Semi-Classical Calculations of Multiple Trajectories in High-Harmonic Generation

Abstract

The purpose of this thesis is to investigate the High-Harmonic Generation (HHG) process by simulating electron trajectories, and their resulting Extreme Ultra Violet (XUV) output. The HHG process is one in which a focused beam of infrared (IR) light can rival (in terms of intensity) the potentials of atoms, which makes tunnelling likely -- this sets off a chain of events resulting in an XUV pulse.

The thesis utilises a semi-classical method in order to predict where one might look for further trajectories. This method is programmed into MATLAB in order to run simulations and investigate the results.

The code allows for a deep-dive into different aspects of the process, including laser profile shape, laser properties (wavelength and intensity) and number of atoms within the beam.

One of the conclusions of the thesis is the reaffirmation that finding the third trajectory is not simply a case of knowing what settings to apply, but moreso the principle that trajectories past the second are much less likely to be taken by electrons (even in a purely classical regime, before taking into account phenomena like Electron Wave Packet (EWP) spreading). The thesis also demonstrates an approximation of the HHG process to the tenth trajectory, where usually only up to the second is shown, which provides an interesting insight into how they are grouped around certain harmonics.

Popular Abstract

Imagine going to the park with your dog and playing fetch. We’re going to assume that your dog always at least attempts to fetch the ball once you throw it. Let’s also assume that upon returning the ball to you, the dog shows her excitement by barking in a frequency (your dog is a tad odd) that depends on the speed she returns to you. This basic premise takes place on an atomic level within the field of atomic physics, in a process called “Higher-order Harmonic Generation” (HHG).

How hard would you have to throw the ball before it leaves the park and your friend can no longer retrieve it? Or if you have a penchant for annoying others, you might ask the question “How hard do I have to throw this ball so that my dog sounds like a nail scratching a chalkboard?”

These questions have analogues in HHG. The frequency of your dog’s bark in this analogy corresponds to the frequency (and by extension: energy) of the light that comes out of the HHG process.

There’s more to the process than just you and the dog though -- one of the reasons the HHG process can take place at all is because of the ability of electrons to “tunnel through the potential barrier”. In our dog analogy, this means that your willingness to play fetch as the owner will change depending on your environment. