- Email: [email protected]
Coupling structures for terahertz near-field microspectroscopy
Infrared Physics & Technology 49 (2006) 122–127 www.elsevier.com/locate/infrared
Coupling structures for terahertz near-field microspectroscopy G. Staats b
a,*
, L. Fernandez a, K. Holldack b, U. Schade b, D. Schondelmaier
b
a Technische Universita¨t Dresden, Mommsenstraße 13, 01069 Dresden, Germany Berliner Elektronenspeicherring-Gesellschaft fu¨r Synchrotronstrahlung m.b.H. (BESSY), Albert-Einstein-Street 15, 12489 Berlin, Germany
Available online 7 March 2006
Abstract Near-field optical elements for free space focussing of terahertz (THz) radiation were studied using analytical and numerical approaches for conical waveguides. One of the most promising candidates, a self-similar logarithmic periodical coupling structure (LPCS) embedded into a conical parabolic waveguide, was further experimentally studied with respect to spectral transmission losses using a scaled model at GHz frequencies. Since both studies confirmed the expected broadband high transmission properties of LPCS structures compared to conventional conical waveguides, a prototype structure for THz frequencies as realized by a X-ray lithography technique is presented. Published by Elsevier B.V. PACS: 41.20.Jb; 07.79.Fc; 07.85.Qe
1. Introduction THz-imaging has found applications in the range of quality control, semiconductor measurement, chemical analysis and biological investigations [1–4]. The main problem for imaging is the spatial resolution limit due to diffraction. Therefore, only features with a dimension of the wavelength are resolvable, e.g. structures in the range of 1 mm to 100 lm. With new near-field imaging techniques [5], however, it is possible to reach spatial resolutions of up to k/1000 [6]. Unfortunately, most methods [7–13] require extremely brilliant sources to compensate high losses by apertures used to confine the radiation field. Using the highly brilliant and broadband coherent synchrotron radiation (CSR) available at BESSY from the electron storage ring [15,16] a THz scanning near-field imaging technology (SNIM) employing the time structure of the synchrotron radiation was developed [17,18]. Here, conical near field probes together with a Martin–Puplett spectrometer [19] enable spectroscopic mapping of strongly absorbing, e.g. water containing objects with a spatial *
Corresponding author. E-mail address: [email protected] (G. Staats).
1350-4495/$ - see front matter Published by Elsevier B.V. doi:10.1016/j.infrared.2006.01.025
resolution well below the diffraction limit. However, the results were achieved using a strong source but at cost of up to four orders of magnitude power losses using coaxial near-field probes as proposed by Keilmann [7]. Recently, an antenna-based approach to near-field imaging and spectroscopy has been proposed built up of a pyramidal tip made from low-loss dielectric material which is partially metal plated [14]. Here, we report on an antenna approach which improves the concept of the coaxial near-field probe and is based on the combination of self similar THz antennas embedded into a conical waveguide. Unlike the pyramidal tip approach it effectively suppresses unwanted stray light and offers a large acceptance angle for the plane wave entering the probe. 2. Theoretical background A conical waveguide as shown schematically in Fig. 1a drastically attenuates the incident free-space THz radiation for radii shorter as the limiting radius at its exit. Conical waveguides can be analytically calculated using the vector potentials as given by a complete set of tesseral harmonics. In spherical coordinates the radial components of electric A
G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
123
Fig. 1. Schematic of different waveguide structures applicable for near-field microscopy: conical waveguide (a), conical waveguide with one axial wire (b) and conical waveguide with a two-wire structure (c).
