An ultrathin terahertz lens with axial long focal depth based on metasurfaces Xiao-Yan Jiang,1 Jia-Sheng Ye,1,2,∗ Jing-Wen He,1,3 Xin-Ke Wang,1,2 Dan Hu,1,3 Sheng-Fei Feng,1,2 Qiang Kan,4 and Yan Zhang1,2,3,5 1 Department of Physics, Capital Normal University and Beijing Key Lab for THz Spectroscopy and Imaging, Key Lab of THz Optoelectronics, Ministry of Education, Beijing 100048, China 2 Beijing Center for Mathematics and Information Interdisciplinary Sciences, Harbin Institute of Technology, Harbin 150001, China 3 Department of Physics, Harbin Institute of Technology, Harbin 150001, China 4 State Key Laboratory for integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China 5 [email protected] ∗ [email protected]
Abstract: The plasmonic resonance effect on metasurfaces generates an abrupt phase change. We employ this phase modulation mechanism to design the longitudinal field distribution of an ultrathin terahertz (THz) lens for achieving the axial long-focal-depth (LFD) property. Phase distributions of the designed lens are obtained by the Yang-Gu iterative amplitude-phase retrieval algorithm. By depositing a 100 nm gold film on a 500 µ m silicon substrate and etching arrayed V-shaped air holes through the gold film, the designed ultrathin THz lens is fabricated by the micro photolithography technology. Experimental measurements have demonstrated its LFD property, which basically agree with the theoretical simulations. In addition, the designed THz lens possesses a good LFD property with a bandwidth of 200 GHz. It is expected that the designed ultrathin LFD THz lens should have wide potential applications in broadband THz imaging and THz communication systems. © 2013 Optical Society of America OCIS codes: (080.3630) Lenses; (240.6680) Surface plasmons; (250.5403) Plasmonics.
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#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30030
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1.
Introduction
The axial long-focal-depth (LFD) property of lenses and mirrors is critically important in optical coupling, optical imaging and optical interconnections, because it can provide a focusing range rather than a definite focal position. In the past, several researchers have designed the three-dimensional large-sized axilenses and axicons from geometrical optics and analyzed their LFD properties based on the scalar diffraction theory [1–3]. Dong et al. applied a generalized amplitude-phase retrieval algorithm to designing LFD diffractive phase elements, i.e., the YangGu algorithm [4]. In all of the above works, the phase modulation for the LFD property was accumulated by the optical path difference. Therefore, thicknesses of the optical elements are larger than or comparable to the incident wavelength. In order to reduce the thickness further,
#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30031
new phase modulation mechanism needs to be explored. In recent years, scientists have discovered that refractive index and phase modulation exists in metal-dielectric stratified structures [5–7], electromagnetic resonant cavities [8, 9], metallic nanoparticle clusters [10], and plasmonic antennas [11]. Quite recently, Yu et al. have disclosed that an abrupt phase change is encountered on an air-metal interface with subwavelength structures and formulated generalized laws of reflection and refraction [12]. Through fabricating the V-shaped thin gold antennas on a silicon substrate, experimental measurements have proved their theoretical predictions. The phase change is originated from plasmonic resonance on the nanostructured metal surface, therefore, it is named as a metasurface. An obvious merit of the optical elements based on metasurfaces is that, they (only about 100 nm) are much thinner than the conventional optical elements, especially for the terahertz (THz) region. For instance, for a 1.0 THz wave with wavelength of 300 µ m, the thickness is only 1/3000 of the wavelength. By using the metasurface, a lot of optical functions have been realized including optical focusing [13,14], dispersive focusing [15], optical imaging [16], computer generated holograms [16], ultrahigh refractive index modulation [17], optical vortexes [12, 18, 19], the dual polarity plasmonic metalens [20], quarter-wave plate for generating circularly polarized light [21], Fresnel zone plate [22], helicity dependent surface plasmon excitation [23], and the photonic spin Hall effect [24]. In previous papers, the optical focusing function on a definite transverse focal plane has been successfully realized by using the metasurfaces [15, 16]. In this paper, we extend to modulate the longitudinal field distribution with metasurfaces for obtaining the axial LFD property of a THz lens, which can broaden its applications in THz imaging and THz communication systems. The Yang-Gu amplitude-phase retrieval algorithm [4, 25, 26] is adopted to calculate the phase distributions of the designed ultrathin LFD THz lens. For generating the desired phase changes, we design a metasurface with V-shaped air holes on a thin metal film. Compared with the V-shaped gold antenna in [12], this complementary structure is superior in reducing the background noise in the transmitted region due to blocking the incident field. The designs of the structured metasurfaces are implemented by using the ‘Concerto’ commercial software, which is based on the finite-difference time-domain method [16, 27]. Then, we fabricate the designed lens by the micro photolithography and lift-off technologies. Finally, in order to characterize the performance of the fabricated LFD THz lens, we have developed a THz near-field imaging system. The experimental setup and its working principles were described in [28, 29]. This paper is organized as follows. In Section 2, firstly, the principle of the Yang-Gu iterative amplitude-phase retrieval algorithm is described in detail with formulas. Secondly, the designing parameters of the ultrathin LFD THz lens are given and phase distributions are calculated by the Yang-Gu algorithm. Thirdly, the calculated phases are quantized into eight quantization levels and the designed eight V-shaped air hole structure units are presented with detailed parameters. In Section 3, the designed LFD THz lens is fabricated and its LFD properties are measured in experiments. Numerical simulations are also carried out for comparison with physical explanations. In Section 4, a brief conclusion is drawn with some discussions. 2.
