Abstract

We derive generic phase and amplitude coupling relations for beam splitters–combiners that couple a single port with three output ports or input ports, respectively. We apply the coupling relations to a reflection grating that serves as a coupler to a single-ended Fabry–Perot ring cavity. In the impedance-matched case such an interferometer can act as an all-reflective ring mode cleaner. It is further shown that in the highly undercoupled case almost complete separation of carrier power and phase signal from a cavity strain can be achieved.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Bunkowski, O. Burmeister, P. Beyersdorf, K. Danzmann, R. Schnabel, T. Clausnitzer, E.-B. Kley, and A. Tünnermann, Opt. Lett. 29, 2342 (2004).
    [CrossRef] [PubMed]
  2. A. Bunkowski, O. Burmeister, K. Danzmann, and R. Schnabel, Opt. Lett. 30, 1183 (2005).
    [CrossRef] [PubMed]
  3. A. E. Siegmann, Lasers (University Science Books, 1986), p. 401.
  4. T. Clausnitzer, E.-B. Kley, A. Tünnermann, A. Bunkowski, O. Burmeister, K. Danzmann, R. Schnabel, A. Duparré, and S. Gliech, Opt. Express 13, 4370 (2005).
    [CrossRef] [PubMed]
  5. G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
    [CrossRef]

2005 (2)

2004 (1)

1998 (1)

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Beyersdorf, P.

Bunkowski, A.

Burmeister, O.

Clausnitzer, T.

Danzmann, K.

Duparré, A.

Gliech, S.

Heinzel, G.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Kley, E.-B.

Mizuno, J.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Rüdiger, A.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Schilling, R.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Schnabel, R.

Siegmann, A. E.

A. E. Siegmann, Lasers (University Science Books, 1986), p. 401.

Skeldon, K. D.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Strain, K. A.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Tünnermann, A.

Willke, B.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Winkler, W.

G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, and K. Danzmann, Phys. Rev. Lett. 81, 5493 (1998).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

(Color online) Two examples of the three-port (3p) beam splitters and/or combiners. Input fields a i and output fields b i denote complex amplitudes of the electric field. (a) Asymmetric triangular grating in second-order Littrow configuration. (b) Binary grating in non-Littrow configuration.

Fig. 2
Fig. 2

(Color online) Three-port coupled grating in a ring Fabry–Perot interferometer. The grating can be designed such that the laser input is completely sent into port c 1 on cavity resonance. If the cavity is impedance matched this device might serve as an all-reflective mode cleaner. Another interesting case occurs in which the cavity is highly undercoupled. Then almost the complete cavity strain signals are sent to port c 3 . Such a device separates carrier light from its modulation sidebands.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

( b 1 b 2 b 3 ) = ( η 1 e i ϕ 1 η 4 e i ϕ 4 η 5 e i ϕ 5 η 4 e i ϕ 4 η 2 e i ϕ 2 η 6 e i ϕ 6 η 5 e i ϕ 5 η 6 e i ϕ 6 η 3 e i ϕ 3 ) × ( a 1 a 2 a 3 ) ,
1 = η 1 2 + η 4 2 + η 5 2 ,
1 = η 2 2 + η 4 2 + η 6 2 ,
1 = η 3 2 + η 5 2 + η 6 2 ,
cos ( 2 ϕ 4 ϕ 1 ϕ 2 ) = η 5 2 η 6 2 η 1 2 η 4 2 η 2 2 η 4 2 2 η 4 2 η 1 η 2 ,
cos ( 2 ϕ 5 ϕ 1 ϕ 3 ) = η 4 2 η 6 2 η 1 2 η 5 2 η 3 2 η 5 2 2 η 5 2 η 1 η 3 ,
cos ( 2 ϕ 6 ϕ 2 ϕ 3 ) = η 4 2 η 5 2 η 2 2 η 6 2 η 3 2 η 6 2 2 η 6 2 η 2 η 3 ,
cos ( ϕ 6 + ϕ 4 ϕ 5 ϕ 2 ) = η 1 2 η 4 2 η 2 2 η 4 2 η 5 2 η 6 2 2 η 2 η 4 η 5 η 6 ,
cos ( ϕ 6 ϕ 4 ϕ 5 + ϕ 1 ) = η 3 2 η 5 2 η 1 2 η 5 2 η 4 2 η 6 2 2 η 1 η 4 η 5 η 6 ,
cos ( ϕ 6 ϕ 4 + ϕ 5 ϕ 3 ) = η 2 2 η 6 2 η 4 2 η 5 2 η 3 2 η 6 2 2 η 3 η 4 η 5 η 6 .
ϕ 1 = ϕ 2 = ϕ 3 = 0 ,
ϕ 4 = 1 2 arccos ( η 1 2 η 4 2 + η 2 2 η 4 2 η 5 2 η 6 2 2 η 4 2 η 1 η 2 ) π 2 ,
ϕ 5 = 1 2 arccos ( η 4 2 η 6 2 η 1 2 η 5 2 η 3 2 η 5 2 2 η 5 2 η 1 η 3 ) ,
ϕ 6 = 1 2 arccos ( η 2 2 η 6 2 + η 3 2 η 6 2 η 4 2 η 5 2 2 η 6 2 η 2 η 3 ) + π 2 .
η 4 η 6 ( 1 η 2 ) η 4 2 + η 6 2 η 5 η 4 η 6 ( 1 + η 2 ) η 4 2 + η 6 2 .
( c 1 c 2 c 3 ) = S × ( 1 c 2 exp ( 2 i θ ) 0 ) .
c 1 = η 1 + η 4 2 exp [ 2 i ( ϕ 4 + θ ) ] 1 η 2 exp ( 2 i θ ) ,
c 2 = η 4 exp ( i ϕ 4 ) 1 η 2 exp ( 2 i θ ) ,
c 3 = η 5 exp ( i ϕ 5 ) + η 4 η 6 exp [ i ( ϕ 4 + ϕ 6 + 2 θ ) ] 1 η 2 exp ( 2 i θ ) .
η 4 2 = 0.0001 , η 6 2 = 0.0099 , η 2 2 = 0.99 ,
η 5 2 = 0.0394 , η 1 2 = 0.9605 , η 3 2 = 0.9507 ,
ϕ 1 = 0 , ϕ 2 = 0 , ϕ 3 = 0 ,
ϕ 4 3.1349 , ϕ 5 1.5708 , ϕ 6 1.5707 .

Metrics