and magnetic F vector potentials of incident TM- and TEmodes it can be written as XX
XX
sin mu
b 1 ðkrÞ; ð1Þ H cos mu XX XX sin mu b 1 ðkrÞ; ð2Þ ðF r Þmn ¼ C mn P mn ðcos #Þ H Fr ¼ cos mu m n m n
Ar ¼
m
n
ðAr Þmn ¼
m
C mn P mn ðcos #Þ
n
where P mn = associated Legendre functions of the first kind, b 1 ðkrÞ = spherical Hankel r, #, u = spherical coordinates, H function of the first kind, and Cmn = developing coefficients of an incident wave. An incident plane wave can be developed in series of orthonormal eigenmodes having a normal propagation inward the cone down to the limiting radius. In this case most of the power is reflected at exit radii smaller than the wavelength. Hence, the required high spatial resolution
of a SNIM forces its operation in a cut-off regime. One option to avoid this drawback is the use of the TEM-mode, which has no cut-off. Such probes were firstly proposed by Keilmann [7] employing a single bent wire in the centre of a conical waveguide (see Fig. 1b) in coaxial TEM-mode and a bended part in a non-cut-off region. However, here the other modes are lost and a coaxial field distribution in the exit aperture of a conical waveguide is not the optimum for high resolution of a SNIM. A better solution might be the use of a two-wire structure in the centre of a conical waveguide (see Fig. 1c) also in TEM-mode feeding by a logarithmic periodic coupling structure (LPCS). Such logarithmic periodic structures are known from antenna theory. The LPCS is derived from a logarithmic periodic dipol antenna (LPDA) shown in Fig. 2, which was developed first by IsBell [20,21] and
Fig. 2. Self-similar LPCS embedded into a conical waveguide as derived from a LPDA structure.
124
G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
realized later by Carrel [22]. The LPCS is a self-similar structure (also embedded in the cone) without any frequency limit, because it has a transmission characteristics of constant input impedance over the entire frequency range. In a LPCS successive individual dipole antennas are connected alternately to a balanced transmission line called ‘‘feeder’’ [23]. The closely spaced elements are oppositely connected so that radiation flow into the direction of the shorter elements is created and the radiation perpendicular to the feeder tends to cancel. Radiation energy, at a given frequency, travels along the LPCS until it reaches a section of the structure where the electrical lengths of the elements and phase relationships are such as to produce strong coupling. As
the frequency varies, the position of the resonant element is moved smoothly from one element to the next. The upper and lower frequency limit is then determined by lengths of the shortest and longest elements or in other words, these lengths have to be chosen to satisfy the bandwidth requirement. The longest half-element must be roughly 1/4 wavelength at the lowest frequency of the bandwidth, while the shortest half-element must be about 1/4 wavelength of the highest frequency of the desired operation bandwidth [24]. The parameters s, a and r describe the geometry of the LPCS according to Fig. 2. The relationships between a, s, the element dipole lengths ln, and distances Rn to the apex are determined by the geometry and can be written as
Fig. 3. Numerically calculated distribution of the E-field vector at the tip of LPCS mounted into a metallic cone at 100 GHz as excited by an incident plane wave.
Fig. 4. Numerically calculated distribution of the E-field vector in the bulk of the cone for the LPCS at 100 GHz as excited by an incident plane wave.
G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
l1 ln ¼ ¼ 2 tan a; R1 Rn
ð3Þ
where Rn = distance from apex to the nth element, ln = total length of the nth element and a = half-angle subtended by the ends of radiating elements. In addition, the ratios of ln+1/ln, Rn+1/Rn and sn+1/sn are equal to s, which is usually a number less than 1.0. That is lnþ1 Rnþ1 ð1 sÞ Rnþ1 snþ1 ¼ ¼ ¼ ¼ s; Rn ð1 sÞ ln Rn sn
ð4Þ
where sn is the distance between the element n and the element (n + 1). It is often convenient to think of the element spacing sn in terms of wavelength. The free-space wavelength k of a signal that resonates the first largest element, l1, is approximately four times l1, thus
125
the feeder. On the contrary, it is expected that for the higher values of s the LPCS will be less dependent on frequency promising the possibility of an almost frequency independent design. Using such structures in a conical waveguide leads to a self-similar frequency independent three-wire TEM-waveguide with even and odd-modes. With correct design, the even-mode is suppressed and only the odd-mode is propagating. This leads to a high field concentration on the tip of the cone between the two wires and also to a high spatial resolution of the corresponding SNIM. In contrast to a conventional LPDA design and for an even frequency response of the LPCS it seems to better use about 1/3 longer structures with more elements than as for a LPDA. Fortunately, the incident plane waves may couple (without cone reflections) into the LPCS, before and after being reflected by the exit aperture.
