Paper Title (Use Style: Paper Title) s28

Finite Frequency Selective Surface Modelling

R. Dickie, R. Cahill and V.F. Fusco

The Institute of Electronics, Communications and Information Technology (ECIT), Queen’s University Belfast, Northern Ireland Science Park, Queen’s Road, Queen’s Island, Belfast BT3 9DT, Northern Ireland, UK, [email protected]

Abstract— In this paper we describe the development five receiver locations within the instrument. The first of an electromagnetic modelling technique to FSS in the network separates the transmission bands investigate edge illumination effects on finite size FSS centered at 23.8 and 31.4 GHz, from the five reflection performance. The work extends the commonly used bands as shown in Fig. 1. In this paper the modeling of unit cell approach and models the FSS as a linear this FSS is extended from the unit cell method [2] to array with Gaussian beam excitation. Bistatic include edge illumination effects, using the linear array scattering from the FSS is calculated at 23.8 GHz for approach. The FSS has a wide operating band 23 – 230 a 45˚ incident beam. The results presented relate the GHz, and is illuminated by the 23 GHz horn which is the beam size, edge illumination and scattering largest in the QO network. Therefore, it is particularly performance. important to extend the FSS modelling to consider the effects of edge illumination due to the large incident beam at this frequency. Table 1 summarises the FSS Index Terms—atmospheric science instrumentation, specification requirements. frequency selective surface, FSS, microwave, radiometers

Fig. 1. MWS single aperture frequency plan INTRODUCTION Parameter Requirement Spaceborne radiometer instruments enable the retrieval of 23.66 – 23.94 GHz a wide range of geophysical parameters on a global scale. Transmission Bands 31.4 – 31.49 GHz Radiometers operate by detecting thermal emissions from Transmission Insertion Loss < 0.3 dB the Earth’s surface and atmosphere at microwave, 50.21 – 57.67 GHz millimetre, sub-millimetre and THz wavelengths. 87 - 91 GHz Detection of emissions in the microwave range enables 164 - 167 GHz the discrimination of temperature and humidity profile Reflection Bands 175.3 – 191.3 GHz components. FSS (Frequency Selective Surface) 228 – 230 GHz demultiplexing is a critical technology for radiometer instruments. The filters are used to spectrally separate the Reflection Insertion Loss < 0.3 dB thermal emissions that are collected by a single reflector Incident Angle 45° antenna. Physical diameter 250 mm FSS design is generally carried out using the unit cell infinite array approach. However this numerical Table 1. FSS specification technique does not allow investigations into the effects of edge illumination, nor predictions of the radiation pattern. FSS MODEL SETUP AND SPECTRAL RESPONSE These details are particularly important in multichannel COMPARISONS radiometers such as the MicroWave Sounder MWS [1] When Floquet’s Theorem is used in both periodicities to which is currently being developed for the European solve FSS scattering the induced currents are uniform Space Agency. Within this instrument there are four FSS across the array, when excited with a plane wave. In located in the quasi-optical (QO) network beam path. modelling software this can be implemented using a unit Generally if the edge illumination levels are below -35 cell approach as shown in Fig. 2 below. For this case the dB, beam truncation effects can be ignored. However as energy is always in the near field, and the far field part of the QO network design many trade-off’s are radiation patterns cannot be calculated. carried out on component size and placement within the available instrument volume. This can impact on the beam size requiring edge illumination effects to be quantified by additional FSS modelling. The MWS Fig. 2. Model of FSS using Floquet Theorem, unit cell approach instrument has 24 frequency channels over seven frequency bands in the range 23 GHz – 230 GHz. Four FSS are employed to demultiplex the incoming signal to The finite FSS setup proposed using a linear array [3], differs from the infinite FSS model, because the array This work was funded by UK Centre for EO Instrumentation (CEOI) size is finite in two axes. This allows far field BISTATIC SCATTERING calculations to be made in the finite planes which feature The bistatic scattering from the 250 mm long linear FSS the angle of incident vector, as shown in Fig. 3. was calculated for various Gaussian beam radii, including

44 mm, 80 mm and 112 mm. The beam radius (o) is defined as the distance from the beam axis where the energy intensity drops to ≈13.5% of its maximum intensity. Due to the 45˚ incident illumination, the beam is spread by a factor of 2 across the linear array. The Fig.3. Finite FSS linear array model setup, TE 45 incidence illumination beam intensity can be calculated at any axial radius, and taking into account the spreading of the beam, intensity

levels fall to -35dB (o = 2  44 mm), -10 dB (o = 2 In the orthogonal z-axis the array is infinite and uses 80mm), -5dB (o = 2 112mm) at the edge of the periodic boundary conditions to apply Floquets theorem. FSS. This approach keeps the volume of the model to a The corresponding electric field and Poynting vector manageable level, while allowing an investigation into power flow are shown in Fig. 6(a) – 8(a), for the three scattering effects caused by the FSS edges. The linear different sized beams. array consisted of ~200 resonant elements to give an array length of 250 mm. The model was solved using a Fig. 6(b) shows the bistatic scattering radiation commercial FEM (Finite Element Method) solver, HFSS pattern for the -35 dB illumination case. The main lobe [4]. In a previous study using unit cell FSS modelling the points at 45º and the power directed back in the direction spectral response was computed to accuracy better than of incidence is below -32 dB. The -12.7 dB signal which 0.5% using the FEM method [5]. Solving using the FD is reflected from the FSS at - 45º is due to a small (Frequency Domain) has benefits in terms of accuracy and robust convergence of the resonant structure, mismatch at this frequency. The pattern shows the main compared to time domain solvers [6], but requires more beam with side lobes below -20 dB and well suppressed memory. smaller diffraction clutter.

