Pattern prediction of extended hemispherical-lens/ objective-lens antenna system at millimetre wavelengths

W.B.Dou G.Zeng Z.L. Sun

Indexing term: Lens antennas, Pattern prediction, Millimetre-wavelength antennas

Abstract: The far-field patterns of an extended hemispherical-lendobjective-lens antenna system fed by a double-slot antenna is computed using the hybridisation of ray-tracing and diffraction techniques. The difference patterns computed for a monopulse antenna are also presented. The computation results show that this antenna has good performance. Although the double-slot antenna is used as a feed antenna, other antennas such as slot-ring or bowtie antennas can also be used. This antenna can be used in many millimetre-wave systems.

1 Introduction

Integrated antennas have the advantage of low cost and can be readily mass produced using standard IC- fabrication processes. However, integrated antennas suffer from the surface-wave effect at millimetre wavelengths [I]. One way of avoiding this problem is to integrate the antennas on a dielectric lens. This structure does not support surface waves and tends to radiate most of their power into the dielectric side, making the pattern unidirectional on high-relative- permittivity lenses. The dielectric lens also provides mechanical rigidity and thermal stability [2]. There are various dielectric lenses which can be used for receiver applications. Among them, the extended hemispherical lens is practical, since it can synthesise other lenses, such as hemispherical, hyperhemispherical or ellipsoidal types, simply by varying the extension length behind the hemispherical position. In [3], an investigation on such a lens antenna is presented. In [4], slot-ring antennas on dielectric lenses are investigated.

In many applications the extended hemispherical- lens/objective-lens antenna system is more attractive, because it can provide higher gain and may be used in imaging systems [5 ] . This antenna system can also be 0 IEE, 1998 ZEE Proceedings online no. 19901880 Paper first received 9th September 1997 and in revised form 9th January 1998 The authors are with the State Key Laboratory of Millimeter Waves, Southeast University, Nanjing, 210096, Pepole’s Republic of China

used as monopulse antenna. However, no treatments on such antenna systems have so far been published. The purpose of this paper is to deal with the antenna system and provide a prediction of the pattern. The radiation pattern of the antenna system fed by a dou- ble-slot antenna is computed using the hybridisation of ray-tracing and diffraction techniques. The difference patterns computed for a monopulse antenna are also presented. Although the double-slot antenna is used as a feed antenna, other antennas, such as slot-ring or bowtie antennas, can also be used.

4

Fig. 1 Configuration of the extended hemispherical-lens antenna

2 Theoretical analysis

A double-slot antenna is, as an example, chosen as the feed antenna for the extended hemispherical lens. The lens is assumed to be lossless. This antenna has been used previously by many researchers, as stated in [3]. The configuration of extended hemispherical-lens antenna is shown in Fig. 1; the double-slot antenna is placed at the centre of the co-ordinates (x~, y,, 2,) or (rs, e,, $J and at (xo, -I, zo) in co-ordinates (x, y , z ) or ( r , 0, 4). a is the radius of the lens and l is the extension length. n’ is the refractivity of the lens. t is the unit vec- tor of pointing to a point on the hemispherical surface from double-slot; i is the unit-radius vector in co-ordi- nates (Y, 19, $); s^ is the unit vector of the exiting ray.

The double-slot-antenna patterns are calculated assuming a sinusoidal magnetic-current distribution on the slot and using an array factor in the E-plane direc- tion [6]. The double slots lie in the x z plane, and the slots point in the direction of the z axis as shown in Fig. 2. The wavelength of the sinusoidal current distri-

295 IEE Proc.-Microw. Antennas Propag.. Vol. 145, No. 4, August 1998

bution in the slot is the mean wavelength & I ~ E ~ and given by [3]

where k, = 2nl?+,,.,.

= (1 + ~ ~ ) 1 2 . The current in the slot is

(1) I = I, sin{k,(lo - 1 ~ 1 ) ) - Zo < z < 20

I zs

Fig. 2 Configuration of LX- the double-slot antenna

Because a >> d and 21,, at the lenslair interface only far field of the double-slot antenna is considered. The corresponding normalised far-fields are:

1 sind, {cos(keZ~cosO,) - cos k,lo} E4* = - -

r.5 k& - kz cos2 0,

1 1 sin@, {cos(k,lo cos0,) - cos k,lo} Hq = --- rls r s Ikk - k,2 cos2 8,

(2) 1 x cos k , - sin 0, cos 43 ( : ” .

where k, = kdLel = 2dAdIel for the dielectric side, k, = 2n1Aa1, for the air side, and 0, is the angle with respect to the z, axis, I P ~ is the angle from the xs axis in the xsys plane and qe is the wave impedance.

