6 -rad region have been induced and detected in a single-mode all-fiber Mach-. Zehnder interferometer by stretching the fiber with a piezoelectric cylinder driven ...
April 1980 / Vol. 5, No. 4 / OPTICS LETTERS
139
Measurement of small phase shifts using a single-mode
optical-fiber interferometer D. A. Jackson,* A. Dandridge,
and S. K. Sheem
Naval Research Laboratory,Washington, D.C.20375 Received January 14,1980 6 Periodic phase changes in the 10- -rad region have been induced and detected in a single-mode all-fiber MachZehnder interferometer by stretching the fiber with a piezoelectric cylinder driven at frequencies between 40 and 104Hz.
Introduction There is considerable interest in using optical fibers as the sensing element in devices such as hydrophones and
microphones. Recently the first all-fiber MachZehnder interferometer was demonstrated and used to detect acoustic waves.' If the fiber interferometer is to compete with the currently used piezoelectric detectors in hydrophones, the device must be capable of detecting pressure-induced fluctuations of 30 dB relative to 1 ,Pa. In a typical fiber, the resultant refractive-index fluctuation from pressure changes of this order of magnitude corresponds to 1.8 X 10-9 rad/m. Consequently, in a typical device in which a maximum of -103 m of fibers can be used,2 the total phase change expected would be of the order of 10-6 rad. This is
equivalent to an optical path-length change in one arm of the fiber of -10-3 A. In this Letter we give details, together with our calibration and measurement procedure, of a simple technique for producing linear phase shifts in the 10- 6-1-rad range in an all-fiber interferometer. Modulation
output current will be -2A 1A2 cos 0(t), where Al and A2 are the amplitudes of the individual beams transmitted or reflected, respectively, onto the detector. Components at twice the laser frequency have been neglected. The current has the followingform: 1o(t)a cos 00
no-
X Jo(kxo) + 2 E J2 n(kX 0)Cos[2n(Wmt + (km)]
n={
-sin
(00 2
J2n1,(kxo)
Xsin[(2n+ l)(comt+ Am] where Jn is the Bessel function of order n. Spectral analysis of the photocurrent leads directly to the amplitude of the periodic phase modulation. It is unnecessary, however, to measure the entire spectrum
since either the amplitude of the J1 and J 2 components can be measured simultaneously or (preferably) the interferometer can be maintained in adjustment such that sin ko = 1 (usually termed the quadrature condition) when it is only necessary to measure the amplitude
In order to test the performance of any interferometer, it is necessary to vary the optical path length (phase) in one of its arms in a controlled manner. Piezoelectric elements, cylinders, and disks are known to have linear
voltage-expansion coefficients in the angstrom range3 and are an obvious choice for both modulation and calibration of the fiber interferometer if efficient coupling between it and the fiber can be achieved. If the optical length of one of the arms of an interferometer is modulated at a frequency Cm, the phase difference between the beams 0(t) may written as 0(t) = q5o+ kXo sin(wmt + Om),
where 00 is the static phase difference, which will vary with temperature and other factors, and k = 2X, where X is the free-space wavelength of the light, and x0 is the maximum optical path-length change at cwm. Since the optical detector responds to the intensity rather than to the amplitude of the incident light, its 0146-9592/80/040139-03$0.50/0
of the J1 component. Before attempting to modulate one arm of the fiber interferometer, we performed some preliminary studies on several piezoelectric cylinders supplied by Vernitron
(part no. 8-8031). These measurements were performed using a very stable Michelson interferometer, machined out of Invar, loaned to us by Norman Ford of
the University of Massachusetts. A small mirror was mounted on the piezoelectric cylinder, which was mounted in one of the arms of the Michelson interferometer.
