Frequency Response of LIGO
Interferometers
Andrew Weber University of Maryland
(no relation)
SURF Student Lecture Series
Advisor: Andri Gretarsson
Introduction

To Investigate the Frequency
Response of LIGO Interferometers
Above the 1st FSR
•Analytically
•Using the E2E model

To Describe the Angular Response
Above the 1st FSR
Single Arm Fabry-Perot
From R. Schilling 1996
Use this description for the transfer
function and verify with E2E
Transfer Function for Single Arm FP Cavity
• For LIGO 4 km IFO
the second peak is
centered about 37.5
kHz
Response
FP Cavity
Normalized Frequency 
Using the E2E Model
One 4 km FP Arm
Input:
Swept Sine 0-90 kHz
Output:
Frequency Response of One Arm, 4 km IFO
(E2E model)
Single 4 km FP
Cavity in E2E
• 2nd Peak at 37.5 kHz
Same as calculated
above
Two Arm FP IFO 2 km
Two Arms Plus
Recycling Cavity
• Swept Sine
displacement to both
mirrors (differential mode)
Frequency Response of 2 Arm, 2 km IFO
(E2E model)
Peak at 75 kHz or
at normalized
frequency  = 0.5
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?
Angular Response
• Angular Response high
frequencies (37.5 kHz)
has zeros at optimal
orientation!
Amplitude
Angle from x-y plane
2nd Sensitivity Peak
Amplitude
• Angular response at
low frequencies is
expected
1st Sensitivity Peak
Angle from x-y plane
Angular Response
Angular Response of 1st and 2nd
Sensitivity Peak
• Need to develop
description of 2 arm
model
• Should acquire noise
profile at 37.5 kHz
Amplitude
Further investigation
Angle from x-y axis
Earlier This Summer…
“Twin T” Notch Filter
Purpose:
To suppress the 60 Hz (&
higher multiples) power source
noise from AS_Q to
headphones.