bias close to x radians. The output from a fiber interferometer is of the form. Id = 10 (1 4- vCOS$o),. (1) where, 10 is the input intensity, and V is the fringe visibility.
© 1991 OSA/OFC 1991
82
OFC@‘91
Wednesday, February 20
Optimization of phase detectability in a free-running homodynefiber interferometer T.A. Berkoff, A.D. Kersey,and A. Dandridge
WF2
Optical Techniques Branch, Code 6574, Naval Research Laboratory, Washington, D.C. 20375
Fiber-optic interferometric fiber sensors have been developed for the detection of a range of physical parameters, such as acoustic and magnetic fields.Aconsiderableamount of researcheffortin thisarea has been directed at the development of demodulation techniques which provide linearization of the m i n e transfer function of the basic two beam interferometric system. Furthermore, a number of approaches for improving the phase shift detection sensitivity of fiber interferometers based on intensity noise cancellation,’ and phase noise suppression2 have been developed. Intrinsicsourceintensitynoise is rarelya problem insituations where both interferometer outputs are available, as is generally the case when the Mach-Zehnder ( M Z ) configuration is used. In this case, balanced differential detection’ ensures good rejection of source intensity noise when the output is at quadrature (x/2 relative phase differencebehveen the fiber arms). However, in systems based on the use of a configuration with a single output, such as in the case of a Michelson interferometer, or in situations where only a single output is accessible from an MZ interferometer, intensity noise can limit the phase detection sensitivity of thesystem.Hereweshow thatundersuchcircynstances theoptimum phase detection sensitivity is achieved not at quadrature, but at a phase bias close to x radians. The output from a fiber interferometer is of the form Id
=10 (1 4- vCOS$o),
eter (single output) is plotted versus the phase bias point. The source used as a 1.3pm Nd:YAG non-plannar ring laser which exhibited a RIN of - - 1 1 5 d B / a a t thesignal frequency. The visibility of the interferometer output was > 0.95. Clearly, as can be seen improved signal to noise in the detected phase shift was observed for phase bias points removed from quadrature as predicted. This work is supported by the Office of Naval Technology.
REFERENCES 1. A. Dandridge and A.B. Tveten, Appl. Opt. 20,2337 (1981). A. D. Kersey and T. A. Berkoff, Electron. Lett. 26,640 (1990).
2.
20
10
I
n12
3d4
n
I
Phase Bias. rads.
Rg. 1. Theoretical plot of sensitivity to noise ratio versus interferometer phase bias for visibilities from 0.79 to 0.99.
(1)
where, 10 is the input intensity, and V is the fringe visibility. The sensitivity of the output to a small signal perturbation in $0 is
m 75.
-50
p
O
If the relative intensity noise (RIN) of the source is X,the intensity noise at the detected output isAI=yId.Theratioof the interferometer sensitivity to intensity noise is then by Eqs. (1)and (2):
-S VsinOo AJ - ‘tf1+ v COSl$o)
(3) L
This ratio reflects the relativesignal to noiseof theoutput. Figure 1shows a theoretical plot of the ratio S/Al against phase bias $o, for various visibilities from 0.8 to 0.99. Clearly, the ratio of sensitivity to noise increases as the phase bias approaches x radians, until it reaches an optimum leve1before falling off at a bias of x. Furthennore, it can be seen that the bias at which optimum sensitivity tonoise occurs increases with increasing visibility. Figure 2 shows experimental confirmation of this theoretical result. Here, the signal to noise ratio of a weak phase shift signal(2mrad rms at 10 kHz) detected at theoutput of a MZ interferom-
p.
.
5 60d2
3d4
-90
Phase Bias, rads.
Fig. 2. Experimentally observed improvement in output S/N ratio for an interferometer with a visibility V-0.95. Also shown is themeaswdinterferometer sensitivity,dl%& which falls according to the expected sin(C) dependence[Fq.(211.
