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Characterization of T-ray binary lenses S. Wang and T. Yuan Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12180-3590
E. D. Walsby, R. J. Blaikie, and S. M. Durbin Department of Electrical and Electronic Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
D. R. S. Cumming Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8LT, Scotland, UK
J. Xu and X.-C. Zhang Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12180-3590
Received February 13, 2002 Multilevel phase-shift Fresnel diffractive zone plates fabricated on silicon wafers have been used as T-ray imaging lenses. The imaging results, including spatial and temporal distribution of T-rays measured at the focal planes in the frequency range from 0.5 to 1.5 THz, indicate that the performance of the diffractive terahertz (THz) lens is comparable with or better than that of conventional refractive THz lenses. The unique properties of the T-ray binary lens make it possible to fabricate excellent optics for narrow-band THz applications. © 2002 Optical Society of America OCIS codes: 320.7080, 320.7100, 320.7160, 320.7110, 320.7150, 190.7110.
Lenses are basic elements in an optical imaging system. In imaging and terahertz (THz) time-domain spectroscopy technologies, T-ray focusing and collimating has relied mainly on parabolic mirrors, silicon lenses, and polyethylene lenses. However, for a THz beam, it is impossible to fabricate lenses with short focal lengths and large numerical apertures by using silicon or polyethylene. For two-dimensional CCD THz imaging, it is very diff icult to obtain a high-quality THz image on a ZnTe sensor by using parabolic mirrors because of their aberration and the difficulty of alignment. However, fabricating a large-numerical-aperture T-ray binary lens with a short focal length is possible by using modern planar microfabrication technology, which makes such lenses attractive for THz applications. To our knowledge, binary lenses1 – 4 have not yet been used as THz diffraction optics for maneuvering THz wave fronts. Binary lenses are much lighter and more compact than conventional THz optics and lend themselves to unique beam forming, and so they may see increasing application in the future. Furthermore, the investigation of T-ray binary lenses can provide a bridge to the study of microwave binary lenses. To acquire as much information as possible in THz imaging and THz time-domain spectroscopy applications, researchers have used THz space and time properties to extract characteristic data from objects under study.5,6 Therefore, in this Letter, we investigate the performance of T-ray binary lenses by studying temporal and spatial THz distributions. We apply an electro-optic (EO) T-ray imaging technique7 to acquire 0146-9592/02/131183-03$15.00/0
the two-dimensional amplitude, frequency, and phase properties of T-rays after they pass through binary lenses. Figure 1 shows a plot of the phase prof ile versus the square of the radius of a binary lens with phase level L, where L 苷 2M , M 苷 1, 2, 3, . . .. The diffracted wave amplitude, u共z兲, along the z axis with the binary lens can be written as3 ∑ µ ZZ X n u共z兲 苷 An exp i2p rp 2 n s ∂ ∏ 1 1 (1) 共x2 1 y 2 兲 dx dy , 2lz
Fig. 1. Schematic illustration of a circular multiphaseshift binary lens. L is the level number of the lens, and the origin is at the lens center point. The phase shift, F共r 2 兲, is a function of r 2 苷 x2 1 y 2 . The phase shift for each step is 2p兾L, which corresponds to an etch depth of l兾关L共nTHz 2 1兲兴. For an eight-level silicon lens at 1 THz, the etching depth step is 15.5 mm. N is the total number of zones. © 2002 Optical Society of America
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OPTICS LETTERS / Vol. 27, No. 13 / July 1, 2002
Table 1. Calculated and Measured Diffraction Eff iciency (%) of T-ray Binary Lenses Phase Level L h
2
4
8
Al Zone Plate
Theory Exp.
41 11
81 75
95 90
41 38
where An 苷 sinc共n兾L兲, n is an integer, rp 2 is the Fresnel zone period with the area dimension, s is the area of the binary lens, and l is the wavelength. If n兾rp 2 1 1兾共2lzn 兲 苷 0, a maximum diffraction intensity can be obtained at focal point zn : zn 苷 2
rp 2 , 2ln
n 苷 61, 62, · · · .
Figure 3 shows the binary lenses under study and their focal plane THz intensity distribution. Comparing the THz distributions on the focal plane of the three binary lenses, we find that the focused THz intensity increases with the level number of T-ray binary lenses. As the level number of the binary lens increases, a smaller focal area and a more sharply focused THz peak are observed. These results correspond to enhanced diffraction eff iciency, which increases dramatically with the level number of binary lenses. Table 1 lists the calculated and measured diffraction efficiencies of binary lenses at 1 THz. For convenience of testing, an Al T-ray Fresnel zone plate
(2)
The diffraction eff iciency h is def ined as h 苷 jA21 j2 苷 sinc2 共1兾L兲 .
