Abstract

We built an ultra-low-noise angle sensor by combining a folded optical lever and a Sagnac interferometer. The instrument has a measured noise floor of 1.3prad/Hz at 2.4kHz. We achieve this record angle sensitivity using a proof-of-concept apparatus with a conservative N=11 bounces in the optical lever. This technique could be extended to reach subpicoradian/Hz sensitivities with an optimized design.

© 2011 Optical Society of America

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References

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  1. P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
    [CrossRef] [PubMed]
  2. M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
    [CrossRef]
  3. O. Lorrain, Opt. Lasers Eng. 15, 197 (1991).
    [CrossRef]
  4. Signal integration times are not given in , so we cannot directly compare noise performance.
  5. C. A. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, Ultramicroscopy 42–44, 1509 (1992).
    [CrossRef]
  6. D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
    [CrossRef]
  7. J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
    [CrossRef]
  8. K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, Phys. Rev. Lett. 91, 260602 (2003).
    [CrossRef]

2010 (2)

M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
[CrossRef]

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

2009 (2)

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

2003 (1)

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

1992 (1)

C. A. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, Ultramicroscopy 42–44, 1509 (1992).
[CrossRef]

1991 (1)

O. Lorrain, Opt. Lasers Eng. 15, 197 (1991).
[CrossRef]

Ando, M.

M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
[CrossRef]

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

de Grooth, B. G.

C. A. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, Ultramicroscopy 42–44, 1509 (1992).
[CrossRef]

Dixon, P. B.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

Greve, J.

C. A. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, Ultramicroscopy 42–44, 1509 (1992).
[CrossRef]

Howell, J. C.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

Ishidoshiro, K.

M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
[CrossRef]

Jordan, A. N.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

Kokuyama, W.

M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
[CrossRef]

Lorrain, O.

O. Lorrain, Opt. Lasers Eng. 15, 197 (1991).
[CrossRef]

Numata, K.

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

Otsuka, S.

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

Putman, C. A.

C. A. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, Ultramicroscopy 42–44, 1509 (1992).
[CrossRef]

Starling, D. J.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

Takamori, A.

M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
[CrossRef]

Tsubono, K.

M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
[CrossRef]

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

van Hulst, N. F.

C. A. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, Ultramicroscopy 42–44, 1509 (1992).
[CrossRef]

Vudyasetu, P. K.

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

Yagi, K.

M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
[CrossRef]

Yamamoto, K.

M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
[CrossRef]

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

Opt. Lasers Eng. (1)

O. Lorrain, Opt. Lasers Eng. 15, 197 (1991).
[CrossRef]

Phys. Rev. A (2)

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, Phys. Rev. A 80, 041803 (2009).
[CrossRef]

J. C. Howell, D. J. Starling, P. B. Dixon, P. K. Vudyasetu, and A. N. Jordan, Phys. Rev. A 81, 033813 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

K. Numata, M. Ando, K. Yamamoto, S. Otsuka, and K. Tsubono, Phys. Rev. Lett. 91, 260602 (2003).
[CrossRef]

P. B. Dixon, D. J. Starling, A. N. Jordan, and J. C. Howell, Phys. Rev. Lett. 102, 173601 (2009).
[CrossRef] [PubMed]

M. Ando, K. Ishidoshiro, K. Yamamoto, K. Yagi, W. Kokuyama, K. Tsubono, and A. Takamori, Phys. Rev. Lett. 105, 161101 (2010).
[CrossRef]

Ultramicroscopy (1)

C. A. Putman, B. G. de Grooth, N. F. van Hulst, and J. Greve, Ultramicroscopy 42–44, 1509 (1992).
[CrossRef]

Other (1)

Signal integration times are not given in , so we cannot directly compare noise performance.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup consisting of an optical lever inside a Sagnac interferometer. Deflections δ θ of one of the optical lever mirrors are measured using a position sensitive split detector (PD): SF, pinhole spatial filter; PZT, piezoelectric transducer; NBS, nonpolarizing beam splitter; PBS, polarizing beam splitter; P, polarizer; λ / 4 , quarter-wave plate; λ / 2 , half-wave plate; L1, L2, L3, lenses; DBR, 850 nm laser source.

Fig. 2
Fig. 2

Angle noise optimization. The fit (solid, dark curve) is to a noise model that includes shot noise (dashed curve) and technical noise (solid, gray curve).

Fig. 3
Fig. 3

Angle amplitude spectral density. The black (solid) curve is the Sagnac measurement for ϕ = 84.6 ° . The gray (dashed) curve shows the deflection calibration trace with no Sagnac enhancement. The resolution bandwidth is 4 Hz .

Fig. 4
Fig. 4

Sagnac signal response. The response initially increases as ϕ 0 but is then suppressed due to intensity imbalance. For a small ϕ, the theory using the measured intensity ratio η = 1.3 (dashed curve) differs from the results of a single parameter fit ( η = 1.61 ± 0.01 , solid curve).

Equations (2)

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S = p 1 p 2 p 1 + p 2 = 2 π k σ δ θ cot ( ϕ / 2 ) ,
A ( ϕ ) = 1 L eff ( η 1 ) L eff + η γ k σ 2 sin ( ϕ ) 1 + η 2 η cos ( ϕ ) ,

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