光纤耦合器的理论_设计及进展

30120103PROGRESSINPHYSICSVol.30No.1Mar.2010:100020542(2010)0120037244:2009211218:(10674075,10974100,60577018)863(2006AA01Z217)3Email:[e-mail],(,,300071):,;;;X;,:;;;;:TN253;TN929:A0,,:,;;,:X,,,;,;,1,:111(1)1970,Corning()20dB/km[1],,(2)1972,Snyder[2],,Wijngaard[3]1973,SnyderMcIntyre[4]SnyderWijngaard,112(1)1971,Bisbee[5],Dyott[6],BisbeeDyott,,(2)1974,HudsonThiel[7],1T,1(3)1975,Kuwahara[8],,250dB,21dB,,2(4)1976,Yamamoto[9],3,90%,3(5)1976,BarnoskiFriedrich[10]CO2,Corning,4;,,,(6)1976,McMahonGravel[11],T,5,HsuMilton[12]8330,6McMahonHsu,113,,,(1)1977,KawasakiHill[13],,7,011012dB,,6(a);(b)7(2)1978,Tsujimoto[14],,3dB,013dB,8,8931:(3)1979,SheemGiallorenzi[15](HFNH4F=14),02dB,9,,,02dB9(4)1980,Schiffner[16],10,,,,(5)1982,Kawachi[17],,11,SiO22B2O3,,,10(a)(d);(e)11(6)1985,RussellUlrich[18],12,12(7)04301986,Blake[19],LP01LP11,13,,13(8)1992,CryanHussey[20],V,,()(9)1993,Himeno[21],,,14,14(10)1994,Ye[22],,,15,,,,15(11)1998,Zubia[23],16,16(12)2000,Kakarantzas[24],1715m,CO2,,17141:(13)2000,Chiang[25],,18/,18(14)2001,Kakarantzas[26],,,,,,(15)2004,Iliew[27],,19(16)2007,Chen[28],20,3dB,(17),52,;,211,,,21,,;,2430211,,,,2,([50][51][52][53]),,()()(),,,,,,,341:212,[3338][3949][5458,10,16],1,,213(1)(insertionloss),:Li=10lgPoutPindB(1)(2)(excessloss),:Le=10lgPinPoutdB(2)(3)(couplingratio)Pi,Cr=PiPi100%(3)(4)(isolation):I=-10lgPlPindB(4)Pl3,,,,,,:,311[2,5964],()(),,,,,,31111,:Ejp(x,y,z)=e(j)p(x,y)ei(j)pz(5):E(j)3t(x,y,z)=pA(j)p(z)e(j)3p(x,y)(6)n,[2,4]:dAp(z)dz+i(j)pAjp(z)=-ing=1gjallmodesq(j)(g)pqA(g)q(z)(7)pq,jg,(j)pjp,(j)(g)pqjpgq,:(j)(g)pq=p2S(g)((g)-)e(j)pe(g)qdS(8),(7),[4,62,64,65]:dA1(z)dz+i1A1(z)=-i12A2(z)(9)4430dA2(z)dz+i2A2(z)=-i21A1(z)(10)a1(z)=A1(z)ei1za2(z)=A2(z)ei2z(9)(10),[60,61]:da1(z)dz=-i12a2(z)ei2z(11)da2(z)dz=-i21a1(z)ei2z(12)=1-2231112(1),,,R(z)=a1(z)e-izS(z)=a2(z)eiz,:dR(z)dz+iR(z)=-i12S(z)(13)dS(z)dz-iS(z)=-i21R(z)(14)(13)(14):d2R(z)dz2+(1221+2)R(z)=0(15)d2S(z)dz2+(1221+2)S(z)=0(16):R(z)=C1cosz+C2sinz(17)S(z)=i12[(C2+iC1)cosz+(iC2-C1)sinz](18),=1221+2,C1C2R(0)S(0),R(z)S(z):R(z)S(z)=cosz-isinz-i21sinz-i12sinzcosz+isinzR(0)S(0)(19),1221=1,R(0)=1S(0)=0,(19):R(z)=cosz-isinz(20)S(z)=-isinz(21),:P1=|a1(z)|2=R(z)R(z)3=2+2cos2z2(22)P2=|a2(z)|2=S(z)S(z)3=2sin2z2(23),22,/,,=0(1=2)zLc=/(2),100%,z22(2),z[66],:dA1(z)dz+i1(z)A1(z)=-i12(z)A2(z)(24)dA2(z)dz+i2(z)A2(z)=-i21(z)A1(z)(25)541:1(z)=2(z)=(z),12(z)21(z)=(z),:dA1(z)dz+i(z)A1(z)=-i(z)A2(z)(26)dA2(z)dz+i(z)A2(z)=-i(z)A1(z)(27)1,A1(0)=1A2(0)=0,(26)(27):A1(z)=e-i€zcos(…z)(28)A2(z)=-ie-i€zsin(…z)(29)€(z)=1