The radiation patterns from the extended hemispher- ical lenses are computed using a ray-tracing technique. The double-slot-antenna patterns into the dielectric are used to calculate the distribution of the electric and magnetic fields across the spherical surface of the extended hemispherical lenses. To carry out the inte- gration on the surface of the hemispherical lens, eqn, 2 should be transformed to co-ordinates (x, y , z ) or ( r , e>#).

For a given ray, the fields are decomposed into par- allel/perpendicular components at the lens-air interface and the appropriate transmission formulas are used for each mode 171:

2n’ cos a T_L = t.71 (51 2n’ cos Q!

cos a + nl2/1- n l 2 sin2 a qI =

a is the incident angle. If the far field of the extended hemispherical lens is

to be found, the equivalent currents on the hemispheri- cal surface are needed. They

(4)

Then the vectorial potential can be obtained by integration on the surface:

296

x SJ’J, exp(-j kB . T’) exp(jkii., . T’)ds’ S

- exp(-jkr) A, = -

4n r

S

(5) i ’ is the radius vector from origin to source point and dr is the unit vector pointing to far-field point. r is the distance from the origin to the far-field point. exp(- jki .?‘) is the phase of the exiting wave at the source point 181. A matching layer at the lens-air interface is not yet considered in this analysis. A analysis of the reflection from the lens-air interface shows that the reflection will result in an additional loss of about 1.5dB. Therefore in practice a matching layer is needed. In the far field, the transverse electric field is equal to

EQ = -JWA,Q - J w Z ~ A , ~

Fig. 3 antenna system

ConJgurution of the extended hemispherical-lendobjective-lens

The extended hemispherical lenslobjective-lens antenna to be analysed is shown in Fig. 3. For most applications a uniform aperture phase is required for high gain. This implies that all the geometric rays from the phase centre to the reference aperture plane of the lens have identical optical path lengths, It results in a hyperbolic lens as the objective lens. To obtain the far field of the extended hemispherical-lendobjective-lens antenna, the ray tracing is continued. First, the incident fields at point B on the back surface of the hyperbolic lens, which are decomposed into parallellperpendicular components, are obtained. Then the refractive fields within the hyperbolic lens are obtained. Finally the fields at point C on the front surface of the objective lens are obtainted. The manipulation is similar and omitted to save space. According to the relation between the aperture fields and the radiated fields, 191

n n

x exp(jk,z’ + jk,y’)dlc’dy’

(7 ) = 2. fz + Gfy

IEE Proc -Microw Antennas Propag , Vol 145, No 4, August 1998

where Ea (xf,yf) is the aperture field, Sa is the aperture plane, 7' is the position vector at the source point on the plane, and 2 is the unit vector of the exiting ray at the same point. exp(-jko7'.2) is the phase distribution of the aperture field on the aperture. Clearly, if 2 is constant over the aperture, the radiated field will have the maximum in the C direction. For the objective lens, another co-ordinate, as shown in Fig. 3, is used, so the co-ordinate transformation from (x,y,z) to (x',y',z') has to be carried out. Now the origin of the co-ordinate is at the centre of the front surface of the objective lens. The radiated field is expressed as

be changed by varying the diameter and focus length of the objective lens.

0

-5

-10 B

-20

+ cos 0 ( fy cos 4' - f z sin 4') } ( 8 ) -25

3 Calculation results

Some calculated far fields of the extended hemispheri- cal lens are presented first. A double-slot antenna with length 210 = 0.28& and spacing d = 0.16& is consid- ered. The relative permittivity of the lens E, is 11.7. The frequency is 94GHz. The radius of the extended hemi- spherical lens is 18". The computed power patterns in the H plane, for which the double-slot antenna is at position (xo = 0, yo = -1, z0 = 0), are shown in Fig. 4 for different extension lengths. The pattern in the E plane is almost the same. It is seen that the patterns can be changed by varying the extension length.

0

-10

m :- -20

SL al

al .- c 2 -30

-40

60 70 80 90 100 110 120 0, deg.

