Radiophysics and Quantum Electronics, Vol. 36, Nos. 3-4, 1993

BRIEF COMMUNiCATIONS AND LETTERS TO THE EDITOR

EXCITATION OF SEA SURFACE WAVE BY SHORT-WAVE RADIATOR

F;. M. Inspektorov and V. !. Bogdanovich UDC 621.396.67

When a radiator is located above the sea surface, the surface can, especially in the presence of waves, exert a

strong effect on the radiation characteristics. We studied the effect of sea surface waves of finite conductivity on the field

of a vertically polarized radiator and, in particular, on surface-wave excitation. The waves are represented as irregularities

on the sea surface, whose amplitude and period in the short-wave band are commensurate with wavelength. The analysis

is performed by an algorithm employing an integral-equation method [1]; a two-dimensional problem and the case of H-

polarization are examined.

The radiator is a log-periodic antenna (Fig. la) consisting of 20 symmetric vertical elements. The similarity factor

r = 0.935, the angle of inclination c~ = 15 ~ and the suspension height ~ = 0.15X. The excited surface (contour/T) is

arbitrarily shown as being smooth. The surface profile in the presence of irregularities is shown in Fig. lb. In the case of

regular deviations, the surface is described by a sine wave with period T and amplitude H. In the case of amplitude-

modulated deviations, the surface is described by a sine wave with a constant period T and an amplitude H that varies

sinusoidatly with period T 1 = 9T; Hma x is the maximum deviation amplitude over period T 1. The current distribution at

the element terminals is determined by the induced-emf method, and the current distribution on the elements is assumed to

be sinusoidal. The currents on the sea surface (contour/T) are determined by solution of Fredholm's integral equation of

the second kind

e _ re [ I u ( U 2 ) 2 :f u ( U ; ) - i ~ o e G Z ( u ; ) + OG']dlouaj = 2 j=e'cT Tff-aG d l . (1) 2 t T 2 I 2 1

CT

Component H z of the total field is determined by the formula

H z = - ~ z e (u;) -• + 0G d/ - 3,, O--if- (2) u 2 2 1

I T I C T

In (1) and (2), the coordinates u I and u t are along the normal and the tangent to contours l T arid /CT (arms of

elements), G is the two-dimensional Green's function for free space, and Z is the surface impedance on contour l T. For sea

water, the Leontovich boundary conditions are valid and Z is determined only by the parameters of the medium:

/ z = w r (3)

C v

Here we assume/x r = 1 and er = er - i60Xa, where e r and a are parameters of the sea water (e r = 80, a = 5, and X =

50 m), and W is the wave impedance of free space. The current distribution on contour l T and the amplitude and phase distributions of component H z of the total field

on an arc of a circle of radius R = 12X (Fig. la) were studied. The maximum surface-current amplitude is obtained in the

area of y = 0. IX; the current drops very abruptly for y < 0 and drops more smoothly for y > 0. This is due to the

radiator's near-field distribution. The field over the sea surface can in general be considered a sum of space and surface

waves, where the propagated wave is formed due to the direct radiation of the radiator and diffraction by the surface

irregularities. In the case of surface-wave dominance, the field is "pressed" against the plane x = 0.

Gomel State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 3-4, pp. 323-329, March-April, 1993. Original article submitted December 26, 1991; revision submitted September 28, 1992.

206 0033-8443/93/3634-0206512.50 �9 Plenum Publishing Corporation

' ) .... ; F - I - - - , ~ a

---1

Fig. 1

0,9

0,4

1 IT'-

" . / / ..,

7 ~ . . . . . . . T J - I

[ . . . . . . i

Fig. 2

It is known [2] that over a two-dimensional comb-type structure with a constant tooth spacing a, a surface wave

can exist when a < 0.5X' (X' is the surface-wave wavelength); in this case, a TEM wave is excited in the channel. When

a > 0.5X', wave modes that have field variations along the y coordinate can be excited in the channel. Our surface profile

differs greatly from that of a comb in the presence of deviations (Fig, lb). The channel width is variable, its maximum

value is equal to T, and the channel depth is small. The current distribution over period T for regular deviations a t H =

0.1X is shown in Fig. 2. Distance t is read along contour l T. Curves 1, 2, and 3 correspond to T = 0.5X, X, and 2X. TEM

and E0t are apparently excited at T = 0.5X; higher modes ere also ex i t ed at T = X and T = 2X. For a smooth surface

(H = 0), the current distribution practically coincides with the approximation of physical optics inc (2//~an). The current

207

~,0 IIHltl

0,6 2

0,2

0 10 20 ~0 ~, d~g Fig. 3

-0,4

-0,8

-1,2

0

I 2111"

o

J l o

3.1 tO, d~g 1

m" i I I I I I I

~0 20 SO Fig. 4

amplitude drops sharply with an increase in H - for example, it is smaller than 2H~t ~ by a factor of 7-8 when H = 0.15X.

In the presence of a Surface wave, the current amplitude rises and reaches values of (1.3-1.5)2/-/~t ~ . The current distribu-

tion over period T is constant along contour I T and is not a function of H at the studied values of H < 0.15X.

