Multiply Resonant EOM

Introduction

EOM (Electro-Optic Modulator) is a device to modulate the phase/polarization of a laser beam by an electric voltage signal. (http://www.rp-photonics.com/electro_optic_modulators.html) The main use of EOMs in LIGO is to add phase modulation sidebands to the main laser beam. Those sidebands are necessary to extract the information of the positions and orientations of the mirrors. For the advanced LIGO style length sensing scheme, we need two + one sidebands (i.e. three). The first two are used for the length and alignment sensing of the main interferometer. The last one is used for controlling the mode cleaner. The goal of the project is to design the double or triple resonant circuit to use with an EOM so that we can apply phase modulations at multiple frequencies with one EOM crystal.

Basic ideas

An EOM can be regarded as a capacitor in an electric circuit. Therefore, we can form a resonant circuit by combining it with inductances. An example of triple resonant circuit is shown below. At resonances, the impedance across C1 becomes large. Using a transformer (indicated by L5 and L4 in the schematic), we can convert this impedance to 50 Ohm (to match the impedance of the RF signal source). The transformer will also amplify the voltage across the EOM by the ratio of the primary and secondary coils' number of windings. Therefore, we can apply high voltage on the EOM with a relatively small driving signal.

attachment:CircuitExample.png

A circuit simulation shows the input impedance of the above circuit has peaks at three frequencies.

attachment:TripleResonance.png