pi and pi/2 phase shift in MZM

[Dr. Dhiman Kakati]

Hello Everyone,
I am looking for mathematical relationship between phase shift, bias voltage and refractive index of the optical guide used in Mach Zehnder Modulator. Actually I need to calculate the bias voltages for a specific phase shift at the output of a MZZ.
Secondly looking for mathematical relation among the three. There must be length of the MZI waveguide. Thanking you.

With Regards,
Dhiman Kakati

[–]

Basic relation between input optical fields of MZM is given by

Eo(t)=Ei(t)[exp(jP1(t)+exp(jP2(t)]/2; ———–>(1); assuming equal power splitting through both the waveguides.
where,
P1(t)=pi*Vmod1(t)/Vpi————>(2); P2(t)=pi*Vmod2(t)/Vpi———–>(3)
where P1(t) and P2(t) are phase shifts in upper and lower arms resp. And Vmod1(t) and Vmod2(t) are applied drive voltages in the upper and the lower arms.

now the relation of DC bias voltage
Vmod1(t)= Vm1(t) + Vdc
Vomd2(t)= Vm2(t) + Vdc

Vmod1(t) and Vmod2(t) are the input RF voltages.

May be this helps you

[Dr. Dhiman Kakati]

Hi Gokul,
Thank you for the response, I am still not clear about what I have asked, Basically I want to calculated V_pi i.e. bias voltage for which there is a phase change of 180 degree at the output. I am asking this because implementing a dual drive MZM we have only very few flexibility in our hand these are bias voltage V1 and V2, and modulation voltage which we can set from our own. I found some of the expression with bias voltage, rffective refractive index change and length of the cavity inside the interferometer. So I am looking for in terms of V1 and V2.

Regards,
Dhiman

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