also explain the high-frequency components often observed during the growth of these gratings. ... in a germania-doped silica optical fiber by counterprop-.
399
April 1, 1990 / Vol. 15, No. 7 / OPTICS LETTERS
Photosensitive optical fibers used as vibration sensors Sophie LaRochelle, Victor Mizrahi, Kelly D. Simmons, and George I. Stegeman Optical Sciences Center, University of Arizona, Tucson, Arizona 85721
John E. Sipe Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7,Canada Received November 20, 1989; accepted February 8, 1990
We experimentally demonstrate that high-reflectivity photosensitive gratings written in optical fibers can be used to detect vibrations that produce length changes of less than 50 nm. This sensitivity to external perturbations can also explain the high-frequency
components often observed during the growth of these gratings.
The formation of photosensitive gratings in optical
d(Ai3) = #
fibers was first reported in 1978.1,2 It was then ob-
served that a periodic index change could be induced in a germania-doped silica optical fiber by counterprop-
agating laser beams from an argon-ion laser at 488 or 514.5 nm. The study of this phenomenon is still of considerable interest since its origins are not yet fully understood. Furthermore, several applications have been proposed for these gratings, including their use as temperature or stain sensors.3 The development of fiber-optic vibration sensors is also a topic of active
research.4'5 In this Letter we show the extreme sensitivity of photosensitive gratings to vibrations and demonstrate their use as distributed vibration sensors. The frequency response of the reflectivity of a phase grating can be calculated by using coupled-mode theory.6 If we assume that the grating is uniform over the length of the fiber, the reflectivity is given by
_ao
+r
no as
dL
A
(2)
L'
where (1/no)(ano/Os) = -0.29 is the elasto-optic coefficient 2 of fused silica, s is the strain, and dL is the
corresponding length change. For example, a grating with a peak reflectivity of 96% and a length of 26.2 cm has a bandwidth of 944 MHz as calculated from Eq. (1)
with Xo= 488 nm. In that case, if the fiber is stretched by only 283 nm, the reflectivity at the initial peak wavelength will decrease from 96% to 0%. The force required to produce such a strain is 2.5 X 10-4 N, using the value of Young's modulus for fused silica, 7 E = 7 X 1010N/M2 , and a fiber diameter of 65 Am.
The gratings were written by launching a singlelongitudinal-mode argon-ion laser beam (488 nm) into an optical fiber while measuring the reflected, the transmitted, and the incident powers. The transmission of a He-Ne laser (632.8 nm) propagating collin-
R
K2
=
462
sinh 2 (OL)
sinh2 (UL)+ U2 cosh2(QL)'
where A/3= (#i
-
(1)
7r/A) is the wave-vector detuning, A
early with the argon laser beam was also monitored to verify the stability of the coupling. All optical components were placed near normal incidence to avoid po-
is the period of the grating, Q 2 = K2 - A#2, and K = 7rAn/Xois the coupling coefficient when an index variation of the form n(z)
=
1.00 -
no + An cos(27rz/A) is assumed
in the fiber. Also, f3o is the propagation constant of the mode in the optical fiber that is approximated by 27rno/Xo for the calculations, where Xo is the wave-
length in vacuum. The length of the grating is L.
0.80 -
I--
5 0.60 -
The reflectivity is plotted in Fig. 1 as a function of
the normalized detuning
A#/K
for a grating of 96%
peak reflectivity (L = 26.2 cm, Xo = 488 nm). The reflectivity peak will occur when the Bragg condition is satisfied, i.e., Xo= Xp= 2noA. The presence of vibra-
tions can stretch the fiber and modify both the grating period and the refractive index, causing the grating to be detuned from the Bragg condition and changing the reflectivity. If we assume uniform stretching, the
LLJ
I 0.40
0.20
0.00 -f -6.00
AN_1/_ -4.00
-2.00
0.00 2.00 DETUNING
4.00
6.00
change in the wavelength of the peak reflectivity can be obtained by taking the derivative of Xp = 2noA. Also,
Fig. 1. Reflectivity of a uniform phase grating as a function
the strain-induced change in the detuning is
of the normalized detuning
0146-9592/90/070399-03$2.00/0
A#//K
© 1990 Optical Society of America
(KL
= 2.29, X = 488 nm).
400
OPTICS LETTERS / Vol. 15, No. 7 / April 1, 1990
The frequencies fi and f2 can be identified from the frequency spectrum of the reflected power [Fig. 3(b)]. The modulation of the reflectivity of the grating can then be modeled by substitution of Eq. (3) into Eqs. (1) and (2) with fA = 120.12 Hz,
f2
=
125.98 Hz, Al =
0.060 Am,and A2 = 0.045nin. The results are shown in Fig. 4. Good agreement between the experimental results and the theoretical simulation is obtained for an initial detuning of t/'K = 0.7. Such a detuning can be caused, for example, by a temperature variation of only 0.040C relative to the temperature during the formation of the grating. The natural longitudinal stretch vibration frequencies of the fiber are given by' 0
Fig. 2. Experimental setup used to write photosensitive gratings. BS's, beam splitters; IF's, interference filters; OF, optical fiber; P0, argon laser power detector; Pt, transmitted-
(4)
2L
fm
where m is an integer and p is the density of the glass7 (2.2 g/cm3 ). The fundamental vibration frequency of our fiber was estimated to be 10.7kHz. Therefore the frequency peaks at 120.12 and 125.98 Hz observed in Fig. 3(b) do not correspond to vibrational normal
power detector (X = 488 nm); Pr, reflected-power detector (X = 488 nm); Ph, transmitted-power detector (X = 632.8 nm).
larization effects. The experimental setup is shown in Fig. 2. The optical fiber was an elliptical-core, polarization-preserving fiber (Andrew Corporation). This optical fiber has a core of 1 gm X 2 Am and is monomode
at 488 nm. The fiber was held under slight tension at both ends, and its length was 26.2 cm. The input and output couplers were both attached to the optical table (Newport Corporation) but were not otherwise mechanically coupled. The data were taken at a sampling
: 30.00 E EC g
0 0L
20.00
rate of 10 Hz or 1 kHz and were subsequently processed
using a fast-Fourier-transform algorithm to obtain the frequency spectrum of the fiber reflectivity and transmissivity.