Design of the ultrathin LFD THz lens
Figure 1(a) depicts the focusing geometry. The xy plane is the incident plane, and the z-axis is the propagation direction. The input THz plane wave transmits through the ultrathin THz lens, and it is assumed to be focused in an axial range ( f0 − δ f /2, f0 + δ f /2), as shown in Fig. 1(a). On the input plane P1 (z = 0), the wave function is written by U1 = U1 (X1 ) = ρ1 (X1 ) exp[iφ1 (X1 )] ,
(1)
where the vector X1 represents the input-plane coordinates (x1 , y1 ). #198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30032
4
y
x
(b)
2 y(mm)
(a)
0 −2 −4 −4
−2
0 2 x(mm)
4
2.0π 1.75π 1.5π 1.25π 1.0π 0.75π 0.5π 0.25π
Fig. 1. (a) A focusing geometry of the ultrathin LFD THz lens. (b) Eight-level quantized phase distributions of the designed ultrathin LFD THz lens.
The phase distributions of the THz lens are obtained by the Yang-Gu amplitude-phase retrieval algorithm [4]. For evaluating the LFD function, we choose several output sampling planes. The wave function on the α th output plane P2α at z = zα is denoted by U2α = U2α (X2α , zα ) = ρ2α (X2α , zα ) exp[iφ2α (X2α , zα )] ,
(2)
where α = 1, 2, ..., N, indicating the output plane number; the vector X2α stands for the outputplane coordinates (x2α , y2α ). The output wave function is related to the input wave function by the Fresnel diffraction integral as follows Z U2α (X2α , zα ) =
G(X2α , X1 , zα )U1 (X1 )dX1 ,
(3)
where G(X2α , X1 , zα ) represents the Fresnel diffraction integral kernel given by G(X2α , X1 , zα ) =
2π i2π zα iπ (X2α − X1 )2 exp[ + ]. iλ zα λ λ zα
Equation (3) may be written in a compact form as U2α (X2α , zα ) = Gˆ α U1 (X1 ) .
(4)
For showing how accurate the real output wave function is, an error function is defined as follows ∆ = ∑(||U20α − U2α ||)2 , (5) α
represents the ideal complex amplitude on the α th output plane; || · · · || denotes the complex magnitude. Through searching for the minimum value of ∆ with respect to the arguments φ1 and φ2α , we can obtain exp[iφ1 (X1 )] = Q∗ /|Q| , (6a) where U20α
exp[iφ2α (X2α , zα )] =
Gˆ α ρ1 (X1 ) exp[iφ1 (X1 )] , |Gˆ α ρ1 (X1 ) exp[iφ1 (X1 )]|
(6b)
and Q =∑ ρ1 (X1 ) exp[−iφ1 (X1 )]Aˆ α α
−ρ2α (X2α ) exp[−iφ2α (X2α , zα )]Gˆ α ] ,
(7)
#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30033
ˆ where Aˆ α = Gˆ + α Gα . More detailed deductions of Eqs. (6a), (6b) and (7) were written in references [4, 25, 26]. Generally, Eqs. (6a) and (6b) should be solved numerically. In our design, parameters are selected as follows. The input plane has a size of 8 mm × 8 mm, which is equally quantized into 40 × 40 pixels. Therefore, the pixel size is 200 µ m × 200 µ m. The focal length f0 and focal depth δ f are preset to 9 and 10 mm, respectively. Therefore, the preset LFD region locates from 4 to 14 mm. We choose three output sampling planes situating at zα = 4, 9, and 14 mm, respectively, namely the parameter is α = 1, 2, 3 in Eqs. (2)∼(7). The incident wavelength is λ = 400 µ m. The three output planes have the same sizes of 16 mm × 16 mm, which are equally quantized into 32 × 32 pixels. By using the Yang-Gu iterative amplitude-phase retrieval algorithm, we can calculate the phase distributions φ1 (X1 ) on the input plane. After eight-level phase quantization from π /4 to 2π with a π /4 interval, they are displayed in Fig. 1(b). Table1 Structure units and their parameters for eight quantized phases Structure unit mm
Phase change
78
82
90
150
78
82
90
150
130
120
100
60
130
120
100
60
45
45
45
45
135
135
135
135
! 4
! 2
3! 4
!
5! 4
3! 2
7! 4
2!
Next, for producing the above eight quantized phase changes, we design a metasurface with V-shaped air holes on a thin metal film. A schematic diagram of the structure unit is shown in Fig. 2(a). The yellow and gray regions represent the metal film and the air hole, respectively. Each unit has a size of 200 µ m × 200 µ m. The polarization of the incident field E inc is along the x-axis. Through changing the air hole length h, width w, angles θ and β , the cross-polarized transmitted field Ey has different phase changes. The width of the air hole is fixed to w = 5 µ m. By using the commercial software ‘Concerto’ [16, 27], we have optimized eight structure units whose amplitudes are almost the same while their phases vary from π /4 to 2π for every π /4. They can serve as eight phase quantization levels in diffractive optics. Detailed parameters of the eight designed structure units are listed in Table 1. 3.
Performance analysis of the designed ultrathin LFD THz lens
3.1. Axial LFD properties of the designed ultrathin LFD THz lens After determining the above eight structure units, the ultrathin LFD THz lens is formed by putting the corresponding unit in the definite pixel on the input plane in Fig. 1(b). By using the micro photolithography technology, we have fabricated the sample. On a 500 µ m silicon substrate, a 100 nm thick gold film is deposited. Then, we etch the V-shaped air holes by the lift-off technology. Figure 2(b) displays an optical microscopy of the central part of the fabricated sample. Performances of the fabricated LFD THz lens are measured by using the THz near-field imaging system [28, 29]. The incident THz wave is x-polarized (Exinc ), and we measure the perpendicular transmitted intensity |Ey |2 in the xz plane, as shown in Fig. 2(c). It is seen from Fig. 2(c) that the focal region spans an axial range, instead of a focal point. It means that the LFD function is implemented. For demonstrating the LFD property more clearly, theoretical and experimental axial intensity distributions of the LFD THz lens are plotted in Fig. 2(d) by the blue and red curves, respectively. From Fig. 2(d), we can see that the experimental measurements #198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30034
(b)
(a)
y 400 m
4
1
(c)
x(mm)
2 0
0.5
−2 −4
5
10 15 z(mm)
20
0
Normalized axial intensity
x
1.5
(d)
1
LFD lens (theo) LFD lens (exp) Conventional lens
0.5 0 5.5
10
14.5
z(mm)
19
Fig. 2. (a) A schematic of the metasurface in a unit cell. (b) An optical microscopy of the central part of the fabricated ultrathin LFD THz lens. (c) Experimental intensity distributions in the xz plane. (d) The blue and red curves represent the theoretical and experimental intensity distributions of the LFD THz lens along the z-axis. The black curve plots the axial intensity distributions of a conventional THz lens. The dashed lines mark the three focal depths.