k ’ 4l1 ; k2 ’ 42 ; k3 ’ 4l3 ; . . . ; kn ’ 4ln ; knþ1 ’ 4lnþ1 ; . . .
ð5Þ
For any value of n, the ratio sn/4ln is a useful quantity. It is called spacing factor r and can be expressed in terms of s and a as follows: r¼
s1 sn Rn ð1 sÞ 1s . ¼ ¼ ¼ 4l1 4ln 4ðRn tan aÞ 4 tan a
ð6Þ
The performance of an LPCS is a function of the parameters s and a. In particular, the input impedance depends on s and a. For example, if the value of s is 0.95, then the unloaded feeder impedance is 104 X, and if a varies from 10° to 30°, the input impedance falls between the limits of 76 and 53 X. Here, the unloaded feeder impedance refers to the characteristic impedance of the central transmission line without all the elements. As the value of s is decreased, the input impedance will increase up to the value of the unloaded feeder impedance. The reason is that fewer elements per feeder unit length are connected in parallel to
Fig. 5. Measured E-field magnitude at the tip of the cone at 3 GHz without any coupling structure. Surface currents flow around the hole at the tip.
Fig. 6. Measured E-field magnitude at the tip of the cone at 3 GHz with a bent wire as coupling structure in the hole of the cone. A medium spatial resolution appears due to a coaxial field distribution.
Fig. 7. Measured E-field magnitude at the tip of the cone with the LPCS at 3 GHz. Higher spatial resolution and also higher transmission is achieved compared to the previously shown cone geometry.
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G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
transmission in dB
1x109 -30
2x109
3x109
4x109
5x109
6x109
7x109
8x109 -30
-35
-35
-40
-40
-45
-45
-50
-50
-55
-55
-60
-60
-65
-65
-70
-70 without structure bended wire coupling structure
-75 -80 1x109
2x109
3x109
4x109
5x109
6x109
7x109
simulated incident plane wave. The highest field concentration is reached between the two wires of the coupling structure. Fig. 4 shows the E-field in the bulk of the cone for the same structure. Here, a high field concentration in the narrow part of the cone is obtained. Computations using moment methods [FEKO from EM Software & Systems] yield similar results. In general, the numerical simulations indicate much higher field strength at the tip of the cone compared to empty cones and coaxial cones. 4. Model measurements
-75 -80
8x109
frequency in Hz
Fig. 8. Measured frequency response of the three investigated configurations according to Figs. 5–7.
3. Numerical computations For the design of such structures some numerical calculations have been performed using the code HFSS from Agilent Technologies. The graph in Fig. 3 shows the E-field vector at the tip of the cone within the LPCS at 100 GHz. It is excited by a
Numerical calculations for the LPCS structure have been validated using a 100:1 scaled model for a conical THz-waveguide. Employing this model it was possible to cover the frequency range from 1 to 8.5 GHz equivalent to 0.1 to 0.85 THz. The effect of three different geometrical configurations are investigated by observing the electric field magnitudes at the tip of the cone. The results are shown in Fig. 5 for a conical geometry. Here, it is demonstrated that surface currents are flowing around the hole at the tip and that high insertion losses occur. Fig. 6 shows the results for a conical waveguide in a configuration according to Keilmann [7]. This geometry has a better transmission than the conventional cone and a coaxial field
Fig. 9. Prototype of a LPCS produced using the LIGA-technology at BESSY.
