1. Frequency Response of LIGO Interferometers Andrew Weber University of Maryland (no relation) SURF Student Lecture Series Advisor: Andri Gretarsson

2. Introduction  To Investigate the Frequency Response of LIGO Interferometers Above the 1 st FSR Analytically Using the E2E model  To Describe the Angular Response Above the 1 st FSR

3. Leading to a Description of One Arm FP Cavity

4. Single Round Trip

5. One Arm Transfer Function Single Round Trip Response Normalized Frequency  (log Hz) Full Round Trip Magnitudes of forward and round trip are equal Only the Phase is different This leads to Zeros at  = ½ (2n-1)

6. Single Arm Fabry-Perot Use this description for the transfer function and verify with E2E From R. Schilling 1996

7. Transfer Function for Single Arm FP Cavity Normalized Frequency  Response FP Cavity For LIGO 4 km IFO the second peak is centered about 37.5 kHz

8. Using the E2E Model One 4 km FP Arm Input: Swept Sine 0-90 kHz Output:

9. Frequency Response of One Arm, 4 km IFO (E2E model) Single 4 km FP Cavity in E2E 2 nd Peak at 37.5 kHz Same as calculated above

10. Two Arm FP IFO 2 km Two Arms Plus Recycling Cavity Swept Sine displacement to both mirrors (differential mode)

11. Frequency Response of 2 Arm, 2 km IFO (E2E model) Peak at 75 kHz or at normalized frequency  = 0.5

12. What Does This Mean? This Shows that the sensitivity is restored again at multiples of cavity FSR Suggests Search For GWs at Higher Frequencies Might be Possible However… What are the noise characteristics at high frequencies? Is it an interesting place to search?

13. Angular Response Angle from x-y plane Amplitude 1 st Sensitivity Peak 2 nd Sensitivity Peak Angle from x-y plane Angular response at low frequencies is expected Angular Response high frequencies (37.5 kHz) has zeros at optimal orientation!

14. Angular Response Angular Response of 1 st and 2 nd Sensitivity Peak Further investigation Need to develop description of 2 arm model Should acquire noise profile at 37.5 kHz Amplitude Angle from x-y axis

15. Earlier This Summer… Purpose: To suppress the 60 Hz (& higher multiples) power source noise from AS_Q to headphones. “Twin T” Notch Filter