P3-code, with a value of ‘‘0.’’ The OIM checks the first and second inserting chip positions to match the corresponding chip positions of the P3-codes to find the available inserting position for P3-codes. OIM only needs one circle to find the inserting codes. On the other hand, RPM continues to search the inserting code recursively until it cannot find any insert- ing position within one circle, and this searching procedure will then stop. Therefore, OIM is more efficient than RPM in searching the inserting codes. 3. SIMULATION RESULTS Taking the original P7-code system with the simultaneous Ž .  user number of 7 NP7  7 1 , we can obtain the successful Ž number of P7-code from the total successful number of . 823543 for P7 versus the inserting number of P3-code, as shown in Figure 4. For example, VSM, PSM, RPM, and OIM can insert the number of inserting P3-code to be 2, 3, 4, and Ž . 15 into the simultaneous user number of P7-code being 7 with the successful number of 10 for the original P7-code system. According to the simulation results, the interference in PSM is more serious than other models. PSM can only Ž insert the number of inserting P3-code to be 2 by adding the number of inserting P3-code as 3 in the PSM, this multimedia . CDMA system will fail . On the other hand, the successful number of a P7-code system for inserting the number of Ž . P3-code being 3 in VSM is 1847. 4. CONCLUSIONS Considering the multimedia CDMA system with the FTSI method, VSM is better than PSM. The FTSI method is faster than the DTSI method. But the DTSI method can insert more codes than the FTSI method at the price of breaking the limitation of a fixed time slot. OIM needs one circle to determine the inserting code, and RPM needs more than one circle to find the suitable inserting code. Therefore, consider- ing the multimedia CDMA system with the DTSI method, RPM is better than OIM. We conclude that OIM is the better way to process the multimedia CDMA system in consideration of the total system capacity and algorithm efficiency. ACKNOWLEDGMENT This work was supported by the National Science Council, Taipei, Taiwan, R.O.C. under Contract NSC 88-2215-E- 032-003. REFERENCES 1. J.H. Wu and J. Wu, Synchronous fiber-optical CDMA using hard- Ž . limiter and BCH codes, J Lightwave Technol 13 1995 , 11691176. 2. P.R. Prucnal et al., Spread spectrum fiber-optic local area network Ž . using optical processing, J Lightwave Technol 4 1986 , 547554. 3. F.R.K. Chung et al., Optical orthogonal codes: Design, analysis, Ž . and applications, IEEE Trans Inform Theory 35 1989 , 595604. 4. J.G. Zhang and G. Picchi, Tunable prime-code encoderdecoder Ž . for all-optical CMDA applications, Electron Lett 29 1993 , 12111212. 5. Y.-H. Lee, Simulation study of different codes systems division Ž . multiple access DCSCMA for optical communication, Mi- Ž . crowave Opt Technol Lett 1999, accepted .  1999 John Wiley & Sons, Inc. CCC 0895-247799 AN ANALYTICAL STUDY OF THE CUTOFF CONDITIONS AND THE DISPERSION CURVES OF A WAVEGUIDE WITH A CROSS-SECTIONAL SHAPE RESEMBLING AN ELLIPSE COMPRESSED ALONG THE MINOR AXIS Vivek Singh, 1 B. Prasad, 1 and S. P. Ojha 1 1 Department of Applied Physics Institute of Technology Banaras Hindu University Varanasi 221005, India Recei  ed 15 March 1999 ABSTRACT: In this paper, we present an analytical study of the modal characteristics, cutoff conditions, and dispersion cur  es of a special type of an optical wa eguide with a cross-sectional shape resembling an ( ) ellipse compressed along the minor axis ECMI . Using the boundary conditions for the proposed wa eguide under weak guidance, the cutoff equation and the modal characteristic equation ha e been obtained. From the cutoff equation, we find the number of modes propagating for the guiding region. Also, from the modal characteristic equation, we obtain the dispersion cur  es for some low-order modes.  1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 426429, 1999. Key words: modal characteristics; cutoff condition; weak guidance; optical fiber; dispersion cur  es; sustained modes; normalized propagation constant INTRODUCTION The standard circular cross-sectional optical waveguide has   been studied extensively 1  7 . This standard optical wave- guide, called an optical fiber, is used in communication systems. But in recent years, light-wave propagation through various types of symmetrical and nonsymmetrical, noncircular cross sections of the waveguide have constituted an important specialized area in light-wave technology. Initially, only two types of noncircular cross section, namely, the planar and the   elliptical, were studied widely 8  12 . These waveguides are very useful in the field of integrated optics. But in recent years, various noncircular waveguides having unconventional shapes such as rectangular, triangular, pentagonal, annular, Piet  Hein, cardiodic, hypocycloidal, and others have been   studied by many investigators 13  25 . More recently, Singh,   Ojha, and Singh 26 have studied the modal dispersion characteristics of an optical waveguide with a guiding region cross section bounded by two Archimedian spirals. In the present paper, we present an analytical study of the modal characteristics, cutoff conditions, and dispersion curves of a special type of an optical waveguide with a cross-sectional shape resembling an ellipse compressed along the minor axis. Using the boundary conditions for the proposed waveguide under the weak guidance approximation, the cutoff equation and the modal characteristic equation have been obtained. From the cutoff equation, we find the number of modes propagating through the guiding region; from the modal characteristic equation, we obtain the dispersion curves for some low-order modes. THEORY Figure 1 shows the transverse cross section of the proposed waveguide, having a core refractive index n and cladding 1 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 22, No. 6, September 20 1999 426