G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
distribution is observed. Finally, in Fig. 7, the results for the conical waveguide with the LPCS are shown. This geometry yields a better transmission in comparison to the other structures. The field confinement at the tip would allow a much higher spatial resolution. For all three configurations the frequency response was investigated and plotted in Fig. 8. The LPCS shows the highest transmission (20 dB better than the transmission for the wire cone) and an almost flat-top frequency response. 5. Technical realization Encouraged by the positive results of the numerical calculations and the measurements on the scaled model a LPCS structure for the THz range has been designed and produced using micromechanics based on the LIGA-technology (German: ‘‘Lithographie, Galvanik und Abformung’’). A microscope image of the tip of a prototype antenna structure for the range between 0.1 and 1 THz is depicted in Fig. 9. The two metallization layers for the antenna are 10 lm apart of each other (not visible in the photograph) and are buried in a 100 lm thick epoxy film which acts as a mechanical support for the antenna. The complete antenna structure is mounted into a metallic cone (Fig. 10) and was exposed by the BESSY THz source. First measurements indicate the expected high field intensity at the tip of the cone which can even destroy the tip in some cases (1 mW of input power results in up to100 kV/m at the tip). 6. Conclusions and outlook SNIM and similar applications might benefit from the large transmission and the spectral properties of LPCS structures as waveguides for THz radiation. This has been shown by numerical studies together with measurements on scaled models. The concept proposed opens new perspectives to analyze samples spectroscopically with near-field probes in the THz region with sub-wavelength spatial resolution. The LIGA technique is an appropriate way for the technical realization of such probes.
Fig. 10. Schematic of the cone together with the LPCS. Note that the carrier of the LPCS in not shown for clarity.
127
Acknowledgements We are indebted to the support of D. Ponwitz, I. Rudolph (BESSY), and K. Wolf (TU Dresden). References [1] B. Ferguson, X.-C. Zhang, Materials for terahertz science and technology, Nature Materials 1 (2002) 26–33, and references therein. [2] D.M. Mittleman, R.H. Jacobsen, M.C. Nuss, T-Ray imaging, IEEE Journal of Selected Topics on Quantum Electronics 2 (1996) 679–692. [3] D.M. Mittleman, M. Gupta, R. Neelami, R.B. Baraniuk, J.V. Rudd, M. Koch, Recent advances in terahertz imaging, Applied Physics B68 (1999) 1085–1095. [4] T. Lo¨ffler, T. Bauer, K.J. Siebert, H.G. Roskos, A. Fitzgerald, S. Czasch, Terahertz dark-field imaging of biomedical tissue, Optics Express 12 (2001) 616–621. [5] B. Knoll, F. Keilmann, Near-field probing of vibrational absorption for chemical microscopy, Nature 399 (1999) 134–137. [6] H.-T. Chen, R. Kersting, G.C. Cho, Terahertz imaging with nanometer resolution, Applied Physics Letters 83 (2003) 3009–3011. [7] F. Keilmann, Scanning tip for optical radiation, U.S. Patent No. 4,994,818, filed 1989, 1991. [8] F. Keilmann, Far-infrared microscopy, Infrared Physics Technology 36 (1995) 217. [9] B. Knoll, F. Keilmann, Electromagnetic fields in the cutoff regime of tapered metallic waveguides, Optics Communications 162 (1999) 177– 181. [10] S. Hunsche, M. Koch, I. Brener, M.C. Nuss, THz near-field imaging, Optics Communications 150 (1998) 22–26. [11] Q. Chen, Z. Jiang, G.X. Xu, X.C. Zhang, Near-field terahertz imaging with a dynamic aperture, Optics Letters 25 (2000) 1122–1124. [12] O. Mitrofanow, M. Lee, J.W.P. Hsu, I. Brener, R. Harel, J.F. Federici, J.D. Wynn, L.N. Pfeiffer, K.W. West, IEEE Journal of Selected Topics on Quantum Electronics 7 (2001) 600–607. [13] B.T. Rosner, D.W. van der Weide, High-frequency near-field microscopy, Review of Scientific Instruments 73 (2002) 2505–2525, and references cited therein. [14] N. Klein, P. Lahl, U. Poppe, F. Kadlec, P. Kuzel, A metal-dielectric antenna for terahertz near-field imaging, Journal of Applied Physics 98 (2005) 014910. [15] M. Abo-Bakr, J. Feikes, K. Holldack, G. Wu¨stefeld, H.