FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

ient configuration in the lower right is produced by
utilizing both arms of the interferometer aa spatially
separated sensors.
5.1.2 Fiberoptic Acoustic Sensors
5.1.2.1 Acoustic Pressure Sensors
Extending the discussion for an acoustic sensor
in Subsection 4.2.1 and considering Eqa. (4.7) and
(4.8), the pressure variations associated with a sound
wave produce phase fluctuations given by:
A$ = kA(nL) = k(nAL + LAn) (5.1)
is more nearly valid. Thus, the phase of a lightwave
in Hytrelc-jacketed optical fiber, where the croas sectional
area of the Hytrelc is much greater than that
of the fused silica, responds to pressure according to
the Hytrelc compressibility. While the results shown
in Fig. 5.3 are for jacketed optical fibers, similar
results are obtained when bare optical fiber is wound
tightly on a Hytrelc or similar mandrel. In either
case, the more compressible plastic (either jacket
or mandrel), when subjected to fluctuating pressure,
carries (atretches or compresses) the optical fiber
along with it.
A$ = kL(nAL/L + An) (5.2)
where AL/L is the axial strain, S11; k is the wave num -
ber; n is the refractive index of the core; and An is
given by:
An = -(n3/2)[(Pll + P12)S12 + P12S11] (5.3)
where Pll and P12 are the Pockel’s coefficients and S12
is the radial strain. A constant volume assumption
yields the relation S12 = -S11/2. This assumption is
valid only for a material whose Poisson’s ratio is close
to 0.5. It is also quite good for the polyester jacket
material Hytrelc, but not as good for fused silica.
These materials exhibit values of Poisson’s ratio equal
to 0.483 and 0.17 respectively. More exact treatments
sre given in Refs. 2, 3, and 4 in Subsection 5.1.7.
Substituting these relations into Eq. (5.3) yields:
A$ = kLn[l+(n2/4)(Pll - p12)]Sll (5.4)
In fused silica Pll = 0.12, P12 = 0.27 and n = 1.46.
Substituting into Eq. (5.4) results in:
A$ = 0.92kLnSll (5.5)
For an isotropic material:
AL/L = Av/3v :(1/3V)(~V/aP)AP (5.6)
where AL/L = S11 is the axial strain, V iS the volume,
P is the applied pressure and (1/V)(aV/ap) iS the com -
pressibility, K. Thus:
S1l = (1/3)KAP (5.7)
With Kaa the wave number, Eq. (4.7) in Subjection 4.2.1
reduces to $ = kLn. Using this and combining Eqs. (5.5)
and (5.7) results in:
A@/@AP = 0.307K (5.8)
The compressibilities of silica and the pol~~
ester Hytrelc are 2.7 x 10-11 and 2.67 x 10-10 pascals
respectively, leading to:
A$/$AP = 8.3 x 10-12 pascal-l
for bare optical fiber and:
A$/$AP = 8.2 x 10-11 pascal-l
for Hytrelc jacketed optical fiber. Experimental values
of A$/$AP, shown in Fig. 5.3, (See Ref. 5 in Subsection
5.1.7) are 4.5 x 10-12 and 1.0 x 10-10 pascal-l respectively.
The calculated and measured values agree to
within 18% for Hytrelc and a factor of two for fused
silica. These are quite reasonable agreements especially
for Hytrelc where the constant volume assumption
~lo -
In
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FREQUENCY (kHz)
Fig. 5.3 Acoustic sensitivity vs frequency for various
typea of optical fiber jacketing.
Adapted from Lagakos et al., Opt. Soc. Am. ~, 460
(1982).
The discussion above is valid for the mandrelwound
or thick-jacketed fibers. For thinner jackets,
the phase sensitivity is a more complicated function
of the elastic moduli. A low Poisson’s ratio will result
in the thick-jacketed limit being approached with
thinner jackets. Baaed on the criteria of large compressibility
and low Poisson’s ratio, Teflon c appeara
to be an optimum material. In order to demonstrate the
effect of increasing jacket thickness. Ea. (5.2) is rewritten
as:
A$ = kLn(AL/L + An/n)
= kLN[(l/L)aL/aP +
and therefore, since $ = kLn as
A$/$AP = (1/L)aL/aP +
(1/n)an/aP]AP
indicated above:
(1/n)an/aP)
‘CL,Z + Cn,z+cn,r
J
1
(5.9)
where CL z corresponds to the first term in the brackets
and the 2n,z and cn,r correspond to the fiber axial and
transverse components of the second term in the brackets.
The last two terma are both associated with the
pressure-dependence of the refractive index, n. The
various values of the three components of A$/$AP are
shown in Fig. 5.4 (see Ref. 4 in Subsection 5.1.7). As
can be seen, the thick-jacketed fiber results were obtained
for a jacket thickness of approximately 600Pm.
5-2