Figure 3 shows the distribution of I Hz ] for T = 0.5X. Curves 1, 2~ 3, and 4 correspond to H = 0, 0.03X,

0.04X, and 0.15X. For H = (0.03-0.05)7r there exists in the angle sector ~, = 0-5 ~ a surface wave whose amplitude

decreases nearly as e -px. The field is the sum of thespace and surface waves with the latter dominant. With an increase

in H, there exists only a space wave, the amplitude is reduced, and the maximum deviates from the plane x = 0. Shown

in Fig. 4 is the distribution of argH z for T = 0.5T. Curves 1, 2, and 3 correspond to H = 0, 0.03X, and 0.04X. In the

region of ~ = 0-5 ~ where the surface-wave field is dominant, the surface and space waves have phase-shift differences,

which increase with an increase in H. The space-wave field is dominant for ~ > 8-10 ~

Analysis of the current and H z distributions showed that for T < 0.5X and H = (0.03-0.05)X there exists a surface

wave the components of whose field vary as e-PXe-ihy. For the given polarization, a surface wave exists with an inductive

component of impedance Z, which is related to the surface-wave parameters as follows [3]:

208

0,6 t%t

g"V'... .-;', .. 0,4

. . . . .

0,2 ! .....

;. I ! I | ! t I,

0 t 0 2 0 ~0 ~, deg

Fig. 5

z = i p / ~ c , P = J h ~ - ~'~ (4)

The retardation factor ~" = h/k can be determined in two ways.

I) By using the function e -P x to approximate the distribution of H z over the x axis and then determining p.

2) By taking into account the phase difference between the fields of the surface wave and the space wave, which

travels at distance R = 12},.

Both methods provide the identical result: ~ = !.015-1.025 for T = 0.5X and H = (0.03-0.05)X.

As a check, a version was calculated in which the entire contour l T was a smooth surface with impedance Z =

i108 ~, which corresponds to p = 0.285k and f = 1.04. The p and ~ values obtained by the above-described methods on

the basis of the H z distribution coincided with those selected in the specification of Z.

The finite conductivity of the sea surface does not have an appreciable effect on the current and field distributions,

since the impedance Z as determined by formula (3) is close to zero for the selected e r, c~, and ~-.

The effects of modulation of the sea-surface deviations and of the establishrnent of a smooth impedance surface on

a part of contour i T (L 1 and L2) were investigated. Figure 5 shows the distribution of [ H z [ for the following versions:

1) The entire contour l T is a sea surface with regular deviations (T = 0.5X and H = 0.03X).

2) The entire contour l T is a sea surface with modulated deviations (T = 0.5X, T 1 = 9/', and Hma x = 0.03X).

3) Regions L 1 = X and L 2 = 1.5X are an impedance surface with Z = i108 [~; the remainder is as in version 2).

4) The entire contour l T is a smooth surface with Z = i108 ~.

5) The entire contour l T is a smooth sea surface.

All t Hz t were normalized for version 4) for ~o = 1 ~

Modulation of the sea-surface deviations has practically no effect on the conditions of surface-wave formation; the

wave amplitude is somewhat increased. The establishment of an impedance surface on regions L I and L 2 contributes to

more-effective surface-wave excitation. This is true over a wide range of Z values, and also when Z, being complex,

contains a real part. Such an impedance can be realized in the form of a system of conductors situated above the earth's

surface. A method of approximate determination of Z for such a system has been examined [4].

For selected % ~, and X, the properties of the sea surface are close to those of an ideal conductor and can be

considered a reflective grating. It is of interest to compare our results with those of Shestopaiov et at. [5] for periodic

reflective gratings. Of those examined by Shestopalov et aL [5], the closest to our problem were an echelon grating and a

grating formed by system of half-cylinders situated on a plane. We note that for plane-wave incidence on such gratings,

under certain conditions the amplitudes of the harmonics propagated along the grating are comparable with the amplitude

of the zeroth harmonic (which corresponds to the mirror-reflected wave) and can even exceed it. For an echelon grating,

for example, this is observed over a wide range of periods T and angles of incidence of from 0 to 70-75 ~ with respect to

209

the normal to the grating (the data are for T >_ X). For wave incidence at angles of 75-90 ~ which corresponds to our problem, the amplitudes of the harmonics propagated along the grating are considerably smaller than that of the zeroth harmonic. This agrees with our data; when T = Xand T = 2X, field concentration near the sea surface is not observed. On the whole, the data of Shestopalov et al. [5] are in qualitative agreement with our results; differences in the specifica- tions of the incident field and the surface geometry do not permit a quantitative comparison to be made.

LITERATURE CITED

2. 3.

4. 5.

l~.. M. Inspektorov, Izv. Vyssh, Uchebn. Zaved., Radio61ektron., 27, No. 11, 103 (1984). L. A. Vainshtein, Electromagnetic Waves [in Russian], Sovet-skoe Radio, Moscow (1957). G. T. Markov and D. M. Sazonov, Antennas [in Russian], t~nergiya, Moscow (1975). t~. M. Inspektorov, Izv. Vyssh. Uchebn. Zaved., Radio61ektron., 27, No. 7, 82 (1984). V. P. Shestopalov et al., Wave Diffraction by Gratings [in Russian], Kharkov State Univ. (1973).

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