Ž.Ž. Figure 5 a , b Characteristics of 1552 and 1522 nm FBG, respec- tively optimized by selection of the lasing wavelength, loss in the cavity, and quality of the FBG. For the current examples, we have obtained a good clamping effect of 21.8 dB gain with a variation of 0.4 dB and a maximum input signal power of  10 dBm for the FBG with reflectance at 1552 nm. For the second FBG, the optimum result gives a 25.4 dB gain with a variation of 0.7 dB and a maximum input signal power of  15 dBm. REFERENCES 1. M. Zirngibl, Gain control in erbium-doped fibre amplifiers by an Ž . all-optical feedback loop, Electron Lett 27 1991 , 560561. 2. M. Cai, X. Liu, J. Cui, P. Tang, and J. Peng, Study on noise characteristic of gain-clamped erbium-doped fiber-ring lasing am- Ž . plifier, IEEE Photon Technol Lett 9 1997 , 10931095. 3. A. Bononi and L. Barbieri, Design of gain-clamped doped-fiber amplifiers for optimal dynamic performance, J Lightwave Technol Ž . 17 1999 , 12291240. 4. Y. Zhao, Gain-clamped erbium-doped fiber amplifiers Modeling and experiment, IEEE J of Select Topics Quantum Electron 3 Ž . 1997 , 10081012.  2001 John Wiley & Sons, Inc. DUAL-SURFACE COMBINED-FIELD INTEGRAL EQUATION FOR THREE-DIMENSIONAL SCATTERING V. V. S. Prakash 1 and Raj Mittra 1 1 Electromagnetic and Communication Laboratory Pennsylvania State University University Park, Pennsylvania 16807-2705 Recei  ed 6 December 2000 ABSTRACT: In this paper, a dual-surface combined-field integral equa- ( ) tion DSCFIE formulation is presented for computing electromagnetic ( ) scattering from perfectly conducting arbitrary three-dimensional 3-D bodies. The formulation has the ad antage that it does not suffer from the internal resonance problem associated with the closed ca ity modes. Con ergence is typically obtained in a few iterations, and the formulation is relati  ely insensiti  e to the location of the  irtual surface. Numerical results are presented for the case of plane-wa  e scattering from a conducting sphere and a cube to  alidate the present approach.  2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 293296, 2001. Key words: dual-surfaces; integral equations; scattering; radar cross section; conjugate-gradient method I. INTRODUCTION Numerical solutions of electromagnetic scattering problems Ž . often use the method-of-moments MoM based on a variety of integral equations. Both the traditionally used electric-field Ž . integral equation EFIE , as well as the magnetic-field inte- Ž .  gral equation MFIE proposed by Maue 1 , suffer from the internal resonance problem. At frequencies where these reso- nances occur, the solutions of these integral equations be- come nonunique, and several techniques have been proposed   to circumvent this problem 2  6 . Most of these methods utilize integral equations on dual surfaces to create a well-   conditioned problem 5  6 that eradicates the cavity reso- nances. The methods enforce the boundary conditions on the tangential magnetic field on the surface of the body, and also on a virtual surface located inside it, with a view to suppress these interior resonances. This DS MFIE is very sensitive to the location of the virtual surface, which is typically chosen to be parallel to the surface of the conducting object with a   separation distance of 4 5, 6 . Generally, it is preferable to have a solution which is independent of the location of the virtual surface. We propose an alternative form of a dual-surface integral equation for computing the scattering from perfectly conduct- Ž . ing, three-dimensional 3-D bodies of arbitrary shape. This formulation uses the conventional MFIE on the surface of the body, with the EFIE enforced on the virtual surface. This DS CFIE is found to yield a unique solution, which is independent of the spacing between the surfaces, as well as the weighting factor used to combine the EFIE with the MFIE. Just as in the case of conventional dual-surface inte- gral equations, the enforcement of DS CFIE, in the context of MoM, leads to an overdetermined problem of 3 N equa- tions. The overdetermined system is solved in a least squares Ž . sense by using the conjugate-gradient normal CGN method, which does not require an explicit evaluation of the A T A operator. Numerical results have been presented to show that this approach indeed suppresses the interior resonances of 3-D bodies. The problem of evaluating the contribution of MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 29, No. 5, June 5 2001 293