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Diffractively coupled Fabry-Perot resonator with power-recycling

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Abstract

We demonstrate the optical coupling of two cavities without light transmission through a substrate. As the all-reflective coupling component, we use a dielectric low-efficiency 3-port diffraction grating. In contrast to a conventional transmissive coupling component, such an all-reflective coupler avoids all thermal effects that are associated with light absorption in the substrate. An all-reflective scheme for cavity coupling is of interest in the field of gravitational wave detection. In such detectors light that is resonantly enhanced inside the so-called power-recycling cavity is coupled to (kilometre-scale) Fabry-Perot resonators representing the arms of a Michelson interferometer. We realized such an all-reflective coupling in a table-top experiment. Our findings are in qualitative agreement with the theoretical model incorporating the characteristics of the 3-port grating used, and therefore encourage the application of all-reflective cavity couplers in future gravitational wave detectors.

©2011 Optical Society of America

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Figures (6)

Fig. 1
Fig. 1 Michelson-type interferometer with power-recycling cavity and arm resonators. The transmissive beamsplitter (BS) and the coupling mirrors to the arm cavities (CMn) are exposed to high thermal load (red blur). Each arm cavity (coupling mirror CMn and end mirror EMn) together with the power-recycling mirror (PRM) forms a system of two coupled cavities.
Fig. 2
Fig. 2 (a) 3-port grating in second-order Littrow mount. The amplitude diffraction efficiencies are denoted ηn and reflectivity under normal incidence ρ 0, respectively. (b) By inserting a mirror (EM) perpendicular to the grating a 3-port-grating cavity is generated, with the diffraction efficiency η 1 as the coupling efficiency. The light fields are labeled as follows: The backwards reflected field towards the laser source C1, the intra-cavity field C2, the forward reflected field at the additional grating port C3 and the transmitted field T. (c) Inserting the power-recycling mirror PRM in the entrance, a power-recycled 3-port grating coupled cavity is formed. The light fields are denoted C1PR, C2PR, C3PR and TPR.
Fig. 3
Fig. 3 Geometrical configuration of the experiment. The second-order Littrow angle θ in determines the ratio of the waist size at the grating in horizontal and vertical direction w 0,x and w 0,y. The length of the arm L 2 and the radius of curvature of the end mirror R c defines the absolute waist size at the grating. Together with the length of the power-recycling cavity L 1 these parameters determine the radii of curvature of the PR mirror R c,x and R c,y.
Fig. 4
Fig. 4 Experimental setup of a 3-port-grating cavity with power-recycling. Two cylindrical lenses for each dimension l n are needed to provide mode-matching to the eigenmode of the cavity. The spherical lens l0 compensates the distortion due to the PRM substrate. Photodiodes at the ports (PDC n ) and in transmission of the grating PDGT allow monitoring. The beamsplitter BS in the entrance allows access to the back-reflected field C1PR.
Fig. 5
Fig. 5 Intra-cavity power build-up in the arm cavity as a function of the detunings Φ1 and Φ2 of the PR cavity and the arm cavity, respectively. Plot (a) shows the 2-dimensional simulation. Plots (b) and (c) are projections onto one of the axes, respectively. They well reproduce the experimental data as given in plots (d) and (e). The latter two show the intra-cavity powers transmitted through the grating as detected by photo diode PDGT. For both plots one of the cavity lengths was varied slowly whereas the other was varied fast.
Fig. 6
Fig. 6 Output power at the additional grating port C3PR as a function of the detunings Φ1 and Φ2 of the power-recycling cavity and the arm cavity, respectively. Plot (a) shows the 2-dimensional simulation. Plots (b) and (c) are projections onto one of the axes, respectively. They well reproduce the experimental data as given in plots (d) and (e). The latter two show the output powers as detected by photo diode PDC3. For both plots one of the cavity lengths was varied slowly whereas the other was varied fast. The different peak heights in Fig. (d) were due to non-linearities in the PZTs used to vary the cavity lengths.

Equations (17)

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c 1 = η 2 exp ( i ϕ 2 ) + η 1 2 ρ 2 exp [ i 2 ( ϕ 1 + Φ 2 ) ] d 2 ,
c 2 = η 1 exp ( i ϕ 1 ) d 2 ,
c 3 = η 0 + η 1 2 ρ 2 exp [ i 2 ( ϕ 1 + Φ 2 ) ] d 2 ,
t = i τ 2 exp ( i Φ 2 ) c 2 ,
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 PR = [ ρ 1 c 1 exp ( i 2 Φ 1 ) ] d 1 ,
c 2 PR = i τ 1 exp [ i ( Φ 1 + Φ 2 ) ] c 2 d 1 ,
c 3 PR = i τ 1 exp ( i Φ 1 ) c 3 d 1 ,
t PR = τ 1 τ 2 exp [ i ( Φ 1 + Φ 2 ) ] c 2 d 1 ,
0 g g g m 1
g g = 1 L 2 R c , g = 1 and g m = 1 L 2 R c , m ,
w 0 2 = L 2 λ π g m 1 g m .
w out = cos ( θ out ) cos ( θ in ) w in .
R c , y = L 1 + π 2 w 0 , y 4 λ 2 L 1 ,
R c , x = L 1 + π 2 w 0 , x 4 λ 2 L 1 = L 1 + π 2 w 0 , y 4 λ 2 L 1 ( cos θ in ) 4 .
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