A variable d.c. voltage was applied to one of
the electrodes of the cylinder and a variable-amplitude sine wave (com)to the other. The variable d.c. voltage was adjusted to maintain the interferometer in quadrature (sin 'ko = 1). An Ithaco Model 393 lock-in am-
plifier, locked to Cor,was used to detect the output of the photodiode. Calibration of the displacement of the piezoelectric cylinder (at am ) was performed as follows. The variable sine-wave amplitude was increased from C 1980, Optical Society of America
140
OPTICS LETTERS / Vol. 5, No. 4 / April 1980
It is apparent from Fig. 1(a) that the piezoelectric cylinder is ideally suited as a calibration source for the fiber interferometer, provided that this performance can
10
be maintained while the cylinder is intimately linked to one of the fiber arms.
loI 0 I
*
Fiber Interferometer The interferometer is shown in Fig. 3. It is basically a
I0
Mach-Zehnder interferometer in which each of the usually used mirror-beam-splitter combinations is replaced by an optical-fiber bottle coupler (BC) described by Sheem.4 The evanescent couplers are linked by two
107
single-mode optical fibers with the same numerical aperture as that of the couplers. In any typical appli-
DRIVE VOLTAGEVOLTS1
(a)
cation, one of the fibers serves as the reference arm and
the other the signal arm. A laser is then coupled into BC1 and the output detected at either output of B02. In the normal laboratory environment, the outputs of BC2 are constantly varying because of the interferometer's inherent sensitivity to random temperature
1201
fluctuations, air currents, or local acoustic noise, which E
can modulate the optical path length of either fiber.
0L R0
Because we are interested in measuring extremely small
phase changes, we mounted the complete interferometer (with the exception of the laser source) on an isolation platform mounted inside a chamber that could be evacuated. 1o
lo,
103 FREOUENCY (Hz)
(b)
This chamber was mounted on a con-
ventional optical vibration table to further reduce low-frequency coupling into the interferometer.
Fig. 1. (a) Variation of J,(kxo'),, 1 and equivalent peak amplitude as a function of drive voltage V at 1 kHz: Invar Michelson interferometer. (b) Variation of the drive voltage to
produce an average displacement corresponding to J1 (max) with frequency (cor).
2 1) i o 0
zero until the lock-in amplified output reached a first maximum. This corresponds to the maximum value
E1 1.11 "II
of the J 1 component, which for X = 6328 A is equivalent
to an xo value of 926 A. Smaller values of mean displacement (xo')w..,m can then be determined by simply measuring Jl(kxo')wmfor any other value of drive volt-
2 =1
a
age below that corresponding to J 1(max) and comparing
the result with the tabulated values of the Bessel function. A simpler method can be used if the voltageexpansion coefficient of the piezoelectric cylinder is linear with voltage. This can be established by simply plotting Jl(kxo),wmas a function of Vwmjwhere V is the amplitude of the voltage drive at frequency Win. Cali-
bration was performed for a range of frequencies be-
;a
MI Io
a
10
102 ioE (0 FREQUENCY(Hz)
14
110-8
Fig. 2. Variation of the minimum detectable displacement and equivalent phase shift with frequency (w..): * Invar Michelson interferometer, 0 fiber interferometer.
Horizontal
broken lines indicate the shot-noise limit: upper line, fiber interferometer; lower line, Invar interferometer.
tween 40 and i04 Hz. Figure 1(a) shows Ji(kxo'),,m as
a function of drive-voltage V at 1 kHz, and Fig. 1(b) shows the drive voltage required to produce an average
displacement corresponding to Jj(max) for-a range of frequencies. Although these voltage values are frequency dependent, the expansion of the ceramic exhibited a linear voltage-expansion coefficient over 6 orders of magnitude for all frequencies investigated. At frequencies above 300 Hz, displacements as small as
10-i A were detected, with a signal-to-noise ratio of -1, as shown in Fig. 2. The minimum detected displacement was
_10-4
A at 5 kHz.
8C0
8C2
SINGLE MODELASER c P{ZCYLINDER
D.G.OFFSETQTA MAINTAINQUADRATURE
A.C. DRIVE AT LOCK-INAMP
Fig. 3. Schematic of the Mach-Zehnder all-fiber interferometer. BCI and BC2 are the evanescent-wave beam splitters.
