Abstract

All-reflective optical systems are under consideration for future gravitational wave detector topologies. A key feature of these all-reflective systems is the use of Fabry–Perot cavities with diffraction gratings as input couplers; however, theory predicts and experiment has shown that translation of the grating surface across the incident laser light will introduce additional phase into the system. This translation can be induced through simple side-to-side motion of the coupler, yaw motion of the coupler around a central point (i.e., rotation about a vertical axis), and even via internal resonances (i.e., vibration) of the optical element. In this Letter we demonstrate on a prototype-scale suspended cavity that conventional cavity length-sensing techniques used to detect longitudinal changes along the cavity axis will also be sensitive to translational, rotational, and vibrational motion of the diffractive input coupler. We also experimentally verify the amplitude response and frequency dependency of the noise coupling as given by theory.

© 2011 Optical Society of America

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References

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  7. M. P. Edgar, B. W. Barr, J. Nelson, M. V. Plissi, K. A. Strain, O. Burmeister, M. Britzger, K. Danzmann, R. Schnabel, T. Clausnitzer, F. Brückner, E.-B. Kley, A. Tünnermann, Opt. Lett. 34, 3184 (2009).
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2009

2007

A. Freise, A. Bunkowski, R. Schnabel, New J. Phys. 9, 433 (2007).
[CrossRef]

2005

P. Aufmuth, K. Danzmann, New J. Phys. 7, 202 (2005).
[CrossRef]

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

2004

Aufmuth, P.

P. Aufmuth, K. Danzmann, New J. Phys. 7, 202 (2005).
[CrossRef]

Barr, B.

J. Hallam, S. Chelkowski, A. Freise, S. Hild, B. Barr, K. A. Strain, O. Burmeister, R. Schnabel, J. Opt. A 11, 085502 (2009).
[CrossRef]

Barr, B. W.

Beyersdorf, P.

Britzger, M.

Brückner, F.

Bunkowski, A.

Burmeister, O.

Chelkowski, S.

J. Hallam, S. Chelkowski, A. Freise, S. Hild, B. Barr, K. A. Strain, O. Burmeister, R. Schnabel, J. Opt. A 11, 085502 (2009).
[CrossRef]

Chen, Y.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

Clausnitzer, T.

Danzmann, K.

Deshpande, A. J.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

Edgar, M. P.

Freise, A.

J. Hallam, S. Chelkowski, A. Freise, S. Hild, B. Barr, K. A. Strain, O. Burmeister, R. Schnabel, J. Opt. A 11, 085502 (2009).
[CrossRef]

A. Freise, A. Bunkowski, R. Schnabel, New J. Phys. 9, 433 (2007).
[CrossRef]

Hallam, J.

J. Hallam, S. Chelkowski, A. Freise, S. Hild, B. Barr, K. A. Strain, O. Burmeister, R. Schnabel, J. Opt. A 11, 085502 (2009).
[CrossRef]

Hild, S.

J. Hallam, S. Chelkowski, A. Freise, S. Hild, B. Barr, K. A. Strain, O. Burmeister, R. Schnabel, J. Opt. A 11, 085502 (2009).
[CrossRef]

Kley, E.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

Kley, E.-B.

Mueller, G.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

Nelson, J.

Plissi, M. V.

Quetschke, V.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

Reitze, D. H.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

Schnabel, R.

Siegman, A. E.

A. E. Siegman, Lasers (1986), Chap. 18.

Strain, K. A.

Tanner, D. B.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

Tünnermann, A.

Whiting, B. F.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

Wise, S.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

J. Opt. A

J. Hallam, S. Chelkowski, A. Freise, S. Hild, B. Barr, K. A. Strain, O. Burmeister, R. Schnabel, J. Opt. A 11, 085502 (2009).
[CrossRef]

New J. Phys.

P. Aufmuth, K. Danzmann, New J. Phys. 7, 202 (2005).
[CrossRef]

A. Freise, A. Bunkowski, R. Schnabel, New J. Phys. 9, 433 (2007).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, T. Clausnitzer, Phys. Rev. Lett. 95, 013901 (2005).
[CrossRef] [PubMed]

Other

A. E. Siegman, Lasers (1986), Chap. 18.

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Figures (5)

Fig. 1
Fig. 1

Translating the incident beam across a grating by Δ x gives an optical path length change ζ B ζ A , where α and β m are the input angle and m-th order diffraction angles, respectively. The same effect is observed if the grating is translated rather than the input beam.

Fig. 2
Fig. 2

Experimental diffractive cavity layout indicating the cavity coupling ports c 1 (back reflected), c 2 t (transmitted) and c 3 (forward reflected). The diffractive optic is a composite element composed of a low-efficiency diffractive coupler on a 1 inch substrate, which is mounted in an aluminum test mass of comparable size and mass to the end mirror.

Fig. 3
Fig. 3

Driving translational grating motion using coil-magnet actuators. (a) pure side-to-side motion produced by actuating from the side and correcting for any additional twisting motion using the rear coils, (b) rear coil actuation drives the mass in yaw causing side-to-side motion of the front surface.

Fig. 4
Fig. 4

Measured translational displacement response to a fixed amplitude driving signal [method (a) in Fig. 3].

Fig. 5
Fig. 5

Predicted and measured signal responses at port c 3 for several grating motions with a fixed amplitude driving signal. The pure-translational and yaw signals [driving methods (a) and (b) respectively] demonstrate clear 1 / f responses. Above 300 Hz the pure-translational signal is dominated by an internal resonance of the diffractive coupler. The longitudinal signal response follows 1 / f 2 , unaffected by grating behavior.

Equations (2)

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ζ m = ζ B ζ A = Δ x ( sin α + sin β m ) = Δ x m λ d ,
a 3 = i p 0 η 1 2 exp ( 2 i ϕ 1 ) π Δ x d ρ 2 ( B u B c ) ,

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