basically agree with the theoretical simulations. The effective focal depth is defined by the axial dimension with intensity over 50% of the maximum intensity [9], as shown by the blue and red dashed lines in Fig. 2(d). The theoretical and experimental LFD regions lie within [7.07, 15.47] mm and [6.40, 15.36] mm, respectively. Hence, the corresponding focal depths are 8.40 and 8.96 mm. Their focal-depth difference is attributed to the experimental fabrication errors. For comparison, we also calculate the axial intensity distributions of a conventional THz lens whose phase distribution is φ1c = exp[−iπ (x2 + y2 )/(λ f0 )], as shown by the black curve in Fig. 2(d). The black lines mark the LFD region, locating within [7.72, 10.13] mm. Its focal depth is only 2.41 mm. Consequently, the designed ultrathin LFD THz lens has successfully realized the LFD function as its focal depth is much longer than that of the conventional THz lens. 3.2. Transverse focusing properties of the designed ultrathin LFD THz lens For the ultrathin LFD THz lens, its lateral resolution inside the focal range is also an important characteristic. Therefore, we select three lateral planes to see the focusing behavior. Figure 3(a) plots the experimental intensity profiles along the x-axis on the three lateral planes at zα = 9 mm (blue solid curve), 11 mm (red dashed curve), and 13 mm (black solid curve), respectively. It is seen in Fig. 3(a) that most of the transmitted energy is concentrated inside the main lobe for all the three focal spots. The full widths at half maximum (FWHM) are 650, 720, and 690 µ m, respectively. Figure 3(b) is the same as Fig. 3(a) except for the theoretical simulations. It is apparent in Fig. 3(b) that the designed THz lens maintains high lateral focusing resolution in the LFD region. Numerical results reveal that the FWHM are 711, 763, and 750 µ m for zα = 9, 11, and 13 mm, respectively. Figures 3(c) – 3(e) illustrate the experimental focal spots on the above three lateral planes. On each lateral plane, the incident THz plane wave has a good focus. It is concluded that the fabricated ultrathin THz lens has successfully realized the LFD function with high lateral resolution. #198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30035
Normalized transverse intensity
Normalized transverse intensity
9 mm 11 mm 13 mm
(a) Experiment 0.8 0.6 0.4 0.2 0 −4
−2
0
2
x(mm)
1
9 mm 11 mm 13 mm
(b) Theory 0.8 0.6 0.4 0.2
4
0 −4
−2
0
x(mm)
2
4
4 (d) z =11 mm 2
4 (e) z =13 mm 3
1
2
2
2
0.8
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y(mm)
4 (c) z =9 mm 1 y(mm)
y(mm)
1
0 −2
−2
0 2 x(mm)
4
−4 −4
0.6 0 0.4 −2
−2
0 2 x(mm)
4
−4 −4
0.2 −2
0 2 x(mm)
4
Fig. 3. (a) Experimental intensity profiles |Ey |2 along the x-axis on the three lateral planes at zα = 9 mm (blue solid curve), 11 mm (red dashed curve), and 13 mm (black solid curve). (b) is the same as (a) except for the theoretical simulations. (c), (d), and (e) are regional intensity patterns on the three lateral planes at zα = 9, 11, and 13 mm, respectively.
3.3. Dispersive LFD properties of the ultrathin LFD THz lens Table2 Experimental dispersive LFD properties of the fabricated ultrathin LFD THz lens Frequency Focal depth Beginning focal Ending focal Real focal (THz) (mm) position (mm) position (mm) position (mm) 0.603 10.10 3.23 13.33 8.60 0.617 10.44 3.13 13.57 9.60 0.632 10.55 3.19 13.74 9.60 0.647 10.51 3.36 13.87 10.10 0.662 10.28 3.69 13.97 10.10 0.676 10.00 4.08 14.08 10.10 0.691 9.18 5.05 14.23 10.10 0.706 8.76 5.67 14.43 10.10 0.720 8.68 6.02 14.70 10.10 0.735 8.73 6.23 14.96 10.10 0.750 8.96 6.40 15.36 10.10 0.764 9.45 6.59 16.04 11.60 0.779 9.57 6.98 16.55 12.60 0.794 9.02 7.83 16.85 13.10 0.809 8.50 8.50 17.00 13.10
In addition, by scanning the frequency from 0.603 to 0.809 THz for every 0.147 THz, experimental dispersive LFD properties of the fabricated ultrathin LFD THz lens are measured, as tabulated in Table 2. The focal performances include the focal depth, the beginning focal position, the ending focal position, and the real focal position. The beginning and ending focal positions correspond to the two ends of the LFD region with 50% of the peak intensity. The real focal position is the axial coordinate with the peak intensity. It is seen from Table 2 that all #198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30036
the focal depths are longer than 8.50 mm for the considered frequencies, much larger than that of the conventional THz lens (2.41 mm). Accordingly, we conclude that the fabricated ultrathin LFD THz lens owns a good LFD property with a bandwidth of 200 GHz. It is also noted that the real focal position enlarges with the increase of the incident frequency for the diffractive phase modulated focusing lens, which is consistent with the results in [15]. 4 (b) 0.706 THz
2 0
0.5
2 0
0.5
−2
−4
5
10 15 z(mm)
20
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1.5 Normalized axial intensity
(d) Experiment 1.2
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10 15 z(mm)
0.617 THz 0.706 THz 0.794 THz
0.9 0.6 0.3 0 2
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(e) Theory Normalized intensity
−2
4 (c) 0.794 THz
1
x(mm)
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x(mm)
x(mm)
4 (a) 0.617 THz
1.2 0.9 0.6 0.3 0 5.5
8
10.5 13 z(mm)
15.5
18
Fig. 4. (a), (b) and (c) represent the experimental intensity patterns |Ey |2 of the fabricated ultrathin LFD THz lens on the xz-plane at frequencies of 0.617, 0.706, and 0.794 THz, respectively. (d) The blue, green, and red curves represent the The experimental axial intensity profiles. The dashed lines illustrate the LFD regions. (e) is the same as (d) except for theoretical simulations.
