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

Use this description for the transfer function and verify with E2E

From R. Schilling 1996

Transfer Function for Single Arm FP Cavity

Normalized Frequency

Res

pons

e

FP Cavity

• For LIGO 4 km IFO the second peak is centered about 37.5 kHz

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

Angle from x-y plane

Am

plit

ude

Am

plit

ude

1st Sensitivity Peak

2nd 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!

Angular Response

Angular Response of 1st and 2nd Sensitivity Peak

Further investigation

• Need to develop description of 2 arm model

• Should acquire noise profile at 37.5 kHz

Am

plit

ude

Angle from x-y axis

Earlier This Summer…

Purpose:

To suppress the 60 Hz (& higher multiples) power source noise from AS_Q to headphones.

“Twin T” Notch Filter