-W. Hu¨bers, Steady-state far-infrared coherent synchrotron radiation detected at BESSY II, Physical Review Letters 88 (2002) 254801. [16] M. Abo-Bakr, J. Feikes, K. Holldack, P. Kuske, W.B. Peatman, U. Schade, G. Wu¨stefeld, H.-W. Hu¨bers, Brilliant, coherent far-infrared (THz) synchrotron radiation, Physical Review Letters 90 (2002) 094801. [17] U. Schade, A. Ro¨seler, E.H. Korte, F. Bartl, K.P. Hofmann, T. Noll, W.B. Peatman, New infrared spectroscopic beamline at BESSY II, Review of Scientific Instruments 73 (2002) 1568–1570. [18] U. Schade, K. Holldack, P. Kuste, G. Wu¨stefeld, H.-W. Hu¨bers, THz near-field imaging employing synchrotron radiation, Applied Physics Letters 84 (2004) 1422–1424. [19] D.H. Martin, E. Puplett, Polarised interferometric spectroscopy for the millimeter and submillimetre spectrum, Infrared Physics 10 (1970) 105–109. [20] R.H. DuHamel, D.E. Isbell, Broadband logarithmically periodic antenna structures, IRE Convention Record (Part 1) (1957) 119–128. [21] D.E. IsBell, Log periodic dipole arrays, IRE Transactions on Antennas and Propagation 8 (May) (1960) 260–267. [22] R.L. Carrel, Analysis and design of the log-periodic dipole antenna, Ph.D.-Dissertation, Elec. Eng. Dept., University of Illinois, 1961, University Microfilms, Inc., Ann Arbor, MI. [23] R.L. Carrel, The design of log-periodic dipole antennas, IRE Convention Record (Part 1) (1961) 61–75. [24] C. Balanis, Antenna Theory, Analysis and Design, second ed., John Wiley and Sons, New York, 1997, pp. 553–566.
Coupling structures for terahertz near-field microspectroscopy G. Staats b
a,*
, L. Fernandez a, K. Holldack b, U. Schade b, D. Schondelmaier
b
a Technische Universita¨t Dresden, Mommsenstraße 13, 01069 Dresden, Germany Berliner Elektronenspeicherring-Gesellschaft fu¨r Synchrotronstrahlung m.b.H. (BESSY), Albert-Einstein-Street 15, 12489 Berlin, Germany
Available online 7 March 2006
Abstract Near-field optical elements for free space focussing of terahertz (THz) radiation were studied using analytical and numerical approaches for conical waveguides. One of the most promising candidates, a self-similar logarithmic periodical coupling structure (LPCS) embedded into a conical parabolic waveguide, was further experimentally studied with respect to spectral transmission losses using a scaled model at GHz frequencies. Since both studies confirmed the expected broadband high transmission properties of LPCS structures compared to conventional conical waveguides, a prototype structure for THz frequencies as realized by a X-ray lithography technique is presented. Published by Elsevier B.V. PACS: 41.20.Jb; 07.79.Fc; 07.85.Qe
1. Introduction THz-imaging has found applications in the range of quality control, semiconductor measurement, chemical analysis and biological investigations [1–4]. The main problem for imaging is the spatial resolution limit due to diffraction. Therefore, only features with a dimension of the wavelength are resolvable, e.g. structures in the range of 1 mm to 100 lm. With new near-field imaging techniques [5], however, it is possible to reach spatial resolutions of up to k/1000 [6]. Unfortunately, most methods [7–13] require extremely brilliant sources to compensate high losses by apertures used to confine the radiation field. Using the highly brilliant and broadband coherent synchrotron radiation (CSR) available at BESSY from the electron storage ring [15,16] a THz scanning near-field imaging technology (SNIM) employing the time structure of the synchrotron radiation was developed [17,18]. Here, conical near field probes together with a Martin–Puplett spectrometer [19] enable spectroscopic mapping of strongly absorbing, e.g. water containing objects with a spatial *
Corresponding author. E-mail address: [email protected] (G. Staats).
