(I)

/ n1>n2

:8 ~10mm50mm125mm

d

d

/

PAGE

12

: E(x,y,z,t)H(x,y,z,t): E(x,y,z)H(x,y,z)E(x,y)H(x,y)E(x,y)H(x,y)

c2w2em-b2n2 k02-b2 b=n(r)k0cosqz,c,.

----;----;----.----,

EzHz,: (1)(TEM): EzHz0; (2)(TE): Ez0, Hz0; (3)(TM): Ez0,Hz0; (4)(HEEH):Ez0, Hz0 HE(EH),TE(TM)

(r)(n); ; dr/dS, n, ;,nr,dr/dS, ,

:

: ::

: NA,

: n1n2

()

: : : NA(r),

: (rip):

drr0dsdzxyz(drdS) |r0sinz(r0)sin(r0)(r ddS)|r0 sinz(r0)cos(r0) (dzdS)|r0 cosz(r0)r0

: n(dz/dS)=const., ,

n(r)dz/dSn(r)cosz(r)=n(r0)cosz(r0) ----

: Vp/c/ (GIOF)z, z,(SIOF)(SIOF)

:

r2d/dz r0n(r0)sinz(r0)cos(r0)

----

r2=r2d/dt= c/ 2 ,r:r;r

r :

2(dr/dz)2g(r)

r,dr/dz,z1z2(dr/dz0),,rzz1z2

:

g(r)0,;g(r)0,g(r) = 0, n2(dr/dz)2g(r)

n2(r)n2(r)-I2 /r2n2(a)- I2 /r2

: n2n(r0) cosz(r0)n1: rg1 < r < rg2

rg1rg2

:

n2> n(r0) cosz(r0)>n22(r02/a2)n2(r0)sin2z(r0)cos2(r0)

: rl1 < r < rl2 r > rl3rl1rl2: rl3

:

0< n(r0) cosz(r0)

,:(1),,,;(2) ,

,EzHz,(1-3-6)~(1-3-9),EzHz

G2(r)0, ;G2(r)0 , , G2(r)0,

n2(r)k02n2(r)k02-l2 /r2n22k02-l2 /r2

n2k0n1k0

: rg1

n22k02 (21/4)a2

0rr1,,,,

TE/TMHE/EH

ccb z kz-bk=n(r)k0zqzc

neff = b/k0

Er,E,Ez,Hr,H,Hz

Jl, Nl Hl (1) , Hl (2) Il , Kl

:; ,;: Jl, Kl: Jl,Kl..

(0

: TETM;HEEH, HE(),EH;: EH,HE;(Ez,Hz)

: : W=0 , : W, : TE0m(TM0m)J0(Uc)0J1(U)0HElm Jl-2(Uc)0Jl-1(U)0EHlm Jl (Uc)0 Jl+1(U)0*HE1m,U: Uc

,V,,V, V=Vc, Vc;Vc2.405, HE11,, ;

: Vc2/0an12n22 2.405 (SIOF : ac1.2020/n12n22: can12n22/ 1.202:fc1.202c/an12n22cffc.,HE11,HE11TE01TM01HE21,Vc2.405

n1n2 nHEl+1,mEHl-1,m

LPlmLPlm,EyHxEzHzExHyEzHzyxLPlmHEl+1,mEHl-1,m

LPlm (0

LPlm (r>a)

LPlm l0LPlmxycoslf sinlfl=0LP0m

LPlm:LPlm,n1n2,HEl+1,mEHl-1,m,,zz,: L2/(1-2) 12Z

r=a Ez

LPlm: : W=0 , : W, : l=0:J1(Uc)0J0(U)0l=1: J0(Uc)0J1(U)0l>1: Jl-1(Uc)0Jl(U)0*LP0m,U: Uc

SIOF# V SIOFV2/2,

V

0--2.405

2.405--3.832

3.832--5.136

5.136--5.520

5.520--6.380

.

.

LP01

LP11

LP02, LP21

LP31

LP12

.

2

2+4=6

6+6=12

12+4=16

16+4=20

.

.

SIOFW1,Jl(U)0U,Jl:cos(U-/4 l/2)0U-/4 -l/2 (2m-1)/2, (m1,2,3...) U V, (l+2m-1/2) 2V/pl-m4N=4V2/p2V2/22V/pnmV/p

yLPlm,,: (Ey)lmA[Jl(Ulmr/a)/Jl(Ulm)]coslUlmJl-1(Uc)0 Jl(U)0 mLPlmm,2l.

LP21: (Ey)21A[J2(U21r/a)/J2(U21)]cos23.823U215.136;0U21r/a5.136J2(U21ra)J2(U21),,cos2,p/4, 3p/4, 5p/4 7p/4 , ,

,,UlmU,U>>1,: U(l2m1/2)/2l2m,U,lm,pp= l2m p,p/2LPlm,LPlm,p2p"",m,""lm

pUp: Upp/2p: pn1k0cospn12k02Up2/a2,pp,Kz: n1sinpUp/ak0p0/4a,,,