Download - Refocusing of backscattered microwaves in target detection by using LHM flat lens

Refocusing of backscattered microwaves in target detection by using LHM flat lens

G. Wang, J. R. Fang, and X. T. Dong Department of Telecommunication Engineering, Jiangsu University, Zhenjiang 212013, P.R. China

[email protected], [email protected]

Abstract: When microwave emitted from a point source is focused on a target by using a left-handed metamaterial (LHM) flat lens, microwave backscattered from the target will be refocused by the LHM lens in the vicinity of the point source. Numerical simulations with two-dimensional (2D) finite-difference time-domain (FDTD) method demonstrate that, even for flat LHM lens of material losses to the order as that reported in some LHM microwave experiments and simulations, the refocusing of backscattered microwave will yield a sub-wavelength lateral resolution and remarkable enhancement of the backscattered microwave, which will benefit the detection and imaging of small target.

©2007 Optical Society of America

OCIS codes: (110.2990) Image formation theory; (290.1350) Backscattering; (220.3630) Lenses

References and links

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2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 –79 (2001).

3. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ ,”

Sov. Phys. Usp. 10, 509-514 (1968). 4. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and Negative Refractive Index,” Science

305, 788-792 (2004). 5. C. Caloz and T. Itoh, “Metamaterials for high-frequency electronics,” Proc. IEEE 93, 1744-1751 (2005). 6. N. Engheta and R. W. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans.

Microwave Theory Tech. 53, 1535-1556 (2005). 7. J.B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000). 8. J. T. Shen and P. M. Platzman, “Near field imaging with negative dielectric constant lenses,” Appl. Phys.

Lett. 80, 3286-3288 (2002). 9. S.A. Cummer, “Simulated causal subwavelength focusing by a negative refractive index slab,” Appl. Phys.

Lett. 82, 1503-1505 (2003). 10. X. S. Rao and C. K. Ong, “Subwavelength imaging by a left-handed material superlens,” Phys. Rev. E 68,

0676011–3 (2003). 11. N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161-163,

(2003). 12. M. W. Feise, and Y. S. Kivshar, “Sub-wavelength imaging with a left-handed material flat lens,” Phys.

Lett. A 334, 326-330 (2005). 13. A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed-

material plate,” Phys. Rev. Lett. 92, 774011-4 (2004). 14. A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-

line lens,” Phys. Rev. Lett. 92, 1174031-4 (2004). 15. K. Aydin, I. Bulu, and E. Ozbay, “Focusing of electromagnetic waves by a left-handed metamaterial flat

lens,” Opt. Express 13, 8753-8759 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-22-8753 16. A. Grbic and G. V. Eleftheriades, “Practical limitations of subwavelength resolution using negative-

refractive-index transmission- line lenses,” IEEE Trans. Antennas Propagat. 53, 3201-3209 (2005). 17. X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, “Perfectly Matched Layer-Absorbing Boundary

Condition for Left-Handed Materials,” IEEE Microwave Wireless Compon. Lett. 14, 301-303 (2004).

#78086 - $15.00 USD Received 14 December 2006; revised 26 January 2007; accepted 2 February 2007

(C) 2007 OSA 19 March 2007 / Vol. 15, No. 6 / OPTICS EXPRESS 3312

18. R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys.: Condens. Matter 13, 1811-1819 (2001).

19. A. Grbic and G. V. Eleftheriades, “An isotropic three- dimensional negative-refractive-index transmission-line metamaterial,” J. Appl. Phys. 98, 431061-5 (2005).

20. T. Koschny, L. Zhang, and C. M. Soukoulis, “Isotropic three-dimensional left-handed metamaterials,” Phys. Rev. B 71, 1211031-4 (2005).

1. Introduction

Stimulated by the pioneer experimental demonstration [1, 2] of Veselago’s left-handed material (LHM) [3], more and more experiments at microwave frequencies have been reported to demonstrate the unique electromagnetic properties of the LHM. The realization of the LHM has provoked great interest in exploring the use of such artificial materials for the design of specific applications [4-6].