Figures 4(a), 4(b), and 4(c) display the experimental intensity patterns of the LFD THz lens on the xz-plane at frequencies of 0.617, 0.706, and 0.794 THz, respectively. It is seen from Fig. 4 that all the incident THz plane waves are focused within long axial regions. Figure 4(d) displays their experimental axial intensity distributions. The blue, green, and red curves correspond to different frequencies of 0.617, 0.706, and 0.794 THz, respectively. The dashed lines illustrate the LFD regions, whose focal depths are 10.44, 8.76, and 9.02 mm, respectively. It is also noted in Fig. 4(d) that the real focal position is increased with the increase of the incident frequency. The corresponding experimental real focal positions are 9.60, 10.10, and 13.10 mm. Figure 4(e) is the same as Fig. 4(d) except for theoretical simulations. The three LFD regions locate within [5.95, 12.67], [6.81, 14.49], and [7.67, 16.31] mm, with focal depths of 6.72, 7.68, and 8.64 mm, respectively. In Fig. 4(e), the fact that an increasing incident frequency leads to a farther focal position is verified. The theoretical real focal positions are 9.57, 10.96, and 12.33 mm for incident frequencies of 0.617, 0.706, and 0.794 THz, respectively. 4.
Summary and discussions
In conclusion, in this paper we have explored the metasurface to modulate the axial intensity distribution for designing the ultrathin LFD THz lens. The Yang-Gu amplitude-phase retrieval
#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30037
algorithm is employed to calculate the phase distributions. By the THz near-field imaging system, focusing performances of the fabricated ultrathin LFD THz lens are measured in experiments. Experimental measurements have exhibited the LFD property, which agree with the theoretical simulations. Moreover, the fabricated ultrathin LFD THz lens maintains a good LFD property with a bandwidth of 200 GHz. Through changing the V-shaped air holes into C-shaped air holes, focusing efficiency of the THz lens can be substantially increased. It is expected that this kind of LFD THz lens should have wide applications in broadband THz imaging and THz communication systems. Other kinds of ultrathin novel devices may also be realized by using the metasurfaces, including multi focus lenses, beam splitters, and so on. Acknowledgments This work was supported by the 973 Program of China (No. 2013CBA01702),the National Natural Science Foundation of China (No. 11374216, 91233202, 11204188, 61205097, 11174211, and 10904099), the National High Technology Research and Development Program of China (No. 2012AA101608-6), the Beijing Natural Science Foundation (No. KZ201110028035 and 1132011), the Program for New Century Excellent Talents in University (NCET-12-0607), and the CAEP THz Science and Technology Foundation.
#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30038
Abstract: The plasmonic resonance effect on metasurfaces generates an abrupt phase change. We employ this phase modulation mechanism to design the longitudinal field distribution of an ultrathin terahertz (THz) lens for achieving the axial long-focal-depth (LFD) property. Phase distributions of the designed lens are obtained by the Yang-Gu iterative amplitude-phase retrieval algorithm. By depositing a 100 nm gold film on a 500 µ m silicon substrate and etching arrayed V-shaped air holes through the gold film, the designed ultrathin THz lens is fabricated by the micro photolithography technology. Experimental measurements have demonstrated its LFD property, which basically agree with the theoretical simulations. In addition, the designed THz lens possesses a good LFD property with a bandwidth of 200 GHz. It is expected that the designed ultrathin LFD THz lens should have wide potential applications in broadband THz imaging and THz communication systems. © 2013 Optical Society of America OCIS codes: (080.3630) Lenses; (240.6680) Surface plasmons; (250.5403) Plasmonics.
References and links 1. N. Davidson, A. A. Friesem, and E. Hasman, “Holographic axilens: high resolution and long focal depth,” Opt. Lett. 16, 523–525 (1991). 2. J. Sochacki, S. Bar´a, Z. Jaroszewicz, and A. Kołodziejczyk, “Phase retardation of the uniform-intensity axilens,” Opt. Lett. 17, 7–9 (1992). 3. Z. Jaroszewicz, J. Sochacki, A. Kołodziejczyk, and L. R. Staronski, “Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions,” Opt. Lett. 18, 1893–1895 (1993). 4. B. Z. Dong, G. Z. Yang, B. Y. Gu, and O. K. Ersoy, “Iterative optimization approach for designing an axicon with long focal depth and high transverse resolution,” J. Opt. Soc. Am. A 13, 97–103 (1996). 5. T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497, 470–474 (2013). 6. X. Y. He, Q. J. Wang, and S. F. Yu, “Investigation of multilayer subwavelength metallic-dielectric stratified structures,” IEEE J. Quantum Electron. 48, 1554–1559 (2012). 7. X. Y. He, Q. J. Wang, and S. F. Yu, “Analysis of dielectric loaded surface plasmon waveguide structures: transfer matrix method for plasmonic devices,” J. Appl. Phys. 111, 073108 (2012).
