Continuous‐wave scanning terahertz near‐field microscope

A versatile cw measurement setup for terahertz near‐field reflectometry is proposed. Propagation, coupling, and focusing of wire guided modes are used to achieve a λ/33 resolution while imaging a metal corner deposited on glass. The setup is source and detector independent owing to wave coupling and decoupling with differential phase plates. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:580–582, 2011; View this article at wileyonlinelibrary.com. DOI 10.1002/mop.25754


INTRODUCTION
Near-field imaging is a key technique for high-resolution imaging. This is especially valuable in the terahertz (THz) range where the very long wavelength has a disastrous influence of the far-field imaging resolution limit. Besides the revamping of scanning near-field optical microscopy in the THz range, original systems taking benefit from Sommerfeld waves (SW) on bare metal rods [1] have been recently developed [2,3] because such waves have been demonstrated to be efficiently guided with low losses and almost no dispersion [4][5][6].
Aiming at developing cw near-field imaging with versatile THz sources, we already showed the SW excitation with a differential phase element (DPE) and the longitudinal field concentration and selectivity at the apex of a tapered needle [3]. Awad et al. [2] showed separately that such a needle might provide large subwavelength resolution up to the lm scale. In this work, we carefully analyze the propagation of SW on stainless steel rods. By combining them with a Y-splitter (as initially proposed by Mittleman [4,6]) and by connecting a metallic needle and two DPE at the three end facets of the systems (as shown in Fig. 1), we propose an original and versatile configuration that transposes cw reflection-mode scanning near-field microscope [7] to THz frequencies. Like optical setups, this system has the advantage to be coupled with external sources and detectors via linearly polarized freely propagating waves.

Propagation and Coupling Losses
The proposed THz microscope system involves the coupling and propagation of SW along metallic wires that we already showed using a set of two parabolic mirrors and a Teflon DPE [3]. The DPE induces a p-phase difference on half the input beam crosssection so that it efficiently overlaps with the radially polarized wire mode. From the known theoretical field profiles [1], we numerically estimated a coupling efficiency of $ 35% for an input Gaussian beam of waist $ 11 mm. To optimize the system design, we conducted preliminary experiments to evaluate the various source of losses. SW excitation is obtained with a microwave synthesizer followed by a 75-110 GHz sextupler electronic source from Spacek Labs Inc delivering $ 0 dBm to a rectangular horn antenna. The linearly polarized beam is focused and transformed into SW using two off-axis parabolic mirrors and a DPE. The detection is ensured by a similar quasioptical system in front of the rectangular horn antenna coupled to a Schottky diode and a microwave spectrum analyzer. With acceptable settings of the spectrum analyzer, the noise detection level of the overall detection is estimated to -80 dBm. Stainless steel wires of 0.8 mm diameter and of known bulk resistivity 1.32 Â 10 6 X À1 m À1 are placed in-between the two DPE couplers of diameter 6 cm. DPEs also serve as wire holders eventually supplemented by a Teflon disk of same diameter if long wires are considered. Emission and detection systems, including DPE and horn antennas, are cross-polarized to reduce any direct coupling. Additionally, an absorbing diaphragm with a clear aperture of 3 cm is used to cancel any direct transmission between horns while keeping a theoretical transmission in excess of 90% for the SW. This was verified by measurements without the wire. Propagation losses are thus obtained from successive cutback experiments applied to the wire length from 65 to 40 cm. Results given in Figure 2 show a linear decrease of the transmission according to propagation losses of 0.2 dB/cm. This slope is important when compared with previous measurements on gold wires [4] and is actually five times larger than the 0.04 dB/cm expected from the theory. We have no clear explanation for this discrepancy except wire surface oxidation or contamination with organic materials that might have induced excess losses in combination with the low $ 1 lm skin depth. From the À26 dBm transmission at the shorter 40 cm length and the knowledge of the À8 dBm direct horn-to-horn transmission  between source and detector, we estimate the transmission provided by each DPE coupler to -5 dB, i.e., $32%. This value is very close to the calculated one and emphasizes the efficiency of this coupling method.

Bending Losses
Bending losses are evaluated with the same setup. We use the natural flexibility of metals by increasing the angle between emission and detection to progressively bend the wires. Figure 2 reports the measured losses per unit length of two wires with different metal nature and diameters. This procedure is different from that used in Refs. 6 and 8, but it produces very similar results. Note that bending radius below 15 cm are unattainable without inducing permanent distortion of the wire, and large radius =60 cm are also impossible because they cannot be distinguished from the natural bending of the wire induced by its own weight. We see in Figure 3 that losses are nearly metal independent, as suggested in [6], because calculations show that the differences between the two experimental curves are most likely due to the different wire radius than to the metal nature.

Overall Microscope Losses
In the final microscope of Figure 1, we found necessary to introduce a right angle between source and detector to cancel the direct coupling due to sample specular reflection. It results in a 90 bend of 20 cm radius on one wire that induces a $30 dB attenuation. One must also account for $10 dB losses along the straight wires and the 10 dB losses of the two DPE couplers. Therefore, even with a perfect Y-splitter and an adiabatic focusing needle, attenuations larger than 50 dB are expected during image acquisition.

