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Investigation of Several Terahertz Electromagnetic Band Gap Structures

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Investigation of Several Terahertz Electromagnetic Band Gap Structures waves due to the multiple scattering from their periodic dielec- INVESTIGATION OF SEVERAL tric and metallic structures. One basic phenomenon is the prohi- TERAHERTZ ELECTROMAGNETIC BAND bition of electromagnetic wave propagation in certain direction, GAP STRUCTURES or total forbiddance of propagation in any direction within cer- tain frequency band, thus the name electromagnetic band gap Ziran Wu,1,2 Abram Young,2 Michael Gehm,1 and Hao Xin1,2 1 Department of Electrical and Computer Engineering, University of (EBG). A multitude of applications such as antennas, filters and Arizona, Tucson, AZ; Corresponding author: [email protected] wave guiding devices [5], microlasers [7], ultrafast switches [8], 2 Department of Physics, University of Arizona, Tucson, AZ and spontaneous emission control [9] from microwave to optical frequencies have been proposed and investigated. Received 17 August 2009 The introduction of EBG into THz region is first motivated by THz wave guiding in THz spectroscopy. Free space THz ABSTRACT: Several THz electromagnetic band gap (EBG) structures propagation devices can be bulky, expensive, and inflexible for are investigated and demonstrated. Various design, fabrication, and many applications, for example, a sample under study may not characterization methods and techniques are utilized and compared. always be accessible by a free space beam. Conventional wave- These THz EBG structures may enable future high performance EBG guides have limitations on THz beam guiding due to their high V based THz components. C 2010 Wiley Periodicals, Inc. Microwave Opt loss and high dispersion, which results in severe THz pulse Technol Lett 52: 678–686, 2010; Published online in Wiley InterScience reshaping and attenuation problems [1]. THz waveguides based (www.interscience.wiley.com). DOI 10.1002/mop.24986 on EBG structures are able to guide THz beam efficiently with advantages of having better confinement, smaller size, low dis- Key words: THz; electromagnetic band gap; rapid prototyping persion and low loss. Continuous efforts have been paid on EBG based THz components, among them, sources, detectors, filters, 1. INTRODUCTION and waveguides [2, 5, 10]. However, the realization of THz EBG Research involving Terahertz (THz) spectrum spanning from components still faces some challenging issues including efficient 100 GHz to 10 THz [1] has enjoyed dramatic growth in terms design and fabrication processes and accurate characterization of technical achievements as well as commercial implementa- methods. In this article, we present the design, fabrication, and tions in recent years [2]. This growth is application driven with characterization of several dielectric and metallic THz EBG interests from widely ranged fields such as chemical and astro- structures with 1D, 2D, and 3D periodicity. Several EM calcula- nomic spectroscopy and sensing [2], medical and biological tion techniques are applied to aid the design of these structures, imaging and analysis [3], defense and security screening, mate- with their respective advantages compared. Different structures rial research and semiconductor industry [4], next generation involve different fabrication techniques, among which the most communication networks and radars [5], etc. The great potential challenging three-dimensional fabrication has been greatly sim- of THz technology originates from the plethora of physical and plified by a THz rapid prototyping technique based on polymer chemical processes occurring in this region and the high resolu- jetting. Three commonly used THz instruments based on distinct tion and bandwidth of THz compared with microwave frequen- physical principles, including THz time domain spectroscopy cies. In addition, free space THz propagation suffers less scatter- (THz-TDS), far-infrared Fourier transform spectroscopy (FIR- ing loss than free space propagation of IR and visible light so FTS) and vector network analyzer (VNA), are utilized for sample that THz systems are able to function under IR and visible blind characterization. Features of each instrument are discussed and a conditions such as smoke, cloud, and sand storm. Many THz common 3D EBG sample is measured as a bench mark compari- applications have become closer to reality with the advancement son for all three instruments. This work demonstrates useful of new THz sources, detectors, and other components. building blocks and provides practical design, fabrication and As the first demonstration in the late 80s, electromagnetic (or characterization guidelines for THz EBG structures which may ‘‘photonic’’ for optical spectra) crystals have been one of the enable future high performance EBG based THz components. most active research areas in microwave and optical engineer- As a revision to the original APMC2008 conference proceeding ing. In analogy to semiconductor crystals [6], electromagnetic [11], this article expands the original paper into complete sections crystals can be used to manipulate the flow of electromagnetic detailing the design, fabrication, and characterization processes of Figure 1 (a) Schematic of the WPS structure [12]. (b) The first BZ of the WPS face-center-tetrahedron (fct) lattice, with apex of its irreducible BZ (characteristic k-points) marked. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com] 678 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 52, No. 3, December 2010 DOI 10.1002/mop material is usually air (n ¼ 1.0). Alternatively, the WPS can be decomposed into unit cells made of any two rods perpendicular to each other (such as any pair of rod 1 and 2 in Fig. 1) which are repeated in a face-centered-tetragonal (fct) lattice over space. Also shown in Figure 1(b) is the first BZ of the WPS fct lattice, with the first irreducible BZ and the characteristic points L, U, X, W, K, C (apex of the first irreducible BZ) marked. The eigen-energy cal- culation is done with the MIT Photonic-Bands (MPB) package based on plane wave basis expansion method [13]. The resulting WPS band diagram is shown in Figure 2. It can be seen that between the normalized frequencies (the normalized frequency x relates to the real frequency f as follows, f ¼ c0x/a,wherec0 is the speed of light and a is the lattice constant) 0.38 and 0.47, there is a blank region without any eigen-mode existing. There- fore, the WPS exhibits a complete 3D band gap in that frequency Figure 2 Calculated band diagram of the silicon WPS. The 3D com- range. Because of the large band gap width (with a gap/mid-gap plete band gap is indicated by the shaded region. [Color figure can be ratio of 21.49%) of this design, it can be very useful in the appli- viewed in the online issue, which is available at www.interscience. cations of antenna substrate [5], waveguides [14], filter [15] and wiley.com] THz thermal radiation source [10]. As verification, the WPS band diagram is also calculated using the commercial 3D finite-element (FEM) electromagnetic several THz EBG building blocks. Different testing methodologies solver Ansoft HFSS [16]. In this case, a simple-tetragonal (st) with focuses on comparing their features are described. In addition, unit cell consists of two of the previous fct unit cells is used. a new THz rapid prototyping technique is included with examples. With appropriate periodic (Master/Slave in HFSS) boundary condition settings, specific k-vectors in the reciprocal lattice 2. DESIGN space can be swept. Good agreement is obtained between the 2.1. Band Diagram Calculation HFSS and MPB eigen-mode results [10]. Although much more It is useful to start with the band diagram when designing a computationally intensive in terms of both CPU and memory THz EBG structure. For a structure with a periodic lattice, the requirements, the main benefit of calculating eigen-modes with band diagram calculation is done within its reciprocal lattice HFSS is that it can handle materials with arbitrary loss and dis- space, or, the k-vector space. Irreducible Brillouin zone (BZ), as persion, whereas in MPB, only lossless dielectrics can be the smallest unit cell reduced by all of the symmetries in the re- included. However, spurious mode may be present in HFSS cal- ciprocal space, describes the entire dispersion relation of the culation, especially for highly resonant structures. structure. Moreover, the edges of the irreducible BZ define the Another option for calculating the band diagram is to use the upper and lower boundaries of each energy band. Eigen-energy MIT electromagnetic equation propagation (MEEP) package [17] calculation is therefore carried out along the edges to map out based on the finite-difference-time-domain (FDTD) method. In this the band diagram of an EBG structure. case, resonance modes of an EBG structure are found by identify- A schematic of the well-known woodpile structure (WPS) is ing sinusoids having sufficient long life-time after the excitation illustrated in Figure 1(a) [12]. It has a unit cell of four layers of pulse is turned off. One advantage of the MEEP eigen-mode solver infinite long square rods made of high refractive index material, over MPB is that the radiation boundary is built in. Therefore, reso- hereby assigned as silicon (n ¼ 3.6). The rods are stacked in the nant modes of open structures, such as EBG structures with finite z-direction with a periodicity D. Each adjacent layers with the size or arbitrary defects, can be simulated. In addition, MEEP same rods orientation (x or y direction) are shifted relative to each allows lossy dielectric and metallic structures to be calculated. other by half of the periodicity d within one layer. Each rod has a A 2D metallic wire array EBG structure, as shown in Figure width w and a height D/4. The background low refractive index 3(a), is studied using MEEP. Metallic wires with radius r are Figure 3 (a) Top view of a 2D metallic wire array. (b) Wire array band diagram, dashed red line for TE polarization, solid blue line for TM polariza- tion.
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