#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30030
8. D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photon. 4, 466–470 (2010). 9. L. F. Shi, X. C. Dong, Q. L. Deng, Y. G. Lu, Y. T. Ye, and C. L. Du, “Design and characterization of an axicon structured lens,” Opt. Eng. 50, 063001 (2011). 10. J. A. Fan, C. H. Wu, K. Bao, J. M. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328, 1135–1138 (2010). 11. L. Novotny and N. V. Hulst, “Antennas for light,” Nat. Photon. 5, 83–90 (2011). 12. N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011). 13. L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10, 1936–1940 (2010). 14. F. Aieta, P. Genevet, M. A. Kats, N. F. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces,” Nano Lett. 12, 4932–4936 (2012). 15. X. J. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light: Sci. Appl. 2, e72 (2013). 16. D. Hu, X. K. Wang, S. F. Feng, J. S. Ye, W. F. Sun, Q. Kan, P. J. Klar, and Y. Zhang, “Ultrathin terahertz planar elements,” Adv. Opt. Mater. 1, 186–191 (2013). 17. M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K. Y. Kang, Y. H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470, 369–373 (2011). 18. P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100, 013101 (2012). 19. J. W. He, X. K. Wang, D. Hu, J. S. Ye, S. F. Feng, Q. Kan, and Y. Zhang, “Generation and evolution of the terahertz vortex beam,” Opt. Express 21, 20230–20239 (2013). 20. X. Z. Chen, L. L. Huang, H. M¨uhlenbernd, G. X. Li, B. F. Bai, Q. F. Tan, G. F. Jin, C. W. Qiu, S. Zhang, and T. Zentgraf, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012). 21. N. F. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarterwave plate based on plasmonic metasurfaces,” Nano Lett. 12, 6328–6333 (2012). 22. X. Q. Zhang, Z. Tian, W. S. Yue, J. Q. Gu, S. Zhang, J. G. Han, and W. L. Zhang, “Broadband terahertz wave deflection based on C-shape complex metamaterials with phase discontinuities,” Adv. Mater. 25, 4566–4571 (2013). 23. L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light: Sci. Appl. 2, e70 (2013). 24. X. B. Yin, Z. L. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013). 25. G. Z. Yang, B. Z. Dong, B. Y. Gu, J. Y. Zhuang, and O. K. Ersoy, “Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33, 209–218 (1994). 26. G. Z. Yang, B. Y. Gu, X. Tan, M. P. Chang, B. Z. Dong, and O. K. Ersoy, “Iterative optimization approach for the design of diffractive phase elements simultaneously implementing several optical functions,” J. Opt. Soc. Am. A 11, 1632–1640 (1994). 27. D. Hu, C. Q. Xie, M. Liu, and Y. Zhang, “High transmission of annular aperture arrays caused by symmetry breaking,” Phys. Rev. A 85, 045801 (2012). 28. X. K. Wang, Y. Cui, W. F. Sun, J. S. Ye, and Y. Zhang, “Terahertz polarization real-time imaging based on balanced electro-optic detection,” J. Opt. Soc. Am. A 27, 2387–2393 (2010). 29. X. K. Wang, W. F. Sun, Y. Cui, J. S. Ye, S. F. Feng, and Y. Zhang, “Complete presentation of the Gouy phase shift with the THz digital holography,” Opt. Express 21, 2337–2346 (2013).
1.
Introduction
The axial long-focal-depth (LFD) property of lenses and mirrors is critically important in optical coupling, optical imaging and optical interconnections, because it can provide a focusing range rather than a definite focal position. In the past, several researchers have designed the three-dimensional large-sized axilenses and axicons from geometrical optics and analyzed their LFD properties based on the scalar diffraction theory [1–3]. Dong et al. applied a generalized amplitude-phase retrieval algorithm to designing LFD diffractive phase elements, i.e., the YangGu algorithm [4]. In all of the above works, the phase modulation for the LFD property was accumulated by the optical path difference. Therefore, thicknesses of the optical elements are larger than or comparable to the incident wavelength. In order to reduce the thickness further,
#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30031
new phase modulation mechanism needs to be explored. In recent years, scientists have discovered that refractive index and phase modulation exists in metal-dielectric stratified structures [5–7], electromagnetic resonant cavities [8, 9], metallic nanoparticle clusters [10], and plasmonic antennas [11]. Quite recently, Yu et al. have disclosed that an abrupt phase change is encountered on an air-metal interface with subwavelength structures and formulated generalized laws of reflection and refraction [12]. Through fabricating the V-shaped thin gold antennas on a silicon substrate, experimental measurements have proved their theoretical predictions. The phase change is originated from plasmonic resonance on the nanostructured metal surface, therefore, it is named as a metasurface. An obvious merit of the optical elements based on metasurfaces is that, they (only about 100 nm) are much thinner than the conventional optical elements, especially for the terahertz (THz) region. For instance, for a 1.0 THz wave with wavelength of 300 µ m, the thickness is only 1/3000 of the wavelength. By using the metasurface, a lot of optical functions have been realized including optical focusing [13,14], dispersive focusing [15], optical imaging [16], computer generated holograms [16], ultrahigh refractive index modulation [17], optical vortexes [12, 18, 19], the dual polarity plasmonic metalens [20], quarter-wave plate for generating circularly polarized light [21], Fresnel zone plate [22], helicity dependent surface plasmon excitation [23], and the photonic spin Hall effect [24]. In previous papers, the optical focusing function on a definite transverse focal plane has been successfully realized by using the metasurfaces [15, 16]. In this paper, we extend to modulate the longitudinal field distribution with metasurfaces for obtaining the axial LFD property of a THz lens, which can broaden its applications in THz imaging and THz communication systems. The Yang-Gu amplitude-phase retrieval algorithm [4, 25, 26] is adopted to calculate the phase distributions of the designed ultrathin LFD THz lens. For generating the desired phase changes, we design a metasurface with V-shaped air holes on a thin metal film. Compared with the V-shaped gold antenna in [12], this complementary structure is superior in reducing the background noise in the transmitted region due to blocking the incident field. The designs of the structured metasurfaces are implemented by using the ‘Concerto’ commercial software, which is based on the finite-difference time-domain method [16, 27]. Then, we fabricate the designed lens by the micro photolithography and lift-off technologies. Finally, in order to characterize the performance of the fabricated LFD THz lens, we have developed a THz near-field imaging system. The experimental setup and its working principles were described in [28, 29]. This paper is organized as follows. In Section 2, firstly, the principle of the Yang-Gu iterative amplitude-phase retrieval algorithm is described in detail with formulas. Secondly, the designing parameters of the ultrathin LFD THz lens are given and phase distributions are calculated by the Yang-Gu algorithm. Thirdly, the calculated phases are quantized into eight quantization levels and the designed eight V-shaped air hole structure units are presented with detailed parameters. In Section 3, the designed LFD THz lens is fabricated and its LFD properties are measured in experiments. Numerical simulations are also carried out for comparison with physical explanations. In Section 4, a brief conclusion is drawn with some discussions. 2.
