Question Regarding the Use of abs() in the Final Gradient Calculation

[shromesh]

Dear Dr. Hughes,

I am Ryoma Yonemoto, an undergraduate student in The University of Tokyo, Japan.
First, I would like to extend my appreciation for your fascinating research on optimizing dielectric laser accelerator structures using AVM. The methodology has greatly inspired me.

While studying the provided code and its outputs, I noticed that the final gradients are computed using the absolute value of the complex gradient variable. I understand that throughout the optimization loop, the real part is used as the key figure of merit for updating the permittivity distribution. However, I am curious about the rationale behind switching to the absolute value in the final evaluation step.

Could you kindly clarify the reasoning or motivation for this approach?

Thank you for your time and for making this exciting work accessible. I look forward to any insights you can share about this detail.

Best regards,
Ryoma Yonemoto

[tylerflex]

Hi Ryoma, there might be some miscommunication on my part:

the "gradient" in accelerator design is referred to as the energy gain per unit length (if I remember). so in the part of the code you linked, this is what is being referred to. not the mathematical gradient (derivative w.r.t. design parameters).

For the accelerator design, we take the complex value of the "acceleration" gradient since the phase just refers to whether the charged particle is in phase with the driving field. we can take abs to "assume" it is.

In the permittivity update, the real part of the mathematical gradient is used as this is how it's defined in the adjoint math.

Does that clear it up?

[shromesh]

Thank you so much for your swift and detailed response.
I’d like to take some time to reflect on this. If I have any further questions, I hope it’s okay to reach out again.