Fresnel-Fizeau effect in a rotating optical fiber ring interferometer V. Vali, R. W. Shorthill, and M. F. Berg University of Utah Research Institute, Geospace Sciences Laboratory, Salt Lake City, Utah 84108. Received 15 April 1977. Linear Fresnel drag was observed more than 100 years ago. 1 Using a low loss optical fiber waveguide as the beam path in ring interferometers, the rotational Fresnel drag coefficient can be measured. The beam path in the moving medium—thefiber—cannow be made very long. This makes the observed fringe shift large even for small angular veloci- ties. 2 This Letter reports on some measurements made in the program of building a fiber ring interferometer gyroscope. The results are accurate enough to detect the presence of the dispersion term in the drag coefficient. Its temperature de- pendence determines some of the temperature sensitivity of the fiber gyroscope. The method is also an alternative way of measuring the fiber dispersion, which determines the maximum pulse rate that can be transmitted through single mode fibers in optical communication systems. Fiber ring interferometers have been built up to 950 m of fiber length. 3 - 4 The optical pathlengths of the counterrotating beams are identical, unless some nonreciprocal effect is in- troduced. The Sagnac effect causes the lengthening of the optical path of the beam traveling with the rotation and shortening for the oppositely traveling beam and, therefore, produces a fringe shift. When the beam path is in a refracting medium (such as an optical fiber waveguide), there are three different configurations (relative motions) of the optical components, giving rise to three different size fringe shifts: First: rotating ring interferometer with corotating medium (fiber beam path). This is the classical Sagnac interferometer with a refracting beam path. The fringe shift ΔZ 1 is 5 where ω is the rotation velocity, A is the area enclosed by the counterrotating beams (A = πR 2 ),R is the radius of the cir- cular beam path, N is the number of turns of the fiber around the area A, L is the length of the fiber (L = N2πR), λ is the free space wavelength of light, c is the free space velocity of light, n is the index of refraction of the fiberα, and is the Fresnel drag coefficient, The last term is the material dispersion term caused by the Doppler effect and is about 2.5% for fused silica at λ = 632.8 nm. 2 When the dispersion term is neglected, the fringe shift ΔZ 1 is independent of the presence of the refracting medium in the beam path. Second: rotating interferometer with stationary medium. The fringe shift ΔZ 2 is 5 This indicates that here the effective wavelength and the ve- locity of light are determined by the refracting medium where λ g = λ/n and c g = c/n. October 1977 / Vol. 16, No. 10 / APPLIED OPTICS 2605
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Fresnel-Fizeau effect in a rotating optical fiber ring interferometer V. Vali, R. W. Shorthill, and M. F. Berg
University of Utah Research Institute, Geospace Sciences Laboratory, Salt Lake City, Utah 84108. Received 15 April 1977. Linear Fresnel drag was observed more than 100 years
ago.1 Using a low loss optical fiber waveguide as the beam path in ring interferometers, the rotational Fresnel drag coefficient can be measured. The beam path in the moving medium—the fiber—can now be made very long. This makes the observed fringe shift large even for small angular velocities.2 This Letter reports on some measurements made in the program of building a fiber ring interferometer gyroscope. The results are accurate enough to detect the presence of the dispersion term in the drag coefficient. Its temperature dependence determines some of the temperature sensitivity of the fiber gyroscope. The method is also an alternative way of measuring the fiber dispersion, which determines the maximum pulse rate that can be transmitted through single mode fibers in optical communication systems.
Fiber ring interferometers have been built up to 950 m of fiber length.3-4 The optical pathlengths of the counterrotating beams are identical, unless some nonreciprocal effect is introduced. The Sagnac effect causes the lengthening of the optical path of the beam traveling with the rotation and shortening for the oppositely traveling beam and, therefore, produces a fringe shift. When the beam path is in a refracting medium (such as an optical fiber waveguide), there are three different configurations (relative motions) of the optical components, giving rise to three different size fringe shifts:
First: rotating ring interferometer with corotating medium (fiber beam path). This is the classical Sagnac interferometer with a refracting beam path. The fringe shift ΔZ1 is5
where ω is the rotation velocity, A is the area enclosed by the counterrotating beams (A = πR2),R is the radius of the circular beam path, N is the number of turns of the fiber around the area A, L is the length of the fiber (L = N2πR), λ is the free space wavelength of light, c is the free space velocity of light, n is the index of refraction of the fiberα, and is the Fresnel drag coefficient,
The last term is the material dispersion term caused by the Doppler effect and is about 2.5% for fused silica at λ = 632.8 nm.2 When the dispersion term is neglected, the fringe shift ΔZ1 is independent of the presence of the refracting medium in the beam path.