Among potential applications of the LHM, lenses having flat surfaces have been proposed [7]. Different from conventional lens with curved surfaces due to positive index of refraction, a flat slab of LHM with negative index of refraction can be used as lens to focus electromagnetic waves. Theoretical analysis and numerical simulations [8-12] indicated that the so-called perfect lens made of LHM with no losses may achieve a focusing resolution better than the diffraction limit. Due to the material losses in practical LHM, the lens is no longer perfect. Several microwave experiments have also been reported [13-15] to demonstrate the focusing. It turned out that the focusing (or imaging) resolution observed in the experiments is generally worse than that described in theoretical and numerical investigation for perfect lens, but sub-wavelength focusing properties of the flat LHM lens were still measured. For example, the half-power beamwidth measured by Grbic and Eleftheriades’ experiment for thin LHM lens (thickness is approximately 0.27 wavelength) is 0.21 effective wavelengths whereas for the diffraction-limited patterns it is 0.36 wavelengths [14]. The full width at half-maximum (FWHM) of the focused beams measured by Aydin and Bulu’s experiment with two-dimensional (2D) LHM slab (thickness is approximately 1.2 wavelengths) for two different point source distances of 0.5 and 1.0 wavelength are 0.36 and 0.4 wavelength [15], respectively, which both are sub-wavelength and below the diffraction limit.

The simulation and experiment demonstration of the unique focusing properties of flat LHM lens makes it quite reasonable to use flat LHM lens for high-resolution microwave target detection and imaging. For such application, microwave emitted from a point source is focused on a target by using a flat LHM lens, and microwave backscattered from the target will be refocused by the LHM lens in the vicinity of the point source. It is the focusing-refocusing property of flat LHM lens that supports the use of flat LHM slab for microwave target detection and imaging.

In this paper, we study the refocusing properties of the backscattered microwave by using a flat LHM lens. First, refocusing of the backscattered microwave is demonstrated by numerical simulation with 2D finite-difference time-domain (FDTD) method. For a cylindrical target of perfect electric conductor (PEC) at the focal point, sub-wavelength refocusing resolution of the backscattered microwave can be observed. Then, remarkable enhancement of the backscattered microwave due to the use of a flat LHM lens is further investigated.

2. Refocusing of the backscattered microwave

For illustration, we may consider the use of a planer LHM slab as lens which has a thickness of d. The artificial LHM is supposed to be isotropic and characterized by permittivity rε and

permeability rμ of the plasmonic form,



2

2( ) 1

2pe

r j

ωε ω

ω δω= −

+, (1)

2

2( ) 1

2pm

r j

ωμ ω

ω δω= −

+. (2)

By choosing different plasma frequencies peω , pmω and losses factor δ (which is related to

the collision frequency) in (1) and (2), we will have different permittivity rε and permeability

rμ . The lossless LHM as described in the study of “perfect lens” [7] can be obtained by

setting 2pe pmω ω ω= = and 0δ = , which yields 1rμ = − and 1rε = − . Complex

permittivity rε and permeability rμ will be obtained if we set 0δ ≠ in (1) and (2), which indicates lossy LHM. For example, at microwave frequency of 10GHz we may set

102 2 2 10 ( / )pe pm rad sω ω ω π= = = × × and 810δ = , thus we have 1 0.006r r iε μ= ≈ − − ,

i.e., 1 0.006n i≈ − − . In fact, the imaginary part of the refractive index defines LHM losses to the same order as in the LHM of Eleftheriades’ experiment [14, 16]. Lens made of such LHM is no longer a perfect lens.

Microwave emitted from a point source on one side of the LHM slab can be focused first at a focal point inside the LHM lens and then at another focal point outside the LHM lens, as shown in Fig. 1. If there happen to be a target at the outside focal point F2, microwave emitted from the source will be focused on the target by the flat LHM lens, the target will backscatter the focused microwave, and the backscattered microwave will be refocused by the flat LHM lens to the vicinity of the source point, as shown in Fig. 1. By analyzing the refocused microwave, target detection and imaging can be carried out. Generally, the refocused microwave field recorded at each receiving point is actually the compound of three parts: the wave emitted from the source, the wave reflected from the entrance and exit surfaces of LHM lens (for lens of negative refraction index 1n ≠ − ), and the refocused wave backscattered from the target. To obtain the backscattered microwave, we substrate the fields recorded when there is no target at F2 from the fields recorded when there is target at F2.

Fig. 1. Focusing and refocusing of microwave in target detection by using flat LHM lens.

To investigate the refocusing properties of flat LHM lens, we may calculate the backscattered microwave field at receiving points in region near the source by using FDTD simulation. As in the previous studies on the focusing properties [13-15], we may depict the beam profile (or distribution) of backscattered microwave field intensity along y-direction, and measure the full width at half-maximum (FWHM) of the beam.

