Biophotonics_Concepts_to_Applications

propagating along thefiber is a linear superposition of these two polarization modes
and depends on the polarization of the light at the launching point into thefiber.
In idealfibers with perfect rotational symmetry, the two modes are degenerate
(that is, they have the same resonant frequency) with equal propagation constants
(βx=nx 2 π/λ=βy=ny 2 π/λ, where nxand nyare the effective refractive indices
along the x and y axes, respectively) [ 5 ]. Thus, any polarization state injected into
thefiber will propagate unchanged. In actualfibers there are imperfections, such as
asymmetrical lateral stresses, noncircular cores, and variations in refractive-index
profiles. These imperfections break the circular symmetry of the idealfiber and lift
the degeneracy of the two modes, so that nowβx≠βy. The modes then propagate
with different phase velocities, and the difference between their effective refractive
indices is called thefiber birefringence,

Bf¼

k

2 p

bxby



ð 3 : 17 Þ

If light is injected into thefiber so that both modes are excited at the same time,
then one mode will be delayed in phase relative to the other as they propagate [ 5 ].
When this phase difference is an integral multiple of 2π, the two modes will beat at
this point and the input polarization state will be reproduced. The length over which
this beating occurs is thefiber beat lengthLB=λ/Bf.
In conventionalfibers, the small degrees of imperfections in the core will cause
the state of polarization tofluctuate as a light signal propagates through thefiber
[ 5 ]. In contrast,polarization-maintainingfibershave a special design that preserves
the state of polarization along thefiber with little or no coupling between the two
modes. Figure3.10illustrates the cross-sectional geometry of two different popular
polarization-maintainingfibers. The light circles represent the core and the cladding
and the dark areas are built-in stress elements that are made from a different type of
glass. The goal in each design is to use stress-applying parts to create slow and fast

Cladding

Stress applying

elements

Core Core

PANDA structure Bowtie structure

Fig. 3.10 Cross-sectional geometry of two different polarization-maintainingfibers

74 3 Optical Fibers for Biophotonics Applications