The regions in which the cladding has been removed
from the fiber are indicated by the single line.
April 1980 / Vol. 5, No. 4 / OPTICS LETTERS
141
2 , where shot-noise current of the detector (2 eOID(,,)Af)"1
eo is the charge on the electron and Af is the bandwidth of the detection scheme. The shot-noise limit is also shown in Fig. 2. From Fig. 2 we see that at frequencies a
;i;
0Of
MI
Io
uI
10o-a lo-, DRIVEVOLTAGE(VOLTS)
above '300 Hz the minimum phase shift detected is within an order of magnitude of the theoretical limit. The curve does rise toward the low-frequency end of the
measurements; this is probably due to acoustic noise produced at the initial coupling of the laser to the fiber and to low-frequency noise present in the laser itself. However, the performance of the all-fiber interferometer is extremely promising since even at 40 Hz we are able to detect phase shifts of 10-5 rad with -5 yW on the detector. Our particular interferometer was optically lossy because of the use of many butt couplers
ometer.
in its construction and the relatively inefficient initial coupling of the laser to the fiber. (This was deliberate since good optical coupling produced higher low-fre-
The output from a single-mode He-Ne laser (-1 mW) was coupled into a single-mode optical fiber with
quency noise levels.) In an optimized system we could expect power levels of up to -500 AuWon the detector, which would yield a detectability of 10-6 rad at 40 Hz
Fig. 4. Variation of Jl(kxo), 2m and equivalent peak amplitude as a function of drive voltage V at 1 kHz: all-fiber interfer-
an in-house-designed coupler. 5 This fiber was then fed
into the vacuum chamber through a specially designed vacuum seal6 and then butt-coupled into BC1. The output of the interferometer was detected with a P-I-N photodiode mounted on the inner isolation platform. The plastic coating of a' small section of one of the fibers joining the bottle couplers was removed and glued
(Eastman 910) onto the outside of the piezoelectric cylinder such that the axis of the fiber was parallel to the cylinder axis. The cylinder was driven as before, again using the d.c. voltage to maintain the interferometer in quadrature. (Inside the chamber, especially when it has been evacuated, the drift is small and measurements are
straightforward, whereas outside the chamber the drift rates were such that it was impossible to make any accurate measurements.) Initial experiments indicated that the change in length of the fiber was close to that of the piezoelectric cylinder alone. The linearity of the induced phase change, as a function of applied voltage, was measured by using the procedure described above and is shown in Fig. 4, where co.. is 1 kHz. The minimum detectable
phase shift as a function of frequency was also determined.
This is plotted in Fig. 2. The minimum de-
tectable phase shift that can be determined (signalto-noise ratio = 1) occurs when the signal equals the
and make the fiber interferometer an attractive alternative to current hydrophones. In a subsequent paper, we will describe a method for eliminating the problems associated with drift. We are indebted to R. P. Moeller for the loan of his laser-to-fiber coupler and for general technical assistance. * Permanent address, Physics Department, University of Kent, Canterbury, England. References 1. S. K. Sheem and T. G. Giallorenzi, Appl. Phys. Lett. 35,914 (1979). 2. J. A. Bucaro, H. D. Dardy, and E. F. Carome, J. Acoust. Soc. Am. 62, 1302 (1977); J. H. Cole, R. L. Johnson, and P. G. Bhuta, J. Acoust. Soc. Am. 62, 1136 (1977), 63, 1232 (1978). 3. P. R. Dragsten, W. W. Webb, J. H. Paton, and R. R. Capranica, J. Acoust. Soc. Am. 60, 665 (1976). 4. S. K. Sheem and T. G. Giallorenzi, Opt. Lett. 4, 29 (1979).
5. R. P. Moeller, Naval Research Laboratory, unpublished design. 6. C. Villarruel, Naval Research Laboratory, unpublished design.
