Fiber Modes
•For each βmn, we write the corresponding solution for H or E as
HEmn or EHmn, depending on whether H or E dominates the
other.
•In the special case when m=0, the modes are called TE0n and
TM0n modes, corresponding to transverse electric (i.e., Ez=0) and
transverse magnetic (Hz=0) modes, respectively.
Fiber Modes
•Normalized frequency: Define
V = k 0 a (n12 − n22 )1/ 2 ≈ (2π / λ )an1 2∆
•Normalized propagation constant:
b=
Normalized propagation constant b as a function
of normalized frequency V for low-order fiber
modes
β / k0 − n2
n1 − n2
=
n − n2
n1 − n2
•V determines how many
modes a fiber can support: see
figure on the left.
•For single mode operation, only
HE11 (called the fundamental
mode) should be supported.
Single Mode Fibers
•For single mode operation, only
HE11 (called the fundamental
mode) can be supported.
•Thus, single mode implies that
both TE01 and TM01 must not be
supported.
Normalized propagation constant b as a function
of normalized frequency V for low-order fiber
modes
•Thus, TE01 and TM01 must both
be below their cutoff V’s. See the
horizontal intercept for TE01 and
TM01 and conclude that
V < 2.405
Must hold for single mode operation