FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

modes. Since at point (a) the two electric fields are
assumed to be in phase, the relative phase angle o (Az)
at some distance Az displaced from (a) la given by
O(AZ) = (Bx - BY)Az (4.2)
Thus at (b) ~ =m/2 and at (c) @c = II and ao forth. At
(e) where Az = L:
o(L) = 2T (4.3)
= (M-BY)L (4.4)
Earlier in Eq. (4.1) the birefringence, B, was defined
as:
B = (BX - BY)I(2TIA) (4.5)
So that for a two-mode fiber that has, at a given wavelength,
A, a birefringence, B, one obtaina:
L = h/B (4.6)
where L la defined as the beat length.
Over the distance, L, the polarization state
of light propagated in a two-mode fiber may pasa through
the entire cycle ahown at the left in 4.8. In terma of
this process there are some applications where it is
deairable to have a fiber with a long beat length, or
small birefringence, B, and others for which a short
beat length, or large birefringence, is preferable.
For example, in the deaign of an optical
fiber electric current aensor employing the Faraday effect
as the transduction mechanism, a relatively ahort
fiber element may be employed and a long beat length,
L, is preferable. When attempting to detect magnetically-induced
birefringence, any slight changes in a
large inherent birefringence, B, i.e., small L, might
maak the polarization changea induced by the magnetic
fielda associated with the electric current under measurement.
In certain applications of interferometrictype
sensora, “two-mode” fibers with high birefringence,
and short beat lengtha can be uaed to advantage. As
already indicated, the output beams from the two patha
of the interferometer not only must be equal in amplitude
but alao polarized in the same direction if they
are to totally cancel one another when they are out of
phaae by~ radians. In many interferometer sensor applications
fiber path lengtha of aeveral tens to aeveral
hundreds of metera are employed. It is irnpoaaible
to draw perfect fibers without variations and fluctuations
in core dimensions and refractive indices, and
without core-cladding interface ripplea. Therefore,
even when the direction of polarization of the injected
light la along one of the preferred axes in an elliptical
fiber, there will be at least random coupling due
to auch perturbations. Thus, as the propagation distance
increases, light originally in the HEIIX mode, ia
transferred into the HE1lY mnde. If the birefringence,
B, is different from zero, (even if it only fluctuates),
there will be some changes in the direction of polarization
and theae could reault in a reduction in the detection
sensitivity of the interferometer.
One method of improving detection sensitivity
is to employ fibers that have high birefringence and
short beat lengtha. In this case, due to the large difference
in the electric field profilea associated with
the HE1lX and HE ~y modes, the probability that a given
perturbation wil 1 cauae a transition between modea la
much lower than in the case of a fiber with amall birefringence,
B. In this senae, a high B fiber is a polarization-maintaining
fiber and therefore may be uaed to
advantage in Interferometric-type senaors.
One way in which a high-birefringence fiber
may be made is shown in Fig. 4.9. At the left an
~] (,3J)
/“n\
~cQER
IDEAL FIBER \ /
PREFORM
Fig. 4.9 The production of high birefringence optical
fibera.
idealized fiber having a rectangular core and cladding
structure is shown. Ita bimodal structure can be reprepresented
as the sum of two planar waveguide modes,
one where the height of the core croas section is the
determining factor and the other where the length of
the core croaa aection la the determining factor. These
modes would have substantially different propagation
constants and the B value would be large.
Several approaches have been taken to produce
fibers that approximate this ideal atructure. One
technique is shown at the center of Fig. 4.9. A preform
is produced consisting of a circular core and a
two-layered circular cladding. The dotted line in the
figure la the outline of its original outer circumference.
Large semi-circular segments of the outer cladding
along the length of the preform are removed aa
indicated and then two additional slots are cut to
expoae a section of the inner cladding. Thia element
is then heated until, under the action of surface tension,
it returns to a circular croaa section. The core
and inner cladding each aasume an elliptical ahape.
Fibera are then pulled from this modified preform. The
reaulting fibers have relatively large birefringence, B.
4.2 PHASE AND INTENSITY DETECTION
4.2.1 Phase Detection
As will be ahown, phaae modulation will be
converted to amplitude modulation prior to detection.
Thus, it is useful to first conaider the procesa involved
in amplitude modulation. An optical source input,
Iin, into an intensity-type aenaor la ahown in
Fig. 4.10. A graph of the optical input to the sensor
versus time is shown at the bottom left. In the aensor,
a baseband input signal, Sb, amplitude modulatea
the optical aource input, Iin, to produce the output
signal from the sensor aa ahown in the graph at the
bottom center. Finally, the amplitude-modulated optical
output signal from the aenaor is photodetected resulting
in an amplitude-modulated electrical output
aignal from the photodetector aa ahown at top and bottom
right of Fig. 4.10. Phaae modulation cannot be
directly detected due to the fact that the light frequency
is approximately 1014 Hz. Photodetectors are
unable to respond to such high frequencies, i.e., they
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