1350-4495/$ - see front matter Published by Elsevier B.V. doi:10.1016/j.infrared.2006.01.025
resolution well below the diffraction limit. However, the results were achieved using a strong source but at cost of up to four orders of magnitude power losses using coaxial near-field probes as proposed by Keilmann [7]. Recently, an antenna-based approach to near-field imaging and spectroscopy has been proposed built up of a pyramidal tip made from low-loss dielectric material which is partially metal plated [14]. Here, we report on an antenna approach which improves the concept of the coaxial near-field probe and is based on the combination of self similar THz antennas embedded into a conical waveguide. Unlike the pyramidal tip approach it effectively suppresses unwanted stray light and offers a large acceptance angle for the plane wave entering the probe. 2. Theoretical background A conical waveguide as shown schematically in Fig. 1a drastically attenuates the incident free-space THz radiation for radii shorter as the limiting radius at its exit. Conical waveguides can be analytically calculated using the vector potentials as given by a complete set of tesseral harmonics. In spherical coordinates the radial components of electric A
G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
123
Fig. 1. Schematic of different waveguide structures applicable for near-field microscopy: conical waveguide (a), conical waveguide with one axial wire (b) and conical waveguide with a two-wire structure (c).
and magnetic F vector potentials of incident TM- and TEmodes it can be written as XX
XX
sin mu
b 1 ðkrÞ; ð1Þ H cos mu XX XX sin mu b 1 ðkrÞ; ð2Þ ðF r Þmn ¼ C mn P mn ðcos #Þ H Fr ¼ cos mu m n m n
Ar ¼
m
n
ðAr Þmn ¼
m
C mn P mn ðcos #Þ
n
where P mn = associated Legendre functions of the first kind, b 1 ðkrÞ = spherical Hankel r, #, u = spherical coordinates, H function of the first kind, and Cmn = developing coefficients of an incident wave. An incident plane wave can be developed in series of orthonormal eigenmodes having a normal propagation inward the cone down to the limiting radius. In this case most of the power is reflected at exit radii smaller than the wavelength. Hence, the required high spatial resolution
of a SNIM forces its operation in a cut-off regime. One option to avoid this drawback is the use of the TEM-mode, which has no cut-off. Such probes were firstly proposed by Keilmann [7] employing a single bent wire in the centre of a conical waveguide (see Fig. 1b) in coaxial TEM-mode and a bended part in a non-cut-off region. However, here the other modes are lost and a coaxial field distribution in the exit aperture of a conical waveguide is not the optimum for high resolution of a SNIM. A better solution might be the use of a two-wire structure in the centre of a conical waveguide (see Fig. 1c) also in TEM-mode feeding by a logarithmic periodic coupling structure (LPCS). Such logarithmic periodic structures are known from antenna theory. The LPCS is derived from a logarithmic periodic dipol antenna (LPDA) shown in Fig. 2, which was developed first by IsBell [20,21] and
Fig. 2. Self-similar LPCS embedded into a conical waveguide as derived from a LPDA structure.
