Specialty Optical Fibers Handbook

argument. The normalized transverse propagation and decay constants are

defined, respectively, as

u ¼ b

t1

a ¼ a(n

2

1

k

2

0

 b

2

)

1=2

and w ¼ b

t2

jj

a ¼ a(b

2

 n

2

2

k

2

0

)

1=2

: (2:10a)

Then the complete solution can be written as

E

z

¼ AJ

q

(ur=a) sin (qf) exp (jbz) for r  a, and (2:10b)

E

z

¼ CK

q

(wr=a) sin (qf) exp (jbz) for r  a: (2:10c)

Note that the f and z dependences are identical in the core and cladding, as

expected by intuition, with the solutions differing only in the radial dependence.

The form of the solution for E

r

, E

f

, H

r

, H

z

, and H

f

can be derived from the

solution for E

z

using the Maxwell equations. The solutions are characterized by

q, the mode order, or azimuthal mode number, which takes on integer values

q ¼ 0, 1, 2, and so on. The eigenvalues are the ...