Introduction

A brief overview of the problem of pulse-characterization

My disertation centered on the use of optimization and compressive sensing to solve for the complex time domain profile of ultrafast optical pulses. The techniques were highly effective, and through these tutorials I aim to give a brief overview of the techniques presented in my thesis along with some example code.

For a more in depth description of techniques I of course recommend reading my disertation. If you’re not in the mood to read I recommend the Youtube recording of my defense bellow.

Some framing to help me organize thoughts while I flesh this out

\(e^{j \theta}\)

We can do some latex.

Ultimately I think the layout I want to follow is:

Introduction, problem from the top and talk about why this problem is difficult. talk about how everything gets integrated and how theres this difficulty with abs values Talk about a couple existing techniques and maybe have some links in page.

Some theory on Wirtinger gradient stuff, some code samples and plots about recovering forwards from complex functions maybe a cubic and quadratic term. split into real/imag then differentiate. or do Wirtinger and make it much easier on yourself. Maybe talk about holomorphic?

Non-linear functions and tensors small point to talk about linearizing any non-linear function using tensors

Hierarchy of problems in ultrafast optics. Show some of the pictures from the thesis here, just good page for showing other problems.

Compressed sensing and this problem. maybe a mention of new compressed sensing and computational imaging page. A desire to do computational holography

Primary contributions theory talk about how I studied variations of the problem that integrate in spectrum and how I integrate in time, and talk about the primary problem here being one of the fourth order and overlapping fourth order.

Primary contributions results – pictures of recovered pulses, an example of how to do this tutorial, new code.