To solve the problem all of the workstations 80 GB of When the incident beam radius is increased to available memory was required to adaptively mesh the 80 mm, or -10 dB edge illumination, the power directed problem which used 3.4 million tetrahedral mesh cells. back to the source increases to -24 dB, as shown in Fig. Fig. 4(a) shows good monotonic convergence for the 7(b). The main beam side lobes increase to -10.3 dB, linear array with pass number. The final pass converged solution provides a well developed mesh around the compared to the below -20 dB for the -35 dB illumination critical features of the resonant structure, Fig. 4(b). case. For 112 mm illumination the main beam side lobe Poynting vector calculations were made over surfaces levels increase significantly to -8.1 dB, as shown in Fig. defined above and below the FSS, close to the radiation 8(b). Overall for the wider beams the main beam boundaries. The results depicted in Fig. 5 show excellent narrows which is attributed to higher array efficiency. agreement at 23.8 GHz, with the unit cell predictions Both show increasing levels of the pattern clutter, which using CST, and spectral measurements reported starts to obscure the main lobe at 45˚. previously [2]. Note that while the unit cell simulation yields usable transmission data along the main angle of incidence, Fig. 5, the transmission spatial energy (a) distribution is not forthcoming hence the bistatic pattern needs to be calculated using the finite array strategy. (b) Fig.6. 45 TE incidence Gaussian beam 44 mm radius, (a) electric field and power flow (b) bistatic scattering radiation pattern

(b) (b) Fig. 4. (a) Convergence of linear array with pass number, (b) Fig.7. 45 TE incidence Gaussian beam 80 mm radius, (a) electric field tetrahedral mesh produced at final pass and power flow (b) bistatic scattering radiation pattern

(a) Fig.5. Comparison of measured transmission data and CST [2, 6] unit cell predictions with the developed linear array illuminated by a Gaussian beam, adaptively solved at 23.8 GHz

(b) Fig.8. 45 TE incidence Gaussian beam 112 mm radius, (a) electric the transmitted and reflected beams, any de-pointing of field and power flow (b) bistatic scattering radiation pattern the beams can be detected.

ACKNOWLEDGEMENTS CONCLUSIONS Measurements at 23 – 30 GHz were carried out by Dr Manju Henry at STFC Rutherford Appleton Laboratory, Electromagnetic modelling of a finite FSS Oxford. structure has been demonstrated at 23.8 GHz. The method REFERENCES uses the linear array approach and provides radiation pattern scattering related to the edge illumination levels. V. Kangas, S. D’Addio, M. Betto, H. Barre and G. Mason, “MetOp second generation microwave radiometers”, Microwave Radiometry The model demonstrated that higher edge illumination and and Remote Sensing of the Environment (MicroRad), ESA, The corresponding diffraction combine to increase energy Netherlands, pp. 1-4, March 2012. levels away from the main beam direction. Containing Dickie R, Cahill R, Huggard P, Henry M, Kangas V and de Maagt P: the energy to the main beam is desirable as radiation ‘Development of a 23-230 GHz FSS for the MetOp Second Generation Microwave Sounder Instrument’, Proc 7th European Conference on outside this direction reduces instrument efficiency and Antennas and Propagation, EUCAP 2013, Gothenburg, Sweden, April may cause interference in the other channels. 2013. Ben A. Munk, “Finite Antenna Arrays and FSS, Wiley Interscience, The computer model developed allows the radiometer 2003. instrument designer to relate beam size, edge illumination High frequency structural simulator (HFSS) is a commercially available and radiation patterns. The results can be incorporated finite element method solver used for antenna design. http://www.ansys.com/Products/Simulation+Technology/Electromagnet into quasi-optical network models to give improved ics/High-Performance+Electronic+Design/ANSYS+HFSS system performance, and provides a means to investigate R. Dickie, R. Cahill, H. Gamble, V. Fusco, M. Henry, M. Oldfield, P. spillover effects and spurious lobes. Features such as the Huggard, N. Grant, Y. Munro, and P. de Maagt, “Submillimeter Wave FSS mounting brackets and absorbing materials at the Frequency Selective Surface With Polarisation Independent Spectral Responses”, Proc. IEEE Antennas and Propagation, vol. 57, pp. 1985- FSS edges can now be included in the simulations. In 1994, 2009. addition, the radiation pattern provides the directions of Computer Simulation Technology CST, www.cst.com /Products/CSTMWS