2.4. Polarization Mode Dispersion for Nonuniform Material in the Longitudinal Axis Sometimes, due to its nonuniformity of a sample, the birefrin- gence axis may randomly rotate in the z axis and the birefrin- gence value may also fluctuate along the length. Under such conditions, although there is still local birefringence, we cannot define whole birefringence as given above. But, we can use polarization mode dispersion (PMD) or DGD between two prin- cipal polarization axes, this theory comes from fiber optics, as it is more accurate to describe such samples. Using the methodol- ogy of PMD measurement in the optical fiber, put the sample in the THz-TDS without rotation. From its frequency-domain am- plitude spectrum (it would not have any periodicity like Fig. 5), we can calculate the PMD in the THz band. The equation has been given from the fiber optics theory [10]: Dt ¼ N/2Df, where N is the peak and valley numbers in the scanning frequency band, and Df is the total scanning frequency band. Under such conditions, PMD will be proportional to the square root of the sample’s thickness or distance. But this problem may not be encountered in the near future because currently, the THz power is not strong enough to propagate long distance. 3. CONCLUSIONS In this article, we have proposed some simple methods to mea- sure partial polarization parameters in the THz band–like bire- fringence and PDL by using the current THz-TDS system. We have also discussed about PMD in a long and randomly distrib- uted sample. ACKNOWLEDGMENTS This work is partially supported by Singapore, A*Star, SERC grant No.: 082 141 0039 and SBIC grant No.: SBIC RP C-014/2007. REFERENCES 1. P.C. Ashworth, E. Pickwell-MacPherson, E. Provenzano, S.E. Pinder, A.D. Purushotham, M. Pepper, and V.P. Wallace, Terahertz pulsed spectroscopy of freshly excised human breast cancer, Opt Express 17 (2009), 12444–12454. 2. Q. Wu and X.-C. Zhang, Free-space electro-optic sampling of tera- hertz beam, Appl Phys Lett 67 (1995), 3523. 3. H. Dong, Y.D. Gong, V. Paulose, P. Shum, and M. Olivo, Effect of input states of polarization on the measurement of Mueller ma- trix in a system having small polarization-dependent loss or gain, Opt Express 17 (2009), 13017–13030. 4. S.N. Danilov, B. Wittmann, P. Olbrich, et al., All Electrical Detec- tion of the Stokes Parameters of IR/THz Radiation, IRMMW-THz 2009, R2A02, Pusan, Korea, 2009. 5. H. Dong, Y. Gong, V. Paulose, and M. Hong, Polarization state and Mueller matrix measurements in terahertz time domain spec- troscopy, Opt Commun 282 (2009), 3671–3675. 6. Y.D. Gong, H. Dong, M.H. Hong, O, Malini, P.S.P. Thong, and R. Bhuvaneswari, Polarization Effect in Liver Tissue in Terahertz Band, IRMMW-THz 2009, T4D02, Pusan, Korea, 2009. 7. H. Dong, Y.D. Gong, and M. Olivo, Measurement of Polarization Dependent Loss in Terahertz Time Domain Spectroscopy, IRMMW-THZ 2009, R3A04–0134, Busan, Korea, Pusan, Korea, 2009. 8. D.H. Auston, K.P. Cheung, J.A. Valdmanis, and D.A. Kleinman, Cherenkov radiation from femtosecond optical pulses in electro- optic media, Phys Rev Lett 53 (1984), 1555–1558. 9. G.X. Ning, S. Aditya, P. Shum, et al., Tunable microwave filter that uses a high-birefringent fiber and a differential-group-delay element, J Opt Soc Am A 22 (2005), 913–915. 10. C.D. Poole and D.L. Favin, Polarization mode dispersion measure- ments based on transmission spectra through a polarizer, J Light- wave Technol 12 (1994), 917–929. V C 2010 Wiley Periodicals, Inc. COPLANAR WAVEGUIDES WITH OR WITHOUT BARIUM FERRITE THIN FILMS T. Zhou, 1 M. Le Berre, 1 E. Benevent, 1 * A.-S. Dehlinger, 1 F. Calmon, 1 E. Verney, 2 S. Perrot, 3 and B. Payet-Gervy 2 1 Institut des Nanotechnologies de Lyon, Universite ´ de Lyon, INL-UMR5270, CNRS, INSA de Lyon, Villeurbanne, F-69621, France; Corresponding author: tao.zhou@insa-lyon.fr 2 Laboratoire DIOM, Universite ´ de Saint-Etienne, Universite ´ de Lyon, 23 rue Paul Michelon 42023, Saint-Etienne, France 3 Radiall, Voiron F-38500 France Received 23 November 2009 ABSTRACT: The attractive properties of coplanar waveguides with or without ferrite thin films are presented in this article. The microwave characteristics are measured from 1 to 55 GHz. Also, analytical calculations and simulations are performed. The influence of ferrite thin film with remanent magnetization in-plane or out-of-plane is studied. V C 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 2007–2010, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25393 Key words: coplanar waveguides; barium ferrite thin film; nonreciprocal effect; filters; isolators 1. INTRODUCTION CPWs have the attractive features of easy integration, simple fab- rication, size reduction without limit and radiation loss reduction; they are widely used in microwave integrated circuits (MICs) and in monolithic microwave integrated circuits (MMICs) [1–3]. The coplanar waveguides (CPWs) with ferrite material were first pro- posed by Wen [4] in 1969. The ferrite materials are indeed very important for microwave and millimeter passive component design [5–8]. Bulk ferrites are usually used for nonreciprocal passive components such as isolators, circulators, and filters. However, such bulk ferrites magnetized by a dc magnetic field are not com- patible with MMICs. Thus, components integrating hard ferrite thin film may play an important role in MMICs. Recently, there are several studies carried out on ferrite thin film for microwave and millimeter-wave applications [9–12]. In particu- lar, the properties of several ferrite thin films and CPWs were pre- sented by D. Vincent and B. Bayard et al. but the simulations and numeric analysis of S-parameters of CPWs with barium ferrite thin films were not compared to experimental results in these works. In this article, a comparison between experimental results and computational results on CPW with substrate alumina are presented. In particular, the transmission parameters are meas- ured and simulated. Finally, we study the influence of the ferrite thin film with different remanent magnetization direction on the CPW transmission parameters. 2. CPWS WITH ALUMINA SUBSTRATE A conventional CPW on alumina substrate is shown in Figure 1. The center conductor width is W, the gap width between center conductor and ground is S, the length of the CPW is L. The *E. Benevent is currently at Universita ` Mediterranea di Reggio Calabria, Reggio Calabria, Italy. DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 52, No. 9, September 2010 2007