NEAR-FIELD MEASUREMENT
To complete the final setup of Figure 1, we mechanically attach a 4-cm-long metal needle to one end of the Y-splitter. Needle diameter fits that of the wire and its end is tapered over a distance of 5 mm up to a spike with a 50 lm radius of curvature. This sharp end thus operates as a near-field probe sensitive to the longitudinal electric field [2,3]. The sample is rasterscanned right beneath the needle apex using two motorized translation stages, and the probe height is adjusted before the scan with a manual translation stage of micrometer resolution. No active height control is applied during scans.
Imaging properties and resolution ability of our setup is tested by scanning one metal (Au) right angle corner deposited on glass substrate. For an estimated $10 lm flyover distance, a 1D scan obtained with a 5 lm linear step is given in Figure 4, and a 2D image obtained over a 20 Â 20 lm 2 mesh is given in Figure 5. The linear scan exhibits a piecewise evolution with a linear transition from the upper level (probe over the metal) to the lower level (probe over the glass substrate). The transition between both occurs over a distance of 90 lm (10 to 90% edge criterion). This value corresponds to k/33 and is close to the 50 lm characteristic size of the needle apex. The measured varying signal then comes from the near-field and corresponds to the detection of the longitudinal electric-field component [2,3]. This was confirmed by calculating from the theoretical field profiles [1], a 660 lm radial field extension at À3 dB for a 50 lm diameter stainless steel wire. As a consequence, any variation in the detected signal that may originate from the radial field component would have extended over more than the spans used in experiments and just produced an increase of the background. The 2D image of Figure 5 shows the ability of the setup to map planar objects with the same features. Similar spatial resolutions are roughly obtained in both dimensions although scan steps are four times larger.

CONCLUSIONS
We have built a versatile cw measurement setup for terahertz nearfield reflectometry with k/33 resolution. Both measurement  examples show a detected power of only $30 pW (i.e., À75 dBm) very close to the detection background level. As characterized, most of the losses come from the wire bending. Changing the geometry in next evolutions of the setup can eventually reduce them efficiently. Improvements are also expected both in resolution and sensitivity by using sharper needles for which high electric field enhancements are expected in the near-field [8].

INTRODUCTION
Long-term evolution (LTE) is an emerging standard for nextgeneration personal wireless communications applications. LTE supports the multiple-input-multiple-output (MIMO) communi-cation technique for higher data rates and enhanced performance. Implementation of multiple antennas in MIMO-enabled handsets for 700 MHz LTE systems is a technical challenge. The size of a handset is a fraction of the wavelength at 700 MHz and multiple antennas implemented on such a small ground plane are highly coupled, which can lead to degradation of MIMO performance. Thus, a typical MIMO antenna for handset applications should have sufficient port isolation. Various methods have been reported in the literature to enhance isolation. Additional parasitic elements between the driven antennas are used for enhancing the port isolation [1]. As the size of additional element depends on the operating frequency, significant space is required at low frequencies. This technique is therefore unsuitable for mobile handsets. Port isolation can be achieved by using a suspended inductive line, which is connected to the antenna elements [2][3][4]. As it takes significant time to find the width, the length, and the position of the inductive line through simulations, this method is also not attractive. A rat-race hybrid can be used to achieve port isolation [5]. However, this method also requires significant space, which makes it unsuitable for mobile handsets. Another method, in which port isolation is achieved by introducing a second antiphase current in a dual antenna system, as reported in [6], is very attractive. The parameters of the decoupling network can be easily calculated only from the measured coupling coefficient (S 21 ). However, sophisticated design of the decoupling network cannot be expected because reflection coefficients (S 11 , S 22 ) also have an effect on the operating frequency of the decoupling network. Also, this technique has not been evaluated in the context of MIMO antennas for handset applications.
To design an exquisite decoupling network, this letter proposes a decoupling method considering all S-parameters. Using this method, a built-in MIMO antenna for LTE-standardized handsets in 700-MHz band is eventually implemented. For performance evaluation of the designed antenna, the envelope correlation coefficient (ECC), radiation efficiency, and channel capacity have been investigated in a reverberation chamber (RC).

DECOUPLING METHOD
A port decoupling technique consisting of a shunt reactive element with susceptance B and two transmission lines (TLs) with electrical length y, and characteristic impedance Z 0 (¼ 50 X) has been reported [6] in which researchers designed the antenna at 2.45 GHz. This technique assumes perfectly matched and highly coupled antennas. In order words, only the coupling coefficient of a dual antenna system needs to be considered. Consequently, calculation of the parameter values, B and y, is simple. However, in practice, the antennas are never perfectly matched. The calculated values of B and y through this procedure become inaccurate. Thus, a more accurate calculation of the values is required for real applications. In this section, we will explain the decoupling method, which is more delicate and can work at any desired frequency within the bandwidth of the antenna.
Let the scattering matrix of a MIMO antenna be denoted as A TL is connected to each antenna's port, and then a shunt reactive element is connected to the end of the TLs. [S A ] and