(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
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..
,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 (r>a)
LPlm l0LPlmxycoslf sinlfl=0LP0m
LPlm:LPlm,n1n2,HEl+1,mEHl-1,m,,zz,: L2/(1-2) 12Z
r=a Ez
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,,,
Top Related