A.K.Taneja and E.K.Sharma Vol.16,No.11/November 1999/J.Opt.Soc.Am.A 2785 T Ver1a)+exp(2+1)erte[a(2+1]Vert(aa) b= .(A9) 1π a Vzerf(V2aa)+ 1 2a2aexp(-2a2a) and the normalization constant is given by 1/2 B= 1 (A10) a Vzerf(v2aa)+ h agexp(-2aa) Address correspondence to E.K.Sharma at waveguides,"J.Lightwave Technol.12.1543-1549(1994). enakshi@bol.net.in. 4.A.K.Taneja,S.Srivastava,and E.K.Sharma,"Closedform expressions for propagation characteristics of diffused pla- nar optical waveguides,"Microwave Opt.Technol.Lett.15. REFERENCES 305-310(1997). 5. S.I.Najafi,ed.,Introduction to Glass and Integrated Optics 1.E.K.Sharma,S.Sharma,and J.P.Meunier."Design of re- (Artech House,London,1992). fractive ion exchange integrated optical components,"IEEE 6.M.Stern."Finite-difference analysis of planar optical J.Sel.Top.Quantum Electron.2.163-175 (1996). waveguides,"in Methods for Modeling and Simulation of 2.W.-H.Tsai,S.-C.Chao,and M.-S.Wu,"Variational analysis Guided-Wave Optoelectronic Devices,W.P.Huang.ed., of single mode inhomogeneous planar optical waveguides," Progress in Electromagnetic Research,Vol.10(EMW,Cam- J.Lightwave Technol.10.747-751 (1992). bridge,Mass.,1995),pp.123-186. 3.S.-C.Chao,M.-S.Wu,and W.-H.Tsai,"Variational analysis 7.H.Nishihara,M.Haruna,and T.Suhara,Optical Inte- of modal coupling efficiency between graded-index grated Circuits (McGraw-Hill,New York).Address correspondence to E. K. Sharma at enakshi@bol.net.in. REFERENCES 1. E. K. Sharma, S. Sharma, and J. P. Meunier, ‘‘Design of re￾fractive ion exchange integrated optical components,’’ IEEE J. Sel. Top. Quantum Electron. 2, 163–175 (1996). 2. W.-H. Tsai, S.-C. Chao, and M.-S. Wu, ‘‘Variational analysis of single mode inhomogeneous planar optical waveguides,’’ J. Lightwave Technol. 10, 747–751 (1992). 3. S.-C. Chao, M.-S. Wu, and W.-H. Tsai, ‘‘Variational analysis of modal coupling efficiency between graded-index waveguides,’’ J. Lightwave Technol. 12, 1543–1549 (1994). 4. A. K. Taneja, S. Srivastava, and E. K. Sharma, ‘‘Closedform expressions for propagation characteristics of diffused pla￾nar optical waveguides,’’ Microwave Opt. Technol. Lett. 15, 305–310 (1997). 5. S. I. Najafi, ed., Introduction to Glass and Integrated Optics (Artech House, London, 1992). 6. M. Stern, ‘‘Finite-difference analysis of planar optical waveguides,’’ in Methods for Modeling and Simulation of Guided-Wave Optoelectronic Devices, W. P. Huang, ed., Progress in Electromagnetic Research, Vol. 10 (EMW, Cam￾bridge, Mass., 1995), pp. 123–186. 7. H. Nishihara, M. Haruna, and T. Suhara, Optical Inte￾grated Circuits (McGraw-Hill, New York). b 5 A p 2a2 1 1 erf~A2a2 1 1a! 1 Ap exp@2a2a2~2a2 1 1!#erfc @a~2a2 1 1!# 2 a V2 Ap 2 erf~A2aa! 1 a Ap 2 erf~A2aa! 1 1 2a2a exp~22a2a! , (A9) and the normalization constant is given by B 5 H 1 hF 1 a Ap 2 erf~A2aa! 1 1 2a2a exp~22a2a!GJ 1/2 . (A10) A. K. Taneja and E. K. Sharma Vol. 16, No. 11/November 1999/J. Opt. Soc. Am. A 2785