Measurement of beat length in polarization-maintaining fibers with external forces method Hongxia Zhang ⇑ , Guoqiang Wen, Yaguang Ren, Dagong Jia, Tiegen Liu, Yimo Zhang College of Precision Instrument & Opto-electronics Engineering, Tianjin University, Tianjin 300072, PR China Key Laboratory of Opto-electronics Information Technology, Tianjin University, Ministry of Education, Tianjin 300072, PR China article info Article history: Received 1 November 2011 Revised 13 January 2012 Available online 11 March 2012 Keywords: Polarization-maintaining fibers (PMFs) White light interferometry Beat length Polarization coupling abstract Beat length is a key parameter for the polarization maintaining fibers (PMFs). Based on a white light scan- ning Michelson interferometer, the measurement of the phase beat length in PMFs employing the exter- nal force is presented. When the linearly polarized light propagates along the principal axis of the PMFs, the polarization coupling occurs at the force position of PMFs. The short and long length PMFs are mea- sured respectively, furthermore, the uniformity of beat length measurement is tested. In the end, the advantages and the disadvantages of the method are discussed in detail. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction Among fundamental parameters characterizing the polariza- tion-maintaining fibers (PMFs), the beat-length L b is a critical one [1], because it reflects the quality of a fiber maintains polarization. Fibers with short beat lengths preserve polarization more strongly than those with long beat lengths [2]. Lots of methods have been proposed to measure the beat length L b [3]. In the existing meth- ods, the cutback method is simple, but destructive. The electro-op- tic method is non-contact measurement, whereas it requires high electrical fields and gives only small signals [4]. Photo-elastic mod- ulator method gives very large signals, also provides the desired azimuthal information, but it becomes difficult when the beat length L b is less than 10 mm [4]. The Rayleigh scattering method is still applicable when the L b is less than 10 mm, whereas it cannot be applied at invisible wavelengths or low loss fibers [3,5]. The optical frequency domain reflectometer methods are well suited for measurements up to distances of 1.5 km, but it is difficult when the fiber loss is small [6–9]. Wavelength sweeping method shows high measurement precision, but it needs broadband amplified spontaneous emission (ASE) light source, so group velocity disper- sion is serious in the fiber [9]. In this paper, a method for measuring the phase beat length of PMFs with external force is presented. External stress is imposed on PMFs and the polarization coupling will occur. By analyzing the polarization coupling, the beat length of PMF can be calculated. 2. Principles A linearly polarized light beam is input into the PMFs. The ex- cited mode propagates along the principal axis of PMFs and cou- pling mode is generated at the position of PMFs where external stress is applied. Due to the phase modal birefringence Dn b in the PMF, the excited mode and the coupling mode propagate along the PMFs at different velocities. At the output end of the PMFs, the optical path difference (OPD) between the two modes is expressed as following d ¼ Dn b l ð1Þ where d represents the OPD, l is the distance from polarization cou- pling position to output end of the PMFs. When two forces were ap- plied on the PMFs, the OPDs are expressed as follows d 1 ¼ Dn b l 1 d 2 ¼ Dn b l 2 ð2Þ where l 1 and l 2 are the distances from the stress positions to the ends of PMFs respectively. According to Eq. (2), we can get Dn b ¼ d 1  d 2 l 1  l 2 ð3Þ So the phase beat length L b can be calculated as following L b ¼ k Dn b ð4Þ 3. Experimental apparatus The experiment apparatus is shown in Fig. 1. A superlumines- cent diode (SLD) emitting at 1310 nm is used as the light source. 1068-5200/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.yofte.2012.02.002 ⇑ Corresponding author. E-mail address: hxzhang@tju.edu.cn (H. Zhang). Optical Fiber Technology 18 (2012) 136–139 Contents lists available at SciVerse ScienceDirect Optical Fiber Technology www.elsevier.com/locate/yofte