Question regarding heterodyne calculations in rydiqule

[jun-nan-wang]

Hello,

I'm a new user of rydiqule, and I want to thank you for providing such a powerful tool. However, I have encountered a question while using it. I'm currently learning how to perform heterodyne calculations using rydiqule, specifically aiming to calculate the heterodyne beat signal when the signal and local oscillator fields have a phase difference, as shown in the attached diagram.

Based on the formula for heterodyne calculation and the time-dependent function provided in section 5.5.4 of your documentation, I noticed that there doesn't seem to be a phase term included in the function. How can I incorporate a phase difference into my calculations?

Thank you in advance for your help!

[dihm]

@jun-nan-wang I sincerely hope you have already figured this out. In case you haven't, or somebody else wants to know.

A little care is needed here since phase difference between oscillators at different frequencies is not a well defined quantity. A phase offset of a single field manifests as a e^(i\phi) factors in the rotating frame, and can result in an observed phase shift of the resulting heterodyne beat. Multiplying the beating term by the phase term should get you what you are looking for.