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^{1}, Hongsheng Chen (陈红胜)

^{1,a)}and Herbert O. Moser

^{2}

### Abstract

Previous cylindrical hyperlenses were realized with metamaterial with only one component of the constitutive parameters negative. In this letter, we show that metamaterials with different combinations of negative and positive constitutive parameters can also be used to realize hyperlenses. The metamaterial forming the cylindrical hyperlens is based on the S-string architecture, which shows two components of the constitutive parameters negative, i.e., and . Both simulation and experimental studies of the cylindrical hyperlens show that a spatial resolution of about 1/10 of the vacuum wavelength can be obtained.

This work was sponsored by the National Natural Science Foundation of China under Grants Nos. 60801005, 60990320, and 60990322; the Foundation for the Author of National Excellent Doctoral Dissertation of People’s Republic of China under Grant No. 200950; the Zhejiang Provincial Natural Science Foundation under Grant No. R1080320; and the Ph.D. Programs Foundation of MEC under Grant No. 200803351025.

### Key Topics

- Metamaterials
- 11.0
- Evanescent waves
- 4.0
- Mechanical waves
- 4.0
- Wave sources
- 3.0
- Dispersion relations
- 2.0

## Figures

The schematic of the hyperlens: many cylindrical shells are stacked to form a cylindrical ensemble.

The schematic of the hyperlens: many cylindrical shells are stacked to form a cylindrical ensemble.

Transmission character at the interface in Fig. 1. The circles represent the dispersion of electromagnetic wave in air, while the hyperbolic lines represent the dispersion of electromagnetic wave in hyperlens. The & arrow represents energy vector and wave vector of the source wave from air since these two vectors are in the same direction. The arrow describes the wave vector, while the arrow describes the energy direction of the transmitted wave at the interface between air and the material we defined. (a) The dispersion relation of Eq. (1) when , , and which is used in many existing designs. (b) The dispersion relation of the ideal case of electromagnetic wave in hyperlens when , , , and is very close to zero. (c) The dispersion relation of Eq. (1) when , , and which is used in our design. (d) The dispersion relation of the ideal case of electromagnetic wave in hyperlens when , , , and is very close to zero.

Transmission character at the interface in Fig. 1. The circles represent the dispersion of electromagnetic wave in air, while the hyperbolic lines represent the dispersion of electromagnetic wave in hyperlens. The & arrow represents energy vector and wave vector of the source wave from air since these two vectors are in the same direction. The arrow describes the wave vector, while the arrow describes the energy direction of the transmitted wave at the interface between air and the material we defined. (a) The dispersion relation of Eq. (1) when , , and which is used in many existing designs. (b) The dispersion relation of the ideal case of electromagnetic wave in hyperlens when , , , and is very close to zero. (c) The dispersion relation of Eq. (1) when , , and which is used in our design. (d) The dispersion relation of the ideal case of electromagnetic wave in hyperlens when , , , and is very close to zero.

(a) -field distribution when the waves of two sources propagating through a hyperlens. The frequency of the TE wave is 3.97 GHz. The value of the inner radius of the hyperlens is 8 mm, while the outer one is 104 mm. The measurement trace (red dotted line) is 50 mm away from the outer radius of hyperlens. The value of the distance of the two sources is 7 mm, which is less than 1/10 of the vacuum wavelength. (b) -field distribution when the waves of two sources propagate through just air (without hyperlens case). All the geometric parameters are the same as the ones in (a).

(a) -field distribution when the waves of two sources propagating through a hyperlens. The frequency of the TE wave is 3.97 GHz. The value of the inner radius of the hyperlens is 8 mm, while the outer one is 104 mm. The measurement trace (red dotted line) is 50 mm away from the outer radius of hyperlens. The value of the distance of the two sources is 7 mm, which is less than 1/10 of the vacuum wavelength. (b) -field distribution when the waves of two sources propagate through just air (without hyperlens case). All the geometric parameters are the same as the ones in (a).

(a) The schematic of the experimental setup. (b) The prototype of hyperlens in microwave band. The values of inner and outer radii of the prototype are 8 and 104 mm, respectively. (c) The unit of S-string structure. The geometric parameters of the unit of copper S-string structure are the same as in Ref. 8, , , , , and the size of substrate FR4 is with .

(a) The schematic of the experimental setup. (b) The prototype of hyperlens in microwave band. The values of inner and outer radii of the prototype are 8 and 104 mm, respectively. (c) The unit of S-string structure. The geometric parameters of the unit of copper S-string structure are the same as in Ref. 8, , , , , and the size of substrate FR4 is with .

(a) Plot of simulation and experiment data without hyperlens. (b) Plot of simulation and experiment data with hyperlens. All the data have been normalized referring to their own maximum value. The abscissa means the number of the measured spots, a total of 37 spots for 180°.

(a) Plot of simulation and experiment data without hyperlens. (b) Plot of simulation and experiment data with hyperlens. All the data have been normalized referring to their own maximum value. The abscissa means the number of the measured spots, a total of 37 spots for 180°.

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