Abstract

We describe a free-space common-path polarization Sagnac interferometer. The polarization Sagnac interferometer is used in a symmetric fashion with detection on the dark fringe of the interference to avoid photodetector saturation when high-powered illumination is used. By modulating the carrier field that is reflected from the interferometer, we generate a local oscillator for heterodyne detection of the signal field. We calculate the effect of optical element misalignments and imperfect polarization on the shot-noise–limited sensitivity of the interferometer. The predictions are experimentally verified with a 2-m arm-length tabletop polarization Sagnac interferometer.

© 1999 Optical Society of America

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References

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  1. S. E. H. J. Arditty, ed., Fiber-Optic Rotation Sensors and Related Technologies (Springer-Verlag, New York, 1982), Vol. 32.
  2. D. A. Jackson, A. D. Kersey, and A. C. Lewin, “Fibre gyroscope with passive quadrature detection,” Electron. Lett. 20, 399–401 (1984).
    [CrossRef]
  3. M. A. Novikov, “Polarization ring interferometer–ellipsometer,” Opt. Spektrosk. 61, 424–427 (1986).
  4. K.-X. Sun, M. M. Fejer, E. K. Gustafson, and R. L. Byer, “Balanced heterodyne signal extraction in a postmodulated Sagnac interferometer at low frequency,” Opt. Lett. 22, 1485–1487 (1997).
    [CrossRef]
  5. K.-X. Sun, E. K. Gustafson, M. M. Fejer, and R. L. Byer, “Polarization-based balanced heterodyne detection method in a Sagnac interferometer for precision phase measurement,” Opt. Lett. 22, 1359–1361 (1997).
    [CrossRef]
  6. B. Wilke, N. Uehara, E. K. Gustafson, R. L. Byer, P. J. King, S. U. Seel, and R. L. Savage, Jr., “Spatial and temporal filtering of a 10-W Nd: YAG laser with a Fabry–Perot ring-cavity premode cleaner,” Opt. Lett. 23, 1704–1706 (1998).
    [CrossRef]
  7. K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac interferometer for gravitational-wave detection,” Phys. Rev. Lett. 76, 3053–3056 (1996).
    [CrossRef] [PubMed]
  8. E. Hecht, Optics, 3rd ed. (Addison-Wesley, Reading, Mass., 1998), pp. 321–326.

1998 (1)

1997 (2)

1996 (1)

K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac interferometer for gravitational-wave detection,” Phys. Rev. Lett. 76, 3053–3056 (1996).
[CrossRef] [PubMed]

1986 (1)

M. A. Novikov, “Polarization ring interferometer–ellipsometer,” Opt. Spektrosk. 61, 424–427 (1986).

1984 (1)

D. A. Jackson, A. D. Kersey, and A. C. Lewin, “Fibre gyroscope with passive quadrature detection,” Electron. Lett. 20, 399–401 (1984).
[CrossRef]

Byer, R. L.

Fejer, M. M.

Gustafson, E.

K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac interferometer for gravitational-wave detection,” Phys. Rev. Lett. 76, 3053–3056 (1996).
[CrossRef] [PubMed]

Gustafson, E. K.

Jackson, D. A.

D. A. Jackson, A. D. Kersey, and A. C. Lewin, “Fibre gyroscope with passive quadrature detection,” Electron. Lett. 20, 399–401 (1984).
[CrossRef]

Kersey, A. D.

D. A. Jackson, A. D. Kersey, and A. C. Lewin, “Fibre gyroscope with passive quadrature detection,” Electron. Lett. 20, 399–401 (1984).
[CrossRef]

King, P. J.

Lewin, A. C.

D. A. Jackson, A. D. Kersey, and A. C. Lewin, “Fibre gyroscope with passive quadrature detection,” Electron. Lett. 20, 399–401 (1984).
[CrossRef]

Novikov, M. A.

M. A. Novikov, “Polarization ring interferometer–ellipsometer,” Opt. Spektrosk. 61, 424–427 (1986).

Savage Jr., R. L.

Seel, S. U.

Sun, K.-X.

Uehara, N.

Wilke, B.