In our simulation, we consider a typical situation that a line source of microwave frequency 10f GHz= (wavelength 3cmλ = ) with unit amplitude is set at ( λ− , 0) in the

coordinates in Fig. 1, the 2D flat LHM lens of 1 0.006n i≈ − − and of thickness 2d λ= is set at 0 2x λ≤ ≤ , and a target of PEC cylinder with a diameter of 6φ λ= is centered at ( 2.95λ ,



0) to keep its front surface at the real focal point where maximum field intensity is observed in the focus zone. To verify the refocusing of microwave backscattered from the PEC cylinder, we set 200 receiving points on y-axis with interval of 0.5mm to record the backscattered microwaves. In our 2D FDTD simulation, the computational space is 600*600 cells with

0.5 x y mmΔ = Δ = , which are surround by our 10-cell extended uniaxial anisotropic perfectly matched layer added to truncate the computational space [17].

Fig. 2 depicts the lateral beam profile of refocused microwave backscattered from the PEC cylinder. For comparison, beam profile of the focused microwave (without target at F2) along line 2.95x λ= is also depicted. The FWHM of the refocused beam is approximately 0.4λ , while the FWHM of the focused beam on the target side is approximately 0.377λ . Therefore, we have the observation that the lateral refocusing resolution is slightly worse than the lateral focusing resolution.

Y-axis (in λ)

No

rma

lize

d |E

| 2

-1.5 -1 -0.5 0 0.5 1 1.50

0.25

0.5

0.75

1FocusedRefocused

Y-axis (in λ)N

orm

aliz

ed |E

| 2

-1 -0.5 0 0.5 10

0.25

0.5

0.75

1

Fig. 2. Lateral beam profiles of focused and refocused Fig. 3. Lateral beam profile of refocused microwave microwave by using flat LHM lens. when two PEC cylinders are scanned.

The sub-wavelength focusing/refocusing resolution will generally allow sub-wavelength target detection and imaging. Fig. 3 depicts the lateral beam profile of the refocused microwave backscattered when there are two PEC cylinders of diameter 6φ λ= on line

2.95x λ= with a space of 13 30λ between the cylinder centers. The lateral beam profile is obtained by scanning the source-receiver pair along y-axis with step 0.5 mmyΔ = and

recording the backscattered microwave. The space between the source and receiver is / 5λ in y-direction. We have the observation that the two cylinders can be clearly discriminated.

3. Enhancement of the backscattered microwave

For microwave detection and imaging of small target such as breast tumor at its early stage, high sensitivity is desired. The use of flat LHM to focus the emitted microwave and refocus the backscattered microwave will benefit the improvement of sensitivity because stronger backscattering will occur if more microwave power is focused on the target, and the refocusing of flat LHM lens will further enhance the backscattered microwave. Detailed comparison between the backscattered microwave field levels obtained with and without a flat LHM lens will demonstrate the enhancement of the backscattered microwave.

For the typical situation as defined in our previous simulation with LHM lens of 1 0.006n i≈ − − at 0 2x λ≤ ≤ , Fig. 4(a) shows the focusing of microwave emitted from the

line source of unit amplitude, and Fig. 4(b) shows the refocusing of the microwave backscattered from the PEC cylinder of diameter 6φ λ= located at the outside focal point. We remark that Fig. 4(a) and (b) are shown under different intensity scales.



X-axis(in λ)

Y-a

xis(

in λ

)

-2 -1 0 1 2 3 4

-1

0

1

0.0

0.5

1

Fie

ld I

nten

sity

|E| (

in a

. u.)

(a)

X-axis(in λ)

Y-a

xis(

in λ

)

-2 -1 0 1 2 3 4

-1

0

1

0.0

0.05

0.1

0.15

Fie

ld In

tens

ity |E

| (in

a. u

.)

(b)

Fig. 4. (a) The focusing of microwave emitted by a line source and (b) the refocusing of microwave backscattered from the PEC cylinder of diameter 6φ λ= at the focal point.

Figure 5 shows the distribution of electric field level of incident and backscattered microwave along x-axis. The two blue curves depict the distribution of field level of microwave emitted from the line source, and the two red curves depict the distribution of field level of backscattered microwave. The solid curves indicate the situation where a flat slab of LHM lens is used, and the dashed curves indicate the results without use of LHM lens. As illustrated in Fig. 5, the line source is located at x= λ− , the entrance surface of the flat LHM lens is at 0x = , the exit surface of the flat LHM lens is at 2x λ= , and the PEC cylinder target of diameter of 6φ λ= is centered at 2.95x λ= . The level of source of unite amplitude is 0dB. The two focus zone can be observed clearly. We note that there is a peak at the entrance interface, this is the effects of the so-called surface polaritons [18].

