1110 zyxwvutsrqponm IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-19, NO. zyx 6, JUNE 1983 z Modal Birefringence and Polarization Mode Dispersion in Single-Mode Fibers with Stress-Induced Anisotropy NOH SHIBATA, KATSUNARI OKAMOTO, MITSUHIRO TATEDA, SHIGEYUKI SEIKAI, AND YUTAKA SASAKI Abstract-Modal birefringence at low loss and an approximately zero material dispersion wavelength of around 1.3 pm, and chromatic dis- persion characteristics for polarization mode dispersion in the 0.9-1.3 zyxwvu pm wavelength region are measured in single-mode fibers with stress- induced anisotropy. It is found from the measurements that the quantity Concerned with the difference between the phase and group velocities equals approximately zyxwvutsr -(8.5 r 3) X at the 1.290 pm wavelength in actual silica fibers. In addition, a stress-optical constant is evaluated from the measurements of linear birefringence caused by externally applied pressure, and it is (3.30 i 0.05) X mm2/kg. W at the 1.290 pm wavelength. A I. INTRODUCTION LOW-LOSS and high-birefringence fiber is currently of great interest in coherent optical communication systems and in a number of sensor applications [I]-[4] . Measurements of model birefringence and polarization mode dispersion are very important in knowing the polarization characteristics of such a polarization-maintaining fiber. It is well known that the birefringence and the modal dispersion are quantities which correspond to phase and group delay differences between two orthogonally polarized HEllmodes, respectively, and phase and group velocities are not identical for the guided wave. The quantity concerned with the difference between the phase and group velocitieshas usually been neglectedin attempting to determine a stress-induced birefrigence, the stress-optical constant [5], and modal dispersion due to stress-induced anisotropy [6]. This paper presents the magnitude of the quantity concerned with the difference between phase and group delay difference measurements in single-mode fibers with stress-induced anisot- ropy, and a value of the stress-optical constant of silica fiber around 1.3 pm low loss and zero dispersion wavelength. The internal stress-induced birefringence and linear birefringence induced by externally applied pressure are measured by the SBnarmont method [7], [8]. The polarization mode disper- sion characteristics are measured by a spatial-interference tech- nique [9], [IO] over the 0.9-1.3 pm wavelength region. Manuscript received April 14, 1982; revised August 25, 1982. N. Shibata, K. Okamoto, and Y. Sasaki are with the Ibaraki Electrical Communication Laboratory, Nippon Telegraph and Telephone Public Corporation, Tokai, Ibaraki-ken, Japan. M. Tateda is with the Musashino Electrical Communication Labora- tory, Nippon Telegraph and Telephone Public Corporation, Musashinc- shi, Tokyo, Japan. S. Seikai is with the Research and Development Bureau, Nippon T e l e graph and Telephone Public Corporation, Musashino-shi,Tokyo, Japan. 11. BASIC CONCEPT Internal modal birefringence zyxw B comprises both a geometrical anisotropy Bg and a stress-induced birefringence B,. For a birefringent single-mode fiber with a circular core and a stress- producing structure [l 11, [12], Bg isnegligiblysmall and B equals B,. The birefringence B, is given by an average of ma- terial birefringence over core and cladding with electric field distribution squared as the weighting factor [3]. The bire- fringence B, is written, using the stress-optical constant C and the effective stress difference (u, - oy)e along two principal axes x and zyxwv y over core and cladding for the HEll mode, as B, = zyxwv C(U, - u~)~. (1) Here, C depends on the wavelength as well as the material, and (u, - uy)e is also varied with wavelength because the electric field distribution depends on the normalized frequency zy u de- fined by u = (21rlh)na- (2) where A, n, a, and A denote the wavelength, refractive index of core, core radius, and relative index difference between core and cladding,respectively. From the numerical analysis con- sidering the anisotropic stress distribution and electric field distribution, zyxwv (a, - uy)e is given as [13] In Jm ~ r , e) - oy(r, ~)IIE(~, 6, u)12r dr de (ox - 0y)e = hm Iqr, e, u)12r dr de (3) where E(r, 6, u) and u,(r, 0) - uy(r, e) represent the electric field distribution and the anisotropic stress distribution in the fiber, respectively. The normalized stress difference H(u) is defined as = (ox - qJe/(% - qAJ (4) where (ox - u,,)~ is the stressdifference at the core center. Polarizationmodedispersion,which is agroupdelaydiffer- ence between HEfl and HEYl modes per unit fiber length, is given b y 7p = ( 1 IC) [d(W/dkI - (0, - oy)o - C [CM(u) - X(dC/dA)H(u)] 0018-9197/83/0600-1110$01.00 zyxwv 0 1983 IEEE