Electron. Lett. (1)

D. A. Jackson, A. D. Kersey, and A. C. Lewin, “Fibre gyroscope with passive quadrature detection,” Electron. Lett. 20, 399–401 (1984).
[CrossRef]

Opt. Lett. (3)

Opt. Spektrosk. (1)

M. A. Novikov, “Polarization ring interferometer–ellipsometer,” Opt. Spektrosk. 61, 424–427 (1986).

Phys. Rev. Lett. (1)

K.-X. Sun, M. M. Fejer, E. Gustafson, and R. L. Byer, “Sagnac interferometer for gravitational-wave detection,” Phys. Rev. Lett. 76, 3053–3056 (1996).
[CrossRef] [PubMed]

Other (2)

E. Hecht, Optics, 3rd ed. (Addison-Wesley, Reading, Mass., 1998), pp. 321–326.

S. E. H. J. Arditty, ed., Fiber-Optic Rotation Sensors and Related Technologies (Springer-Verlag, New York, 1982), Vol. 32.

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Figures (6)

Fig. 1
Fig. 1

(a) Minimum-reciprocal-configuration Sagnac interferometer used as a rotation sensor. Necessary elements include a spatial filter (SF) to select a single input and output spatial mode, a linear polarizer (LP) to remove polarization degeneracy of the detected mode, a detector (DET) on the reciprocal port of the beam splitter, and a phase modulator (PM) to produce a modulated phase bias for detection. (b) Polarization Sagnac interferometer in a symmetrical configuration. The in-loop phase modulator has been replaced by an external postmodulation scheme. Dotted line, the input and output plane.

Fig. 2
Fig. 2

Elliptical polarization state of interferometer output. (a) The relative phase shift Δϕ between the orthogonally polarized interfering beams produces an elliptical polarization state. (b) The output is resolved into polarization components along the principle axes of the ellipse. The dark polarization, the minor axis of the ellipse, contains the signal field and is a measure of the phase shift. The bright polarization, the major axis of the ellipse, is the carrier field and contains most of the power.

Fig. 3
Fig. 3

Heterodyne detection scheme. The polarization state of the signal and the local oscillator is shown at (A) selection from the interferometer, (B) after rotation by the half-wave plate HWP, and (C) and (D) on each of the balanced detectors. The phase modulator PM acts only on the vertical polarization.

Fig. 4
Fig. 4

Optical layout of the polarization Sagnac interferometer with linear polarizer (LP), polarizing beam splitters (PBS), half-wave plates (HWP), quarter-wave plate (QWP), spatial filter (SF), electro-optic modulators (EOM), and photodetectors (DET). Each arm contains a 75-bounce, 2-m long-delay line. The beam splitter PBS1 is slightly tilted to leak 0.3% of the cross polarization. Not shown is the stable resonant cavity immediately after the laser.

Fig. 5
Fig. 5

Frequency response of the polarization Sagnac to phase modulation imposed by the electro-optic modulator EOM1. The dc power level is normalized to 1. Dashed curve, the predicted response.

Fig. 6
Fig. 6

Reduction in power observed when an adjustable wave plate was present in the interferometer loop providing various levels of birefringence oriented at various angles with respect to the polarization direction of the beams. Dotted curve, Eq. (13).

Equations (17)

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C=Pbp-PdpPbp+Pdp,
Pˆt=i1-x00x,
Pˆr=x001-x,
Sˆ+=exp(iΔϕ/2)1001,
Sˆ-=exp(-iΔϕ/2)1001
Eout=Hˆ1(Pˆ2,tSˆ-Hˆ2Pˆ2,r+Pˆ2,rHˆ2Sˆ+Pˆ2,t)Hˆ1·Ein,
Eout=i cos(Δϕ/2)[(1-2x2)sin 4θ1 sin 2θ2+2x2(1-x2) cos 2θ2]sin(Δϕ/2)sin 2θ2-i cos(Δϕ/2)[(1-2x2)cos 4θ1 sin 2θ2]|Ein|,
Eout=x1001-x1Eout,
|Δϕ|4π(PLO+Pdp)flPLOPinηiηdC21/2,
Eout=ix1Δϕ(1-x1)/2|Ein|
Cmax(φ)=cos(φ).
Cmax(Δθ1)=1-(2x2-1)2 sin2 4Δθl
ηi=cos2(Γ/2)+cos2(2θ)sin2(Γ/2),
ϕ<3.6°,
Δθ1<0.6°,
Γ<0.02λatθ=45°,
θ<2.5°atΓ=0.25λ,

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