1) An obvious typo: The last phrase in 2) should be B =>k*(n2).
3) For a step index fiber, the phase velocity is (c/n1)/cos(Theta); the
group velocity is (c/n1)cos(Theta); where Theta is the launch angle. Thus,
the product is the core bulk velocity c/n1.
Bob Sciamanda
Physics, Edinboro Univ of PA (Em) http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "Bob Sciamanda" <trebor@WINBEAM.COM>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Wednesday, February 16, 2005 3:51 PM
Subject: Re: Travel distance in a waveguide.
| Perhaps this summary will help:
|
| 1) In a "step-index" fiber, the wave number B in the resultant wave
| E(r)=f(r)exp(i(Bz-wt)) is constrained to:
| (n2)k = k2<= B<=k1=(n1)k, where
| k is the vacuum wave number, n2 is the clad index and n1 is the core
index.
| Thus the fiber phase velocity always "lies" between the bulk phase
| velocities v1 and v2 (n1 and n2 typically vary by less than a few
percent).
|
| 2) In a typical graded index fiber, where n(r) goes, via a power law in
| (r), from a value n1(at r=0) to a final (cladding) value n2, B => n2.
|
| 3) In both cases, the product of the phase and group velocities = c^2.