Terahertz Fabry-Perot interferometer constructed by metallic meshes with micrometer period and high ratio of linewidth/period

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1 Terahertz Fabry-Perot interferoeter constructed by etallic eshes with icroeter period and high ratio of linewidth/period Lu Zhengang 1,, Tan Jiubin, Fan Zhigang 1 1 Postdoctoral Research Station of Optical Engineering, Harbin Institute of Technology, Harbin, 151, P. R. China Ultra-precision Optical & Electronic Instruent Engineering Center, Harbin Institute of Technology, Harbin, 151, P. R. China Tel.: + 86 [451] Fax: +86 [451] E-ail: luzhengang1978@gail.co Abstract The possibility of constructing terahertz Fabry-Perot interferoeter using etallic eshes with icroeter period and high ratio of linewidth/period is investigated, and the effectivity of traditional equivalent circuit ethod is verified by FDTD ethod. Siulation shows that the reflectance and transittance of this kind of eshes calculated by equivalent circuit ethod have considerable deviation fro those obtained by vector analysis of FDTD, so equivalent circuit ethod can be used to roughly evaluate the properties of this kind of etallic eshes. By using a etallic esh with the period of 5 icroeters and the ratio of linewidth/period of.8, a finesse larger than 11 can be achieved while the peak transittance is still larger than. for a Fabry-Perot interferoeter. It is therefore concluded that a high-quality terahertz Fabry-Perot interferoeter can be constructed by using etallic eshes with icroeter period and high ratio of linewidth/period. Keywords: Fabry-Perot interferoeter, etallic esh, terahertz, FDTD 1. Introduction In recent years, terahertz technologies attract ore and ore attention in science and industry. Terahertz filters and terahertz Fabry-Perot interferoeters (FPI) are iportant instruents and widely used in any terahertz applications [1-9]. Metallic eshes are especially preferred as reflectors of this kind of filters and Fabry-Perot interferoeters for their high reflectance, low absorbance, copact size, and no restriction on spectral range [4-7]. High reflectance of etallic eshes is needed to achieve high finesse and high resolution for this kind of filters or FPI [, 5, 9]. However, traditional etallic eshes with period fro several decades to several thousands of icroeters fail to achieve high reflectance at terahertz frequencies, because the period is not far less than the applied wavelengths. Fortunately, with the developent of icro-fabrication technologies such as laser direct writing and electron bea writing, etallic eshes with period of several icroeters and high ratio of linewidth/period can be fabricated, which akes it possible to provide high reflectance at terahertz frequencies. In this paper, the possibility of constructing terahertz FPI using etallic eshes with icroeter period and high ratio of linewidth/period is investigated, and the structural paraeters of etallic eshes are optiized. The accurate calculation of reflectance of a single etallic esh is very iportant because the reflectance is a key factor to decide the transission function and finesse of an FPI. The typical ethod for calculating the reflectance of a single etallic esh is equivalent circuit ethod [7, 1], which is successfully used for etallic eshes with period fro several decades to several thousands of icroeters. However, to the best of our knowledge, for a etallic esh with period of several icroeters and high ratio of linewidth/period, the effectivity of traditional equivalent circuit ethod has not been verified yet. Therefore in this -346

2 paper, the finite difference tie doain (FDTD) ethod is used to calculate the reflectance and transittance of this kind of etallic eshes at terahertz frequencies, and the siulated results are copared with those obtained by equivalent circuit ethod.. Theory of Fabry-Perot interferoeter For an FPI coposed of two parallel etallic eshes, its transission function can be obtained by Airy forula and expressed as follows [, 6]: T FPI 1 A 4R 1 1 sin, (1) T 1 R where T FPI is the spectral transittance of FPI, T, R, and A are the spectral transittance, reflectance and absorbance respectively for a single etallic esh, δ is the phase difference of two interference beas for a Fabry-Perot cavity with thickness d and refractive index n, and expressed as [, 6]: nd, () where is the incident wavelength in vacuu and is the phase-shift for the reflection on one esh. The finesse of an FPI can be obtained by using the reflectance of single etallic esh R and can be siplified as follows when R is larger than.6 [6]: R F, (3) 1 R 3. Optiization of structural paraeters of etallic eshes for an FPI at THz According to equation (1), T FPI of the FPI at different R and A can be shown in Fig. 1. As briefly described in [r7], it can be seen fro Fig.1 that higher R leads to high finesse but decreases the peak value of T FPI, saller A leads to high peak value of T FPI and has slightly effect on finesse. Therefore saller A and higher R are appreciated in the design of etallic esh used in FPI. For an inductive etallic esh with better conductivity, its absorbance at terahertz frequency can be calculated by using equivalent circuit ethod and expressed as [7, 1]: R g A R R, (4) a Zs where is the perittivity of free space, is the bulk dc conductivity of the etallic esh, g is the period and a is the linewidth of the etallic esh, R /Z S is the noralized loss resistance of single etallic esh.it can be seen fro Fig. that saller R /Z S can be obtained by larger ratio of linewideth/period, and R /Z S is saller than.5 and.8 at 1 THz and 1 THz respectively when the ratio of linewideth/period is larger than.8. Fig. 3 shows the peak values of T FPI and finesse of an FPI at different R. For a etallic esh with the ratio of linewideth/period of.8, A is about.5 at 1 THz according to equation (4), and the largest finesse is 35 when the peak values of T FPI are larger than.; while A is about.15 at 1 THz, the largest finesse is larger than 11 when the peak values of T FPI are still larger than.. So the perforance of an FPI coposed of two etallic eshes at low frequency is better than that at high frequency, and high reflectance is especially worth pursuing at low frequency (.1~THz) to iprove the perforance of an FPI. According to the equivalent circuit theory, the transittance T of a single etallic esh can be approxiately obtained by the following equation at the condition of g [6]: -347