Design of the ultrathin LFD THz lens
Figure 1(a) depicts the focusing geometry. The xy plane is the incident plane, and the z-axis is the propagation direction. The input THz plane wave transmits through the ultrathin THz lens, and it is assumed to be focused in an axial range ( f0 − δ f /2, f0 + δ f /2), as shown in Fig. 1(a). On the input plane P1 (z = 0), the wave function is written by U1 = U1 (X1 ) = ρ1 (X1 ) exp[iφ1 (X1 )] ,
(1)
where the vector X1 represents the input-plane coordinates (x1 , y1 ). #198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30032
4
y
x
(b)
2 y(mm)
(a)
0 −2 −4 −4
−2
0 2 x(mm)
4
2.0π 1.75π 1.5π 1.25π 1.0π 0.75π 0.5π 0.25π
Fig. 1. (a) A focusing geometry of the ultrathin LFD THz lens. (b) Eight-level quantized phase distributions of the designed ultrathin LFD THz lens.
The phase distributions of the THz lens are obtained by the Yang-Gu amplitude-phase retrieval algorithm [4]. For evaluating the LFD function, we choose several output sampling planes. The wave function on the α th output plane P2α at z = zα is denoted by U2α = U2α (X2α , zα ) = ρ2α (X2α , zα ) exp[iφ2α (X2α , zα )] ,
(2)
where α = 1, 2, ..., N, indicating the output plane number; the vector X2α stands for the outputplane coordinates (x2α , y2α ). The output wave function is related to the input wave function by the Fresnel diffraction integral as follows Z U2α (X2α , zα ) =
G(X2α , X1 , zα )U1 (X1 )dX1 ,
(3)
where G(X2α , X1 , zα ) represents the Fresnel diffraction integral kernel given by G(X2α , X1 , zα ) =
2π i2π zα iπ (X2α − X1 )2 exp[ + ]. iλ zα λ λ zα
Equation (3) may be written in a compact form as U2α (X2α , zα ) = Gˆ α U1 (X1 ) .
(4)
For showing how accurate the real output wave function is, an error function is defined as follows ∆ = ∑(||U20α − U2α ||)2 , (5) α
represents the ideal complex amplitude on the α th output plane; || · · · || denotes the complex magnitude. Through searching for the minimum value of ∆ with respect to the arguments φ1 and φ2α , we can obtain exp[iφ1 (X1 )] = Q∗ /|Q| , (6a) where U20α
exp[iφ2α (X2α , zα )] =
Gˆ α ρ1 (X1 ) exp[iφ1 (X1 )] , |Gˆ α ρ1 (X1 ) exp[iφ1 (X1 )]|
(6b)
and Q =∑ ρ1 (X1 ) exp[−iφ1 (X1 )]Aˆ α α
−ρ2α (X2α ) exp[−iφ2α (X2α , zα )]Gˆ α ] ,
(7)
#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30033
ˆ where Aˆ α = Gˆ + α Gα . More detailed deductions of Eqs. (6a), (6b) and (7) were written in references [4, 25, 26]. Generally, Eqs. (6a) and (6b) should be solved numerically. In our design, parameters are selected as follows. The input plane has a size of 8 mm × 8 mm, which is equally quantized into 40 × 40 pixels. Therefore, the pixel size is 200 µ m × 200 µ m. The focal length f0 and focal depth δ f are preset to 9 and 10 mm, respectively. Therefore, the preset LFD region locates from 4 to 14 mm. We choose three output sampling planes situating at zα = 4, 9, and 14 mm, respectively, namely the parameter is α = 1, 2, 3 in Eqs. (2)∼(7). The incident wavelength is λ = 400 µ m. The three output planes have the same sizes of 16 mm × 16 mm, which are equally quantized into 32 × 32 pixels. By using the Yang-Gu iterative amplitude-phase retrieval algorithm, we can calculate the phase distributions φ1 (X1 ) on the input plane. After eight-level phase quantization from π /4 to 2π with a π /4 interval, they are displayed in Fig. 1(b). Table1 Structure units and their parameters for eight quantized phases Structure unit mm
Phase change
78
82
90
150
78
82
90
150
130
120
100
60
130
120
100
60
45
45
45
45
135
135
135
135
! 4
! 2
3! 4
!
5! 4
3! 2
7! 4
2!