(3)
The f irst-order focus is def ined as the main focal point, with focal length f 苷 z21 苷 rp 2 兾2l. As can be seen from Eq. (3), the diffraction efficiency increases rapidly with the number of phase levels L, and the calculated diffraction efficiency, htheory , verus L is shown in Table 1. For a binary lens with L 苷 8, the diffraction efficiency reaches 95%, in contrast with an Al zone plate or a two-level lens, which has 41% eff iciency. Two-, four-level, and eight-level lenses, each with a 30-mm diameter consisting of a total of 14 zones, were fabricated on silicon wafers by means of ion etching.9 Silicon has a refractive index of 3.42 in the far-infrared region from 0.5 to 1.5 THz, and therefore the required etch depth, l兾关L共nTHz 2 1兲兴, is small, and thin binary lenses can be fabricated. The lenses are designed for a 1-THz T-ray with a focal length of 25 mm. An Al zone plate of identical dimensions was fabricated on the same silicon substrate material for comparison. Figure 2 schematically illustrates an EO imaging setup with a CCD camera used to characterize the focal properties of these lenses. The laser is a 1-kHz repetition rate amplified Ti:sapphire laser, capable of generating 100-fs pulses with energy of 700 mJ. The laser beam was split into a pump beam and a probe beam, and both beams were expanded to 2.5 cm 共1兾e兲 and collimated. Through a 3-mm-thick 具110典 ZnTe emitter, the pump beam generated THz pulses via optical rectification. The two-dimensional THz image formed on the EO crystal was encoded onto the probe beam via the EO effect,8 and a 4-mm-thick 具110典 ZnTe with an effective aperture of 2 cm was used as an EO sensor. The image carried by the probe beam was focused onto a CCD camera. In this experiment we def ined the laboratory coordinate system as follows: The axis of binary lenses was selected as the z axis, the x axis was parallel to the optical table, and the y axis was perpendicular to the optical table. By scanning the time delay between the THz and probe beam and moving the binary lenses along the z axis, we were able to obtain the spatial and temporal THz distribution for each lens.
Fig. 2. Schematic of the experimental setup of the THz CCD imaging system. The probe beam ref lected from the ZnTe sensor was focused to CCD via a pellicle and a polarizer, P2. The polarization directions of polarizers P1 and P2 are perpendicular to each other.
Fig. 3. (left) Photographs of T-ray binary lenses and (right) their THz wave intensity distribution on the x y plane at a distance of 25 mm (designed focal plane at 1 THz) between the lenses and the ZnTe sensor. The diameter of each lens is 30 mm.
July 1, 2002 / Vol. 27, No. 13 / OPTICS LETTERS
Fig. 4. Variation of THz focal length with THz frequency for an eight-level T-ray binary lens. The line is the calculated result, and the filled circles are the measured experimental data.
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25 mm at 1 THz as designed. We also observed less spherical aberration on the binary lens than with the polyethylene lens. The THz wave distributions in the z y plane for the eight-level binary lens are shown in Fig. 5. The THz wave forms a number of rings after propagating through the T-ray binary lens, and the rings converge to a focal point. The convergence becomes tighter as the level number of the lens increases. If we consider the phase change near the focal point, as the level number of the binary lens increases the phase variation also becomes more and more similar to that of a conventional THz lens. As Fig. 5 shows, a Guoy phase shift11 is clearly demonstrated for the eight-level lens. In summary, we have measured the temporal and spatial THz distribution of T-ray binary lenses. As the level number of the T-ray binary lens increases, not only does the diffraction eff iciency increase from 10% to 90%, but also the THz spatial distribution is more and more similar to that of conventional refractive THz lenses. Therefore, diffractive binary lenses can be used for THz applications. Because the binary lens has many unique properties, such as f lexibility in design, capacity for integration, and more freedom of choice of substrate, it is possible to fabricate excellent optics for narrow-band THz wave imaging and sensing applications. The potential applications of T-ray binary lenses warrant further exploration. This work was supported by the U.S. Army Research Office, the National Science Foundation, the Marsden Fund of the Royal Society of New Zealand, and the New Economy Research Fund (New Zealand). The authors are grateful to Brad Ferguson and Samuel Mickan for useful discussions. X.-C. Zhang’s e-mail address is
[email protected].
Fig. 5. Field distribution of a THz wave on the z y plane at peak amplitude.
References
was also measured, and its eff iciency was quite close to the theoretical value of 41%, which indicates the correct Fresnel zone structure for the binary lenses. In our experiment, as the level number of the binary lens increased, the measured diffraction efficiency approached the theoretical value. This result is in accordance with the rule of thumb that, as the binary level increases, the binary lens is more tolerant of fabrication errors.10 We performed a Fourier transform of the measured THz pulses to allow the frequency-dependent response of the binary lenses to be studied. For each frequency, we determined the focal length by finding the lens –detector separation that resulted in the maximum THz intensity. Figure 4 shows the focal-length increases with the THz frequency for an eight-level T-ray binary lens; the experimental result is well f itted by a theoretical curve derived from Eq. (2). The T-ray binary lens has a focal length of
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