Abstract

We experimentally demonstrate the phase relations of three-port gratings by investigating three-port coupled Fabry–Perot cavities. Two different gratings that have the same first-order diffraction efficiency but differ substantially in their second-order diffraction efficiency have been designed and manufactured. Using the gratings as couplers to Fabry–Perot cavities, we could validate the results of an earlier theoretical description of the phases at a three-port grating [Opt. Lett. 30, 1183 (2005) ]

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K.-X. Sun and R. L. Byer, Opt. Lett. 23, 567 (1997).
    [CrossRef]
  2. A. Bunkowksi, O. Burmeister, P. Beyersdorf, K. Danzmann, R. Schnabel, T. Clausnitzer, E.-B. Kley, and A. Tünnermann, Opt. Lett. 29, 2342 (2004).
    [CrossRef]
  3. A. Bunkowski, O. Burmeister, K. Danzmann, and R. Schnabel, Opt. Lett. 30, 1183 (2005).
    [CrossRef] [PubMed]
  4. R. Schnabel, A. Bunkowski, O. Burmeister, and K. Danzmann, Opt. Lett. 31, 658 (2006).
    [CrossRef] [PubMed]
  5. M. G. Moharam and T. K. Gaylord, J. Opt. Soc. Am. 72, 1385 (1982).
    [CrossRef]
  6. E.-B. Kley, T. Clausnitzer, M. Cumme, K. Zöllner, and B. Schnabel, in Proc. SPIE 4231, 116 (2000).
    [CrossRef]

2006 (1)

2005 (1)

2004 (1)

2000 (1)

E.-B. Kley, T. Clausnitzer, M. Cumme, K. Zöllner, and B. Schnabel, in Proc. SPIE 4231, 116 (2000).
[CrossRef]

1997 (1)

1982 (1)

Beyersdorf, P.

Bunkowksi, A.

Bunkowski, A.

Burmeister, O.

Byer, R. L.

Clausnitzer, T.

Cumme, M.

E.-B. Kley, T. Clausnitzer, M. Cumme, K. Zöllner, and B. Schnabel, in Proc. SPIE 4231, 116 (2000).
[CrossRef]

Danzmann, K.

Gaylord, T. K.

Kley, E.-B.

Moharam, M. G.

Schnabel, B.

E.-B. Kley, T. Clausnitzer, M. Cumme, K. Zöllner, and B. Schnabel, in Proc. SPIE 4231, 116 (2000).
[CrossRef]

Schnabel, R.

Sun, K.-X.

Tünnermann, A.

Zöllner, K.

E.-B. Kley, T. Clausnitzer, M. Cumme, K. Zöllner, and B. Schnabel, in Proc. SPIE 4231, 116 (2000).
[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 (6)

Fig. 1
Fig. 1

Grating in second-order Littrow mount with naming convention given in text.

Fig. 2
Fig. 2

Calculated power back reflectance c 1 2 for a cavity with coupling η 1 2 = 0.1 and an end mirror with ρ 1 = 1 as a function of cavity tuning ( ϕ ) for selected values of second-order diffraction efficiency η 2 2 .

Fig. 3
Fig. 3

Calculated diffraction efficiencies as a function of groove depth obtained with RCW calculations for the gratings used. The circles show the design values of our gratings G1 and G2, respectively.

Fig. 4
Fig. 4

Experimental setup: PZT, piezoelectric transducer; PD, photodetector.

Fig. 5
Fig. 5

Normalized powers at the three photodetectors for three-port coupler G1 as the cavity length was linearly scanned (solid, blue curve) and the calculated values (dashed-dotted, green curve).

Fig. 6
Fig. 6

Normalized powers at the three photodetectors for three-port coupler G2 as the cavity length was linearly scanned (solid, blue curve) and the calculated values (dashed, green curve).

Equations (7)

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

ϕ 0 = 0 ,
ϕ 1 = ( 1 2 ) arccos [ ( η 1 2 2 η 0 2 ) ( 2 ρ 0 η 0 ) ] ,
ϕ 2 = arccos [ η 1 2 ( 2 η 2 η 0 ) ] ,
c 1 = η 2 exp ( i ϕ 2 ) + η 1 2 exp [ 2 i ( ϕ 1 + ϕ ) ] d ,
c 2 = η 1 exp ( i ϕ 1 ) d ,
c 3 = η 0 + η 1 2 exp [ 2 i ( ϕ 1 + ϕ ) ] d ,
t = i τ 1 c 2 exp ( i ϕ ) ,

Metrics