124
G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
realized later by Carrel [22]. The LPCS is a self-similar structure (also embedded in the cone) without any frequency limit, because it has a transmission characteristics of constant input impedance over the entire frequency range. In a LPCS successive individual dipole antennas are connected alternately to a balanced transmission line called ‘‘feeder’’ [23]. The closely spaced elements are oppositely connected so that radiation flow into the direction of the shorter elements is created and the radiation perpendicular to the feeder tends to cancel. Radiation energy, at a given frequency, travels along the LPCS until it reaches a section of the structure where the electrical lengths of the elements and phase relationships are such as to produce strong coupling. As
the frequency varies, the position of the resonant element is moved smoothly from one element to the next. The upper and lower frequency limit is then determined by lengths of the shortest and longest elements or in other words, these lengths have to be chosen to satisfy the bandwidth requirement. The longest half-element must be roughly 1/4 wavelength at the lowest frequency of the bandwidth, while the shortest half-element must be about 1/4 wavelength of the highest frequency of the desired operation bandwidth [24]. The parameters s, a and r describe the geometry of the LPCS according to Fig. 2. The relationships between a, s, the element dipole lengths ln, and distances Rn to the apex are determined by the geometry and can be written as
Fig. 3. Numerically calculated distribution of the E-field vector at the tip of LPCS mounted into a metallic cone at 100 GHz as excited by an incident plane wave.
Fig. 4. Numerically calculated distribution of the E-field vector in the bulk of the cone for the LPCS at 100 GHz as excited by an incident plane wave.
G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
l1 ln ¼ ¼ 2 tan a; R1 Rn
ð3Þ
where Rn = distance from apex to the nth element, ln = total length of the nth element and a = half-angle subtended by the ends of radiating elements. In addition, the ratios of ln+1/ln, Rn+1/Rn and sn+1/sn are equal to s, which is usually a number less than 1.0. That is lnþ1 Rnþ1 ð1 sÞ Rnþ1 snþ1 ¼ ¼ ¼ ¼ s; Rn ð1 sÞ ln Rn sn
ð4Þ
where sn is the distance between the element n and the element (n + 1). It is often convenient to think of the element spacing sn in terms of wavelength. The free-space wavelength k of a signal that resonates the first largest element, l1, is approximately four times l1, thus
125
the feeder. On the contrary, it is expected that for the higher values of s the LPCS will be less dependent on frequency promising the possibility of an almost frequency independent design. Using such structures in a conical waveguide leads to a self-similar frequency independent three-wire TEM-waveguide with even and odd-modes. With correct design, the even-mode is suppressed and only the odd-mode is propagating. This leads to a high field concentration on the tip of the cone between the two wires and also to a high spatial resolution of the corresponding SNIM. In contrast to a conventional LPDA design and for an even frequency response of the LPCS it seems to better use about 1/3 longer structures with more elements than as for a LPDA. Fortunately, the incident plane waves may couple (without cone reflections) into the LPCS, before and after being reflected by the exit aperture.
k ’ 4l1 ; k2 ’ 42 ; k3 ’ 4l3 ; . . . ; kn ’ 4ln ; knþ1 ’ 4lnþ1 ; . . .
ð5Þ
For any value of n, the ratio sn/4ln is a useful quantity. It is called spacing factor r and can be expressed in terms of s and a as follows: r¼
s1 sn Rn ð1 sÞ 1s . ¼ ¼ ¼ 4l1 4ln 4ðRn tan aÞ 4 tan a
ð6Þ
The performance of an LPCS is a function of the parameters s and a. In particular, the input impedance depends on s and a. For example, if the value of s is 0.95, then the unloaded feeder impedance is 104 X, and if a varies from 10° to 30°, the input impedance falls between the limits of 76 and 53 X. Here, the unloaded feeder impedance refers to the characteristic impedance of the central transmission line without all the elements. As the value of s is decreased, the input impedance will increase up to the value of the unloaded feeder impedance. The reason is that fewer elements per feeder unit length are connected in parallel to
Fig. 5. Measured E-field magnitude at the tip of the cone at 3 GHz without any coupling structure. Surface currents flow around the hole at the tip.