The fast Fourier transform was done on a
data set of 1024 points sampled at 1 kHz, leading to a resolution in the frequency domain of 0.98 Hz. The power coupled into the fiber to write the grating was typically 42 mW. The reflectivity of the grating reached 96% after 150 sec. During the growth of the grating the transmitted and reflected argon laser powers were detected with photodiodes, filtered by a
3000
20-
a
00
three-stage resistance-capacitance low-pass filter with a cutoff frequency of 18 Hz, and then digitized at a 10-Hz sampling rate. The response time of this system was therefore similar to that of a mechanical chart recorder. The recorded signals are shown in the inset of Fig. 3(b). On the growth curves of the grating it can be seen that high-frequency components are present; these have been observed by previous researchers.8' 9 When the reflected and transmitted power is instead sampled at a 1-kHz sampling rate, the high-frequency features can be resolved and are seen to be well-defined oscillations instead of noise [Fig. 3(a)]. These oscillations can be modeled by assuming that the length of the fiber is stretched at two different frequencies, L = Lo + Al cos(27rft) + A2 cos(24f2t). (3)
REFLECTED
on.
(b)
wU2000
.TASM ITTED
.
,L. 0 0
.
i'
i ' '
50i
.
i i i
'
16
100
TIME (sec)
00
< 1000 -
L, . m. _ 0.00
100.00
.
200.00 300.00 FREQUENCY (Hz)
40oo.0
Fig. 3. (a) Transmitted (lower curve) and reflected (upper curve) argon laser power from a photosensitive grating sampled at 1 kHz. (b) The amplitude in arbitrary units of the frequency spectrum of the reflected-power signal; the inset shows the growth curves of the grating.
April 1, 1990 / Vol. 15, No. 7 / OPTICS LETTERS 1.00
0.80
0.60 w
0.40
i
W IL 0.20
0.00-
0.00
0.10
. 0.. .20
.4
0..0 . .3
.....
0
. 0..401.5
lIME (sec)
Fig. 4. Calculated modulation of the reflectivity of a photosensitive grating assuming that f, = 120.12 Hz, f2 = 125.98 Hz, Al = 0.060 Am, A2 = 0.045 Am, and
A/cK
=
0.7.
1000-
Vibrations were also acoustically induced in the optical table and were subsequently detected by monitoring the reflection or the transmission of the argon laser beam through the fiber. The spectrum of the transmitted power for an induced vibration frequency of 132 + 1 Hz is represented in Fig. 5, where the peak at 131 A1 Hz is readily identified. The other peaks of less amplitude present in Fig. 5 result from the nonlinear components of the response of the detuned grating (Fig. 1). The argon laser power was also monitored at the output of the laser. A variation of 0.6% of the argon laser power was observed, and the frequency spectrum showed a large zero-frequency peak and peaks at 60.55 and 180.66 Hz with respective amplitudes of 5.5 X 10-4 and 3.5 X 10-4 relative to the zerofrequency peak. In conclusion, we have shown that vibrations of small amplitude (less than 50 nm) can easily detune a photosensitive grating, which can therefore act as a sensitive distributed vibration sensor. This high sensitivity to vibrations also explains the high-frequency noise components that were previously observed on the growth curves of photosensitive gratings. This research was supported by the U.S. Air Force Office of Scientific Research under contract AFOSR87-0344. Sophie LaRochelle thanks the Natural Sciences and Engineering Research Councilof Canada for its financial support.
800
-/ 600 D
References
400
1. K. 0. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).
200 -
0.00
100.00
20.00
300.00
400.00
500.00
FREQUENCY (Hz) Fig. 5.
401
Amplitude in arbitrary units of the frequency spec-
trum of the argon laser power transmitted through a photosensitive grating when a vibration is induced in the fiber at 132 Hz.
modes of the fiber. These frequencies are believed to result from mechanical vibrations (e.g., the laser water pump) present in the environment that were transmitted to the fiber. This is confirmed by the fact that the positions of these peaks did not vary with the length of the fiber.
2. B. S. Kawasaki, K. 0. Hill, D. C. Johnson, and Y. Fujii, Opt. Lett. 3,66 (1978). 3. G. Meltz, J. R. Dunphy, W. H. Glenn, J. D. Farina, and F. J. Leonberger, Proc. Soc. Photo-Opt. Instrum. Eng. 79, 104 (1987). 4. W. B. Spillman, Jr., B. R. Kline, L. B. Maurice, and P. L. Fuhr, Appl. Opt. 28, 3166 (1989).
5. V. T. Chitnis, S. Kumar, and D. Sen, IEEE J. Lightwave Technol. 7, 687 (1989). 6. D. K. W. Lam and B. K. Garside, Appl. Opt. 20, 440 (1981). 7. R. E. Bolz and G. L. Tuve, eds., CRC Handbook of
Tables for Applied Engineering Science (Chemical Rubber Company, Cleveland, Ohio, 1970). 8. J. Stone, J. Appl. Phys. 62, 4371 (1987). 9. J. Bures, J. Lapierre, and D. Pascale, Appl. Phys. Lett. 37, 860 (1980).
10. H. Kolsky, Stress Waves in Solids (Clarendon, Oxford, 1953).