Second: rotating interferometer with stationary medium. The fringe shift ΔZ2 is5
This indicates that here the effective wavelength and the velocity of light are determined by the refracting medium
Fig. 1. Arrangement of the fiber and the interferometer components. Fiber coil is mounted on a rotating table. Only in region C is the fiber bent when the coil is rotated. The table axis carries instruments to measure the rotation angle and the angular velocity. M—fiber end manipulators; BS—beamsplitters; and L—focusing lenses. Two
circular fringe patterns are formed at photodetectors F1 and F2.
Third: stationary interferometer with rotating medium. This is the rotational version of the Fresnel-Fizeau drag experiment. The fringe shift ΔZ3 is5
To determine the rotational α, a fiber ring interferometer was built with the coil radius equal to 25.5 cm (see Fig. 1). Eighty-five meters of single mode fiber (at λ = 632.8 nm) was used as the beam path (53 turns). The fiber was made by ITT, its core diameter is 4.4 μm, the core index of refraction n = 1.457, and its attenuation coefficient γ = 15 dB/km.
The fiber coil is mounted on a rotating table. To minimize the effects of bending, the fiber ends were brought out of the coil to the axis of rotation and then fixed to a nonrotating platform (Fig. 1). This leaves about 5 cm of fiber free to bend as the coil is rotated through about 180°. Care has to be taken to eliminate any twisting of the fiber since torsional strains produce nonreciprocal effects in the fiber. The rotation velocity was varied between ±5 rad/sec. A Spectra-Physics model 138 He-Ne laser was used as the light source. The two fringe patterns that are formed are 180° out of phase with respect to each other. Figure 2 shows the two sets of fringes. The intensity of the fringes at F2 is half the intensity at F1. Photodetectors are placed such that only the centers of the fringes are used. The detectors are optically balanced (by the use of irises) when the fringe centers are at half maximum intensity points. The photocurrent difference is recorded as the output. The effects of laser intensity fluctuations are thus minimized.
A measurement of the fringe shift as a function of the angular velocity ω consisted of recording ω on the horizontal axis and the photocurrent difference on the vertical axis on an x-y scope. One such recording is shown in Fig. 3.
The angular velocity was calibrated by recording the angle and the output of a dc generator (used as the angular velocity transducer) as a function of time. The measurement accuracy
Fig. 3. A typical recording of the fringe shift (vertical axis) vs the angular velocity (horizontal axis). Noise is primarily from the angular
velocity transducer.
was determined by the scope accuracy (≃1%) and by the accuracy of reading the fringe shift on ΔZ3(ω) records (≃1%). The total measurement error for α was therefore 1.4%. This can be improved considerably by the use of digital readouts for ω and the fringe shift and by removing the slight sticking in the dc generator, which caused most of the noise on the fringe shift records (Fig. 3). The experimental result with the present equipment is
3.85 ±0.05 rad/sec/fringe.
Using the theoretical fringe shift formula ΔZ3 with the dispersion term amounting 2.5% and with ω = 3.85 rad/sec, R = 25.5 cm, L = 0.849104 cm, λ = 632.8 nm, c = 3 1010 cm/sec, n = 1.457, and α = 0.542, one gets
Therefore, the drag for rotational Fresnel experiment is, within the errors, equal to that given in an inertial frame of reference (linear drag).
This work was supported by the Office of Aeronautics and Space Technology, National Aeronautics and Space Administration and the Office of Naval Research, Washington, D.C.
References 1. H. Fizeau, Compt. Rend. 33, 349 (1851). 2. H. R. Bilger and A. T. Zavodny, Phys. Rev. A 5, 591 (1972). 3. V. Vali and R. W. Shorthill, Appl. Opt. 15, 1099 (1976). 4. V. Vali and R. W. Shorthill, Appl. Opt. 16, 290 (1977). 5. E. J. Post, Rev. Mod. Phys. 39, 475 (1967).
