Coupling of frequency dependent length changes to the light phase in a double grating setup Volker Quetschke, Stacy Wise, Guido Mueller, David Reitze, David Tanner, Bernard Whiting Department of Physics University of Florida Configurations session, March 17, 2004 LIGO-G040089-00-Z

Geometric layout Verfügbar erläutern!

Geometric layout II The model shown allows a simpler derivation for the optical path L(w), see [1] [1] M.V. Lebedev, Journal of Experimental and Theoretical Physics, Vol. 93, No. 4, 2001, pp. 823-829

Phase vs. Length Common use: But look at the differential form: This leads to:

Phase vs. Length II It has been shown [3] that Fermat‘s principle can be used with diffraction gratings. The optical path is extremal: Therefore: [3] S.D. Brorson and H.A. Haus, J. Opt. Soc. Am. B 5, 247(1988)

Contradiction? Is it possible to have this: geometric (i) And this: infinitesimal (ii) (i) is the “macroscopic” length definition, Fermat’s principle (ii) can still be applicable. ? Yes!

Microscopic view – Very simple model geometric infinitesimal Steps can occur in in the microscopic picture Note: The integral over L is the same for both cases

Consequences What happens to our experiment when we accept and therefore get: ?

Applying This allows us to calculate F by integrating: Rautian integrated [2] the previously given formula for the phase between A and B: To get the phase difference between two different frequencies w1 and w2 calculate: [2] S.G. Rautian, Optics and Spectroskopy, Vol. 93, No. 6, 2002

Results for our Experiment These experimental parameters result in these calculated results: Path length from A to B for 1064nm Phase difference: “Free space” phase difference for p “Classic” phase difference:

Interpretation of this result The Phase difference for the two light fields in this double-grating setup matches the phase difference for the same light fields when traveling through vacuum No measurable effect!

Future work Derive an exact solution for when using gratings Enhance the experiment Evaluate the impact on the white light cavity