave-induced tropospheric refractivity fluctuation are still in the infant stage. There is still a long way to go for the technology development and more applications.

## 5. Conclusion

The idea of this chapter is logical in theory, and its feasibility is qualitatively verified in [18]. The mechanism the artificial dielectric irregularities impacting radio wave propagation is similar to that the atmospheric turbulence impacting radio wave propagation. The Bragg volume scattering theory and Fresnel volume scattering theory provide the theoretical basis for quantitatively analyzing the influences of the artificial irregularities on the amplitude, phase, propagation direction, polarization, and other parameters of an electromagnetic wave. The experiment that effectively controlled Michelson interference fringes by the coherent acoustic waves further qualitatively verifies the feasibility of purposefully changing the phase of the electromagnetic wave by the artificial dielectric irregularities. The technique of altering the properties of an electromagnetic wave by coherent acoustic wave-induced tropospheric refractivity fluctuation is very possible to realize leap-forward development in the fields of emergency troposcatter communication and the over-the-horizon radar stealth in evaporation duct environments. However, the investigation is in its infant stage; there is still a long way to go for the technology development and more applications. In order to further investigate the point of view put forward in this chapter, the following issues need to be considered deeply: quantitatively investigating the spatial distribution of atmospheric refractivity under the interaction of coherent acoustic waves and atmospheric turbulence, determining the specific influence mode of the artificial dielectric irregularities on radio wave propagation, such as reflection, scattering, refraction, and diffraction, quantitatively calculating the physical and electromagnetic properties of the artificial dielectric irregularities, quantitatively estimating the impact degree of the artificial dielectric irregularities on radio wave propagation, and discovering more application modes of this technique.

## Acknowledgments

The authors would like to thank the support of National Natural Science Foundation of China (grant no. 61771375), and they would also like to thank the teachers and students who are devoted to exploring the idea of this chapter.