zz0(z)z,…(z)=1zz0(z)z,:P1=|a1(z)|2=cos2(…z)(30)P2=|a2(z)|2=sin2(…z)(31),23,Lc=/(2…),2331113,,(8):pq=2S(1-2)eqteptdS(32)12epteqt:ept=Bv1Kv1W1a1r1Kv1(W1)cosv11sinv11(33)eqt=Bv2Jv2W2a2r2Jv2(W2)cosv22sinv22(34)J,K,v1v2,a1a2,Bv1Bv2v1v2(33)(34),:pq=QR(-1)v1-v2Kv1-v2W1da1cos(v1-v2)+(-1)v1+v2Kv1+v2W1da1cos(v1+v2)(35),Q=21-2Kv1(W1)Jv2(U2)Av1Av2,R=1U2a22+W1a12Jv2(U2)Kv2W1a2a1,a1=a2=a,W1=W2=W,U1=U2=U,,,v1=v2=v,(v=0),[2,67]:=2aU2V3K0WdaK21(W)(36),[68]:pq=2aU2V3K0Wda+K2vWdacos(2v)Kv-1(W)Kv+1(W)(37),=(n21-n22)/n21,n1n2,V=2a(n21-n22)/,UW,U2=(k20n21-2)a2,W2=(2-k20n22)a2(k0=2/,),K0,Kv0v,d,dzy,d=(d0+z2/)+y2(d0z=0d),,2425,n1=11458n2=6430114551a=310m=015m,,31231211[6971],,31212,262a,2b,x=xi,2t(xi)n1,2t(x),n2TEn-1(TMn-1)nx(x),nx(x),2aTMm-1(TEm-1)Exmn(Exmn),,nx(x),nx(x),[72]:u=gv-gv-vsin(g)1+vtcos(g)(38)26:(a)nx(x);(b)ny(y)u=k[n21-n2x(x)]1/2,v=k(n21-n22)1/2,g=(m+1)/[2(vt+1)],m=0,1,2,,[69]:nx(x)=n21-u2v2(n21-n22)1/2(39)nx(x)d2x/dx2+[n2x(x)k2-2]x=0Cx=(x11-x21)/2,Cy=(y11-y21)/2,x11(y11)x21(y21)Ex11(Ey11)Ex21(Ey21),,CxCy,CxCy,,Cx-Cy,CxCyCx-Cy741:,26(b)ny(y),ny(y),2b,CxCy,[70]:Cx-Cy=R(Cx-Cy)+(Cx-Cy)R+1(40)R=a/b,,=1,=2,,313[7377]205060,,,,,31311,,,,,31312(1),:¨(^-1¨H)-k20H=0inHn=0on1¨Hn=0on2(41),,12,k0,^,:^=x000y000z(42)(41):F(H)=12k(^-1|¨H|2-k20|H|2)d(43)(2),,,27,,,,,27,6,13,Hz,46,(3),,[77]:[K]{H}-2[M]{H}={0}(44),[K][M][78],{H},(44)2{H},8430314[79,80],,,,31411,,,,,,(TETM),,,,BPM,,,31412(1)a,Helmholtz[81]:525x2+525y2+525z2+k2(x,y,z)=0(45)E(x,y,z,t)=(x,y,z)e-it,k(x,y,z)=k0n(x,y,z),k0=2,,n(x,y,z)Z,(x,y,z):(x,y,z)=u(x,y,z)ei…kz(46)…k=k0n0,(46)(45):52u5z2+2i…k5u5z+52u5x2+52u5y2+(k2-…k)u=0(47),,(47):5u5z=i2…k52u5x2+52u5y2+(k2-…k)u(48)(48),u(x,y)(48)x,z,umiim,mm+1:um+1i-umiz=i2…k2x2+(k(xi,zm+12)2-…k2um+1i+umi2(49)2ui=(ui+1+ui-1-2ui),zm+12zm+z2,aium+1i-1+bium+1i+cium+1i+1=di(50)(50)[82]u(x,y,z=0),zb,,,[83,84]:i5^Ex5z=Axx^Ex+Axy^Ey(51)i5^Ey5z=Ayx^Ex+Ayy^Ey(52)Ai,j,:Axx^Ex=12…k55x1n255x(n2^Ex)+525y2^Ex+(k2-…k)^Ex(53)Ayy^Ey=12…k525x2^Ey+55y1n255y(n2^Ey)+(k2-…k)^Ey(54)Ayx^Ex=12…k55y1n255x(n2^Ex)-525y5x^Ex(55)Axy^Ey=12…k55x1n255y(n2^Ey)-525x5y^Ey(56),:[1+izAxx]^Em+1x=[1-iz(1-)Axx]^Emx-izAxy^Emy(57)941:[1+izAyy]^Em+1y=[1-iz(1-)Ayy]^Emy-izAyx^Emx(58),,(57),(58)(2),z[78,85]:(x,y,z)=t(x,y,z)exp(-ik0n0z)+z(x,y,z)exp(-ik0n0z)iz(59),,z:-2in0k0[L]d{ht}dz+([K]-n20k20[M]){ht}={0}(60)[L]=[M]+14n20k20([K]-n20k20[M])(61){ht},[K][M],{0},z,Galerkinsmethod[86]:[A]m{ht}m+1=[B]m{ht}m(62)[A]m=-2in0k0[L]m+z{[K]m-n20k20[M]m}(63)[B]m=-2in0k0[L]m+(-1)z{[K]m-n20k20[M]m}(64),m(m+1)m(m+1),zz,z,z=0,,4,4112222X,,,,,,2