3 T g a lg sin, (5) g Then cobining equation (4), the reflectance of the single etallic esh is: R R 1 T 1 Zs 1. (6) Fig. 1. The noralized transittance T FPI at different R and A. Fig.. The noralized loss resistance of single etallic esh calculated by equation (4). Fig. 3. The peak values of T FPI and finesse of a Fabry-Perot interferoeter at different R. -348

4 According to equation (6), the reflectance of single etallic esh at fixed ratio of linewidth/period and different g can be shown in Fig. 4. It can be seen that a saller period g can result in a higher reflectance at a fixed ratio of linewidth/period. It is therefore anticipated that good reflectance at terahertz frequency can be achieved with a sall period of several icroeters. However, the equivalent circuit ethod is usually suitable for the analysis of transission properties of etallic esh with period fro decades to thousands of icroeters and the not very high ratio of linewidth/period. For the etallic esh with period of several icroeters and high ratio of linewidth/period, which is appreciated for the application of Terahertz FPI, the reflective properties of this kind of etallic eshes should be analyzed and the effectivity of traditional equivalent circuit ethod should be verified. Fig. 4. The reflectance R of a single etallic esh at different periods. 4. Reflective properties of etallic esh with period of several icroeters R. Sauleau et al proposed an FDTD odel for the transission analysis of Fabry-Perot cavity at 6 GHz [11]. Here we use this odel to analyze the reflectance and transittance of a single-layer etallic esh with period of several icroeters and high ratio of linewidth/period at THz. Fig. 5 is the transittance and reflectance of a etallic esh with the period of 5 icroeters and the ratio of linewidth/period of.8, both the ideal linewidth and the effective linewidth are used in equivalent circuit ethod [6, 7]. Fig. 5. The transittance and reflectance of a single etallic esh with the period of 5 icroeters. It can be seen fro Fig. 5 that, the transittance or reflectance curves calculated by different ethods have the sae trend along the frequency axis. However, the calculated results of equivalent circuit ethod have considerable deviation fro vector analysis results of FDTD, which indicates that the traditional equivalent circuit ethod is not accurate for -349

5 analyzing the properties of eshes with period of several icroeters and high ratio of linewidth/period at THz, but it can be used to roughly evaluate the properties of this kind of eshes. Fig.5 also shows that, at terahertz frequency, this kind of eshes can achieve high reflectance and low transittance, for exaple, a reflectance of.9985 and a transittance of 1-8 at 1 THz. It eans that a finesse larger than 11 can be obtained when the peak values of T FPI are still larger than. according to Fig Conclusion In this paper, the possibility of constructing a terahertz Fabry-Perot interferoeter using etallic eshes with period of several icroeters and high ratio of linewidth/period is disscussed. Siulation result shows that using a etallic esh with the period of 5 icroeters and the ratio of linewidth/period of.8, a finesse larger than 11 can be achieved for a Fabry-Perot interferoeter when the peak values of T FPI are still larger than.. It has been shown that the reflectance and transittance of a etallic esh with the period of several icroeters and high ratio of linewidth/period calculated by traditional equivalent circuit ethod have considerable deviation fro those obtained by vector analysis of FDTD, but it can be used to roughly evaluate the properties of this kind of etallic eshes. 6. Acknowledgeents We would like to thank the National Natural Science Foundation of China (No.68788) and China Postdoctoral Science Foundation (No.8449) for their financial support. References 1. C.E. Tucker, P.A.R. Ade. Metal Mesh Filters for THz Applications. Proceeding of 3nd International Conference on International Conference on Infrared and Millieter Waves, and 15th International Conference on Terahertz Electronics. 7, pp J.W. Cleary, C.J. Fredricksen, A.V. Muravjov, et al. Scanning Fabry-Perot Filter for Terahertz Spectroscopy Based on Silicon Dielectric Mirrors. Proceeding of SPIE: Terahertz and Gigahertz Electronics and Photonics VI. 7, vol. 647: 647E. 3. G.D. Holah, O.A. Sipson. High Contrast Multi-pass Fabry-Perot Interferoeter. International Journal of Infrared and Millieter Waves. 198, 3(5), pp M.S. Durschlag, T.A. DeTeple. Far-IR Optical Properties of Freestanding and Dielectrically Backed Metal Meshes. Applied Optics. 1981, (7), pp. 145~ P. Belland, J.C. Lecullier. Scanning Fabry-Perot Interferoeter: Perforance and Optiu Use in the Far Infrared Range. Applied Optics, 198, 19(1), pp K.F. Renk, L. Genzel. Interference Filters and Fabry-Perot Interferoeters for the Far Infrared. Applied Optics. 196, 1(5), pp R. Ulrich, T.J. Bridges, M.A. Pollack. Variable Metal Mesh Coupler for Far Infrared Lasers. Applied Optics. 197, 9(11), pp G.R. Davis, I. Furniss, W.A. Towlson, et al. Design and Perforance of Cryogenic, Scanning Fabry-Perot Interferoeters for the Long-Wavelength Spectroeter on the Infrared Space Observatory. Applied Optics. 1995, 34(1), pp H. Blancher, G. Bachet, R. Coulon, et al. A Far Infrared Scanning Plane Fabry-Perot Spectro Interferoeter. International Journal of Infrared and Millieter Waves. 1985, 6(1), pp L.B. Whitbourn, R.C. Copton. Equivalent-circuit for Metal Grid Reflectors at a Dielectric Boundary. Applied Optics. 1985, 4(), pp R. Sauleau, Ph. Coquet, J.P. Daniel, et al. Analysis of Millieter-Wave Fabry-Perot Cavities Using the FDTD Technique. IEEE Microwave and Guided Wave Letters. 1999, 9(5), pp