Homodyne detection: understanding the laser noise amplitude transfer function

Homodyne detection:understanding the laser noise amplitude transfer function

Jérôme Degallaix

Ilias meeting – June 2007

Going DC

Laser

Carrier local oscillator

PRM

SRM

Stefan’s talk this morning

Measure the laser intensity noise transfer

function• Switch off laser power stabilisation loop• Inject white noise into the laser pump• Record dark port spectrum

101

102

103

10-6

10-5

10-4

10-3

10-2

10-1 Amplitude Spectum comparison MID_VIS 2007-06-12

Frequency (Hz)

[V/s

qrt(

Hz)

]

Reference 10:50:00 13:00:30

Laser

output

After laser After MC

Reflected PRC

Reflected BS

Input ?

The measured TF

Laser

FSR = 125 kHz

Optical fields

Laser

FSR = 125 kHzfMI = 14.9 MHz

Optical fields

Laser

FSR = 125 kHzfMI = 14.9 MHzfSR = 9.01 MHz

Optical fields

Carrier TF

Simple Michelson

Flat response due:• Arm asymetries• Dark fringe offset

Carrier TF

With SRM

Peak due to SRM

Carrier TF

Including the higher order optical modes

• Increase the amplitude of the TF• Flat the response at high frequency

TF with SR sidebands

Resonance peak of the sidebands!

TF with SR sidebands

TF with SR sidebands

Including the higher order optical modes

Shape of the sidebandsresonance different!

TF with MI sidebands

TF with MI sidebands

Including the higher order optical modes

Changing the PRC FSR

A little test to confirm what we understand...

Changing the SRC FSR

Another test...

Does it match the experiment ?

• Adjust the overall gain of the simulated TF• Thanks to Andreas for the tuning of the parameters

To sum up...

Due to the signal recycling mirror

Due to SR sidebands and

higher order optical modes

Due to MI sidebands

Due to second order optical

modes

Overal magnitude depends of:• arm detuning • magnitude of higher order optical modes

So ?