Next, for producing the above eight quantized phase changes, we design a metasurface with V-shaped air holes on a thin metal film. A schematic diagram of the structure unit is shown in Fig. 2(a). The yellow and gray regions represent the metal film and the air hole, respectively. Each unit has a size of 200 µ m × 200 µ m. The polarization of the incident field E inc is along the x-axis. Through changing the air hole length h, width w, angles θ and β , the cross-polarized transmitted field Ey has different phase changes. The width of the air hole is fixed to w = 5 µ m. By using the commercial software ‘Concerto’ [16, 27], we have optimized eight structure units whose amplitudes are almost the same while their phases vary from π /4 to 2π for every π /4. They can serve as eight phase quantization levels in diffractive optics. Detailed parameters of the eight designed structure units are listed in Table 1. 3.
Performance analysis of the designed ultrathin LFD THz lens
3.1. Axial LFD properties of the designed ultrathin LFD THz lens After determining the above eight structure units, the ultrathin LFD THz lens is formed by putting the corresponding unit in the definite pixel on the input plane in Fig. 1(b). By using the micro photolithography technology, we have fabricated the sample. On a 500 µ m silicon substrate, a 100 nm thick gold film is deposited. Then, we etch the V-shaped air holes by the lift-off technology. Figure 2(b) displays an optical microscopy of the central part of the fabricated sample. Performances of the fabricated LFD THz lens are measured by using the THz near-field imaging system [28, 29]. The incident THz wave is x-polarized (Exinc ), and we measure the perpendicular transmitted intensity |Ey |2 in the xz plane, as shown in Fig. 2(c). It is seen from Fig. 2(c) that the focal region spans an axial range, instead of a focal point. It means that the LFD function is implemented. For demonstrating the LFD property more clearly, theoretical and experimental axial intensity distributions of the LFD THz lens are plotted in Fig. 2(d) by the blue and red curves, respectively. From Fig. 2(d), we can see that the experimental measurements #198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30034
(b)
(a)
y 400 m
4
1
(c)
x(mm)
2 0
0.5
−2 −4
5
10 15 z(mm)
20
0
Normalized axial intensity
x
1.5
(d)
1
LFD lens (theo) LFD lens (exp) Conventional lens
0.5 0 5.5
10
14.5
z(mm)
19
Fig. 2. (a) A schematic of the metasurface in a unit cell. (b) An optical microscopy of the central part of the fabricated ultrathin LFD THz lens. (c) Experimental intensity distributions in the xz plane. (d) The blue and red curves represent the theoretical and experimental intensity distributions of the LFD THz lens along the z-axis. The black curve plots the axial intensity distributions of a conventional THz lens. The dashed lines mark the three focal depths.
basically agree with the theoretical simulations. The effective focal depth is defined by the axial dimension with intensity over 50% of the maximum intensity [9], as shown by the blue and red dashed lines in Fig. 2(d). The theoretical and experimental LFD regions lie within [7.07, 15.47] mm and [6.40, 15.36] mm, respectively. Hence, the corresponding focal depths are 8.40 and 8.96 mm. Their focal-depth difference is attributed to the experimental fabrication errors. For comparison, we also calculate the axial intensity distributions of a conventional THz lens whose phase distribution is φ1c = exp[−iπ (x2 + y2 )/(λ f0 )], as shown by the black curve in Fig. 2(d). The black lines mark the LFD region, locating within [7.72, 10.13] mm. Its focal depth is only 2.41 mm. Consequently, the designed ultrathin LFD THz lens has successfully realized the LFD function as its focal depth is much longer than that of the conventional THz lens. 3.2. Transverse focusing properties of the designed ultrathin LFD THz lens For the ultrathin LFD THz lens, its lateral resolution inside the focal range is also an important characteristic. Therefore, we select three lateral planes to see the focusing behavior. Figure 3(a) plots the experimental intensity profiles along the x-axis on the three lateral planes at zα = 9 mm (blue solid curve), 11 mm (red dashed curve), and 13 mm (black solid curve), respectively. It is seen in Fig. 3(a) that most of the transmitted energy is concentrated inside the main lobe for all the three focal spots. The full widths at half maximum (FWHM) are 650, 720, and 690 µ m, respectively. Figure 3(b) is the same as Fig. 3(a) except for the theoretical simulations. It is apparent in Fig. 3(b) that the designed THz lens maintains high lateral focusing resolution in the LFD region. Numerical results reveal that the FWHM are 711, 763, and 750 µ m for zα = 9, 11, and 13 mm, respectively. Figures 3(c) – 3(e) illustrate the experimental focal spots on the above three lateral planes. On each lateral plane, the incident THz plane wave has a good focus. It is concluded that the fabricated ultrathin THz lens has successfully realized the LFD function with high lateral resolution. #198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30035
Normalized transverse intensity
Normalized transverse intensity
9 mm 11 mm 13 mm
(a) Experiment 0.8 0.6 0.4 0.2 0 −4
−2
0
2
x(mm)
1
9 mm 11 mm 13 mm
(b) Theory 0.8 0.6 0.4 0.2
4
0 −4
−2
0
x(mm)
2
4
4 (d) z =11 mm 2
4 (e) z =13 mm 3
1
2
2
2
0.8
0 −2 −4 −4
y(mm)
4 (c) z =9 mm 1 y(mm)
y(mm)
1
0 −2
−2
0 2 x(mm)
4
−4 −4
0.6 0 0.4 −2
−2
0 2 x(mm)
4
−4 −4
0.2 −2
0 2 x(mm)
4
Fig. 3. (a) Experimental intensity profiles |Ey |2 along the x-axis on the three lateral planes at zα = 9 mm (blue solid curve), 11 mm (red dashed curve), and 13 mm (black solid curve). (b) is the same as (a) except for the theoretical simulations. (c), (d), and (e) are regional intensity patterns on the three lateral planes at zα = 9, 11, and 13 mm, respectively.