Farlfield patterns of the extended hemispherical-lens antenna Fig. 4 (i) L = 5.9mm, (ii) L = 6.5" (iii) L = 7.1"

For the extended hemispherical-lens/objective-lens antenna system, a calculated far-field pattern in the E plane at the 3mm band is shown in Figs. 5 and 6. The pattern in the H plane is similar. The extended hemi- spherical lens is made of silicon of permittivity 11.7 and diameter 35.8". The objective lens is made of poly- styrene, of permittivity 2.54, diameter 200" and focus length 260". Extension lengths L were 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4, and 5.6mm, respectively. When L is equal to 5.2mm, it approaches that of the hyperhem- ispherical lens. The exiting ray from its surface coin- cides with the ray radiating from the focus of the objective lens, so it results in a good radiated field pat- tern. It may be deduced that the far-field pattern of the extended hemispherical-lensiobjective-lens system can

IEE Proc.-Microw. Antennas Propag.. Vol. 145, No. 4, August 1998

-30 0 1 2 3 4

0, deg. Fig. 5 (i) L = 4.2, (ii) L = 4.4, (iii) L = 4.6, (iv) L = 4.8"

Pattern of the extended hemispherical-lendobjective-lens antenna

-50 I I I I 1 0 1 2 3 4

0, deg. Pattern of the extended hemispherical-lens/objective-lens antenna Fig. 6

(i) L = 5.0, (ii) L = 5.2, (iii) L = 5.4, (iv) L = 5.6"

0

-1 0

-20 m e U ._

-30 ._ s c - e!

-40

-50

-60

e, deg. Fig. 7 objective-lens

Monopulse dgerence pattern of the extended hemispherical-lens/

(i) X = &251ho, Z = 0 (ii) X = 0, Z = +0.203h0

291

We are also interested in the monopulse different patterns of the extended hemispherical-lens/objective- lens antenna system. In Figs. 7 and 8 some calculated results are shown where the extension length L is 5.2”. In Fig. 7 the fed antennas are placed at (X, = -c0.251&, 2, = 0) and (X , = 0, 2, = .-0.203&), in Fig. 8 they are placed at (X , = 20.203&, 2, = 0) and (Xs = 20.219&, 2, = 0). It is seen that the sharp-null per- formance is very good. Clearly, it may be deduced that by changing the diameter and focus length of the objec- tive lens or the extension length of the monopulse, dif- ferent pattern can also be changed.

-50 -401 -60 L I . I , I . I , ..

-8 -4 0 4 a 8, deg.

Fig. 8 objective-lens (I) X = z0.219ho, Z = 0 (ii) X = 20 203A,, Z = 0

Monopulse dgerence pattern of the extended Izemirpherical-lens/

4 Conclusions

The far-field patterns of an extended hemispherical- lendobjective-lens antenna system fed by a double-slot

antenna are computed using ray-tracing and diffraction integration methods. Both patterns for the extended- hemispherical-lens antenna only and for the extended- hemispherical-lens/objective-lens antennas are pre- sented. The extended hemispherical-lendobjective-lens antennas have good radiation properties. The pattern can be changed by varying the extension length. The difference patterns computed for a monopulse antenna are also presented. The computation results show that this antenna has good performance of the sharp null of the difference pattern. It may be deduced that the pat- tern can also be changed by changing the diameter and focus length of the objective lens. Although the double- slot antenna is used as a feed antenna, other antennas, such as slot-ring or bowtie antennas, can be used too. The calculated results will be helpful for engineering applications. This antenna can be used in many milli- metre-wave systems.

5 References

1 RUTLEDGE, D.B., et a1 ‘Infrared and millimeter waves’, in BUTTON, K.J. (Ed.): ‘Integrated circuit antennas’ (Academic Press, New York, 1983), vol 10

2 REBEIZ, G.M.: ‘Millimeter-wave and terahertz integrated circuit antenna’, Pvoc. ZEEE, 1992, 80, (Il), pp. 1748-1770

3 FILIPOVIC, D.F.: ‘Double-slot antennas on extended hemispher- ical and elliptical silicon dielectric lenses’, ZEEE Trans., 1993, MTT-41, (IO), pp. 1738-1749

4 RAMAN, S., and REBEIZ, G.M.: ‘Single- and dual-polarized millimeter-wave slot-ring antennas’, ZEEE Trans., 1996, AP-44, (1 1), pp. 1438-1444

5 RUTLEDGE, D.B., and MUHA, M.: ‘Imaging antennas arrays’, ZEEE Trans., 1982, AP-30, (4), pp. 535-540

6 ELLIOTT, R.S.: ‘Antenna theory and design’ (Prentice-Hall, New Jersey, 1981), chap. 4

7 JACKSON, J.D.: ‘Classical electrodynamics’ (John Wiley & Sons, 1976), chap. 7

8 SILVER, S. (Ed.): ‘Microwave antenna theory and design’ IEE series on Electromagnetic waves (Peter Peregrinus, 1984)

9 COLLIN, R.E.: ‘Antennas and radiowave propagation’ (McGraw-Hill, 1985)

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