Specialty Optical Fibers Handbook

The cross-product model works because with no PDL, any change in s can only

result in a change in orientation (magnitude is fixed at unity). Thus,

s and its

derivatives are perpendicular. A dynamical equation for the PDV can be found

from Eqs. (2.28a and 2.28b) [41]:

@

@z

V(z,v) ¼

@

@v

W(z,v) þ W (z,v)  V(z,v): (2:30)

Under the assumption of a suitably narrow source spectral width, the PDV can

be written as a power series in frequency:

V(z,v)  V(z,v

0

) þ (v  v

0

)

@

@v

V(z,v

0

) þ ...,(2:31)

where the terms on the right-hand side of Eq. (2.31) are the first and second-

order PDVs. Using Eq. (2.31) in Eq. (2.30), one can obtain equations for each

PDV order. In