3.3. Dispersive LFD properties of the ultrathin LFD THz lens Table2 Experimental dispersive LFD properties of the fabricated ultrathin LFD THz lens Frequency Focal depth Beginning focal Ending focal Real focal (THz) (mm) position (mm) position (mm) position (mm) 0.603 10.10 3.23 13.33 8.60 0.617 10.44 3.13 13.57 9.60 0.632 10.55 3.19 13.74 9.60 0.647 10.51 3.36 13.87 10.10 0.662 10.28 3.69 13.97 10.10 0.676 10.00 4.08 14.08 10.10 0.691 9.18 5.05 14.23 10.10 0.706 8.76 5.67 14.43 10.10 0.720 8.68 6.02 14.70 10.10 0.735 8.73 6.23 14.96 10.10 0.750 8.96 6.40 15.36 10.10 0.764 9.45 6.59 16.04 11.60 0.779 9.57 6.98 16.55 12.60 0.794 9.02 7.83 16.85 13.10 0.809 8.50 8.50 17.00 13.10
In addition, by scanning the frequency from 0.603 to 0.809 THz for every 0.147 THz, experimental dispersive LFD properties of the fabricated ultrathin LFD THz lens are measured, as tabulated in Table 2. The focal performances include the focal depth, the beginning focal position, the ending focal position, and the real focal position. The beginning and ending focal positions correspond to the two ends of the LFD region with 50% of the peak intensity. The real focal position is the axial coordinate with the peak intensity. It is seen from Table 2 that all #198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30036
the focal depths are longer than 8.50 mm for the considered frequencies, much larger than that of the conventional THz lens (2.41 mm). Accordingly, we conclude that the fabricated ultrathin LFD THz lens owns a good LFD property with a bandwidth of 200 GHz. It is also noted that the real focal position enlarges with the increase of the incident frequency for the diffractive phase modulated focusing lens, which is consistent with the results in [15]. 4 (b) 0.706 THz
2 0
0.5
2 0
0.5
−2
−4
5
10 15 z(mm)
20
0
1.5 Normalized axial intensity
(d) Experiment 1.2
−4
5
10 15 z(mm)
0.617 THz 0.706 THz 0.794 THz
0.9 0.6 0.3 0 2
6
10 z(mm)
14
1
2 0
0.5
−2
18
20
−4
0
5
10 15 z(mm)
1.5
20
0
0.617 THz 0.706 THz 0.794 THz
(e) Theory Normalized intensity
−2
4 (c) 0.794 THz
1
x(mm)
1
x(mm)
x(mm)
4 (a) 0.617 THz
1.2 0.9 0.6 0.3 0 5.5
8
10.5 13 z(mm)
15.5
18
Fig. 4. (a), (b) and (c) represent the experimental intensity patterns |Ey |2 of the fabricated ultrathin LFD THz lens on the xz-plane at frequencies of 0.617, 0.706, and 0.794 THz, respectively. (d) The blue, green, and red curves represent the The experimental axial intensity profiles. The dashed lines illustrate the LFD regions. (e) is the same as (d) except for theoretical simulations.
Figures 4(a), 4(b), and 4(c) display the experimental intensity patterns of the LFD THz lens on the xz-plane at frequencies of 0.617, 0.706, and 0.794 THz, respectively. It is seen from Fig. 4 that all the incident THz plane waves are focused within long axial regions. Figure 4(d) displays their experimental axial intensity distributions. The blue, green, and red curves correspond to different frequencies of 0.617, 0.706, and 0.794 THz, respectively. The dashed lines illustrate the LFD regions, whose focal depths are 10.44, 8.76, and 9.02 mm, respectively. It is also noted in Fig. 4(d) that the real focal position is increased with the increase of the incident frequency. The corresponding experimental real focal positions are 9.60, 10.10, and 13.10 mm. Figure 4(e) is the same as Fig. 4(d) except for theoretical simulations. The three LFD regions locate within [5.95, 12.67], [6.81, 14.49], and [7.67, 16.31] mm, with focal depths of 6.72, 7.68, and 8.64 mm, respectively. In Fig. 4(e), the fact that an increasing incident frequency leads to a farther focal position is verified. The theoretical real focal positions are 9.57, 10.96, and 12.33 mm for incident frequencies of 0.617, 0.706, and 0.794 THz, respectively. 4.
Summary and discussions
In conclusion, in this paper we have explored the metasurface to modulate the axial intensity distribution for designing the ultrathin LFD THz lens. The Yang-Gu amplitude-phase retrieval
#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30037
algorithm is employed to calculate the phase distributions. By the THz near-field imaging system, focusing performances of the fabricated ultrathin LFD THz lens are measured in experiments. Experimental measurements have exhibited the LFD property, which agree with the theoretical simulations. Moreover, the fabricated ultrathin LFD THz lens maintains a good LFD property with a bandwidth of 200 GHz. Through changing the V-shaped air holes into C-shaped air holes, focusing efficiency of the THz lens can be substantially increased. It is expected that this kind of LFD THz lens should have wide applications in broadband THz imaging and THz communication systems. Other kinds of ultrathin novel devices may also be realized by using the metasurfaces, including multi focus lenses, beam splitters, and so on. Acknowledgments This work was supported by the 973 Program of China (No. 2013CBA01702),the National Natural Science Foundation of China (No. 11374216, 91233202, 11204188, 61205097, 11174211, and 10904099), the National High Technology Research and Development Program of China (No. 2012AA101608-6), the Beijing Natural Science Foundation (No. KZ201110028035 and 1132011), the Program for New Century Excellent Talents in University (NCET-12-0607), and the CAEP THz Science and Technology Foundation.
#198347 - $15.00 USD Received 1 Oct 2013; revised 19 Nov 2013; accepted 21 Nov 2013; published 27 Nov 2013 (C) 2013 OSA 2 December 2013 | Vol. 21, No. 24 | DOI:10.1364/OE.21.030030 | OPTICS EXPRESS 30038