Fig. 6. Measured E-field magnitude at the tip of the cone at 3 GHz with a bent wire as coupling structure in the hole of the cone. A medium spatial resolution appears due to a coaxial field distribution.
Fig. 7. Measured E-field magnitude at the tip of the cone with the LPCS at 3 GHz. Higher spatial resolution and also higher transmission is achieved compared to the previously shown cone geometry.
126
G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
transmission in dB
1x109 -30
2x109
3x109
4x109
5x109
6x109
7x109
8x109 -30
-35
-35
-40
-40
-45
-45
-50
-50
-55
-55
-60
-60
-65
-65
-70
-70 without structure bended wire coupling structure
-75 -80 1x109
2x109
3x109
4x109
5x109
6x109
7x109
simulated incident plane wave. The highest field concentration is reached between the two wires of the coupling structure. Fig. 4 shows the E-field in the bulk of the cone for the same structure. Here, a high field concentration in the narrow part of the cone is obtained. Computations using moment methods [FEKO from EM Software & Systems] yield similar results. In general, the numerical simulations indicate much higher field strength at the tip of the cone compared to empty cones and coaxial cones. 4. Model measurements
-75 -80
8x109
frequency in Hz
Fig. 8. Measured frequency response of the three investigated configurations according to Figs. 5–7.
3. Numerical computations For the design of such structures some numerical calculations have been performed using the code HFSS from Agilent Technologies. The graph in Fig. 3 shows the E-field vector at the tip of the cone within the LPCS at 100 GHz. It is excited by a
Numerical calculations for the LPCS structure have been validated using a 100:1 scaled model for a conical THz-waveguide. Employing this model it was possible to cover the frequency range from 1 to 8.5 GHz equivalent to 0.1 to 0.85 THz. The effect of three different geometrical configurations are investigated by observing the electric field magnitudes at the tip of the cone. The results are shown in Fig. 5 for a conical geometry. Here, it is demonstrated that surface currents are flowing around the hole at the tip and that high insertion losses occur. Fig. 6 shows the results for a conical waveguide in a configuration according to Keilmann [7]. This geometry has a better transmission than the conventional cone and a coaxial field
Fig. 9. Prototype of a LPCS produced using the LIGA-technology at BESSY.
G. Staats et al. / Infrared Physics & Technology 49 (2006) 122–127
distribution is observed. Finally, in Fig. 7, the results for the conical waveguide with the LPCS are shown. This geometry yields a better transmission in comparison to the other structures. The field confinement at the tip would allow a much higher spatial resolution. For all three configurations the frequency response was investigated and plotted in Fig. 8. The LPCS shows the highest transmission (20 dB better than the transmission for the wire cone) and an almost flat-top frequency response. 5. Technical realization Encouraged by the positive results of the numerical calculations and the measurements on the scaled model a LPCS structure for the THz range has been designed and produced using micromechanics based on the LIGA-technology (German: ‘‘Lithographie, Galvanik und Abformung’’). A microscope image of the tip of a prototype antenna structure for the range between 0.1 and 1 THz is depicted in Fig. 9. The two metallization layers for the antenna are 10 lm apart of each other (not visible in the photograph) and are buried in a 100 lm thick epoxy film which acts as a mechanical support for the antenna. The complete antenna structure is mounted into a metallic cone (Fig. 10) and was exposed by the BESSY THz source. First measurements indicate the expected high field intensity at the tip of the cone which can even destroy the tip in some cases (1 mW of input power results in up to100 kV/m at the tip). 6. Conclusions and outlook SNIM and similar applications might benefit from the large transmission and the spectral properties of LPCS structures as waveguides for THz radiation. This has been shown by numerical studies together with measurements on scaled models. The concept proposed opens new perspectives to analyze samples spectroscopically with near-field probes in the THz region with sub-wavelength spatial resolution. The LIGA technique is an appropriate way for the technical realization of such probes.
Fig. 10. Schematic of the cone together with the LPCS. Note that the carrier of the LPCS in not shown for clarity.
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