From Fig. 5 we have the observation that under the illumination of microwave line source of unit amplitude, the field level of incident microwave impinges directly onto the target at F2 is -24.3dB ( dashed blue), the field level of incident microwave at F2 after focused by the flat LHM lens is -10.1dB (solid blue). Therefore, the focused microwave incident on the target is approximately 14.2dB stronger than the field impinging directly onto the target without using the flat LHM lens. Moreover, the field level of backscattered microwave field at the source location refocused by the flat LHM lens is -20.1dB (solid red), while the field level of backscattered microwave at the source location without using a flat LHM lens for focusing and refocusing is -44.8dB (dashed red). Therefore, there is approximately 24.7dB enhancement of the backscattered microwave field intensity due to the use of flat LHM lens.

X-axis (in λ)

Fie

ld L

eve

l 20

lg(|

E|)

(in d

B)

-2 -1 0 1 2 3 4

-40

-30

-20

-10

0

X-axis (in λ)

Fie

ld L

evel

20l

g(|E

|) (in

dB

)

-2 -1 0 1 2 3 4

-60

-50

-40

-30

-20

Fig. 5. Distribution of electric field levels of incident Fig. 6. Distribution of backscattered microwave field levels and backscattered microwave along x-axis. for the detection of PEC cylinders of diameters of 1mm and

3mm, respectively.



For the detection of thinner PEC cylinder target, the enhancement of backscattered microwave could be very helpful. To demonstrate the effects, we replace the PEC cylinder in our previous simulation with thinner cylinders of diameter 10φ λ= (viz. 3mm) and

30φ λ= (viz. 1mm), respectively. After calculating the incident and backscattered microwave field levels, Fig. 6 depicts the distribution of electric field level of the backscattered microwave along x-axis. In Fig. 6, the solid curves represent the situation where a flat slab of LHM lens is used, and the dashed curves indicate the results where no LHM lens is applied. The red curves are for cylinder of diameter of 10φ λ= , and the blue curves are for

cylinder of diameter 30φ λ= . For the detection of cylinder of 10φ λ= , the backscattered field level at the source location is -51.6dB when no flat LHM lens is used (dashed red), while the backscattered field level at the source location goes up to -27.3dB after using the flat LHM lens (solid red). For the detection of cylinder of 30φ λ= , the backscattered field level at the source location is -65.2dB when no flat LHM lens is used (dashed blue), while the backscattered field level goes up to -41.3dB after using the flat LHM lens (solid blue). Therefore, for thinner PEC cylinder, there is more than 23.9dB enhancement of the backscattered microwave field intensity due to the use of flat LHM lens.

To show the effects of target depth d2 on the refocusing property, we may set different source locations (d1) and target locations on x-axis in our simulation, and the target is always set on the focal point F2. For the detection of a PEC cylinder of diameter of 6φ λ= , we read the same FWHM as in Fig. 2 from the lateral beam profiles of refocused microwave by setting

1 0.5d λ= and 1 1.5d λ= , respectively. At the source location, the field levels of backscattered

microwave refocused by the flat LHM lens are -20.3dB and -19.8dB, for 1 0.5d λ= and

1 1.5d λ= , respectively, which indicate that almost the same enhancement of the backscattered microwave field intensity can be observed for target at different depths.

In practice, exact match between the LHM lens and the surrounding medium is hard to achieve. To show the effects of the mismatch, we further simulate two situations with LHM lens of 0.9 0.006n i≈ − − and 1.1 0.006n i≈ − − . By setting the PEC cylinder target of

6φ λ= in the focus zone and keep its front surface at the real focal point, our simulation results indicate that the lateral resolution is approximately 0.483λ and the field level refocused at source position is -23.9dB for 0.9 0.006n i≈ − − , and approximately 0.42λ and -20.6dB for

1.1 0.006n i≈ − − . Therefore, although the mismatch deteriorates the focusing-refocusing to some extent, the sub-wavelength refocusing resolution and approximately the same enhancement of the backscattered field can be observed.

4. Conclusion

Significant enhancement of the backscattered microwave after using flat LHM lens means improvement of the ability of detection and imaging of small target. The sub-wavelength lateral refocusing resolution of flat LHM lens will provide the desired high lateral resolution for application such as in early breast cancer detection. Moreover, the almost unique enhancement of the backscattered wave for target at different depth behind the flat lens will also help to improve the performance of target imaging system with flat LHM lens.

We remark that the near-field target detection and imaging by using LHM lens relies on the isotropic 3-D LHM. The design and fabrication of isotropic 3-D LHM are now under consideration [19, 20]. If considering the rapid development in artificial LHM design, high resolution near-field target detection and imaging by using flat LHM lens is highly desirable.

Acknowledgments

This work is supported in part by the Department of Personnel of Jiangsu Province of China, and Department of Education of Jiangsu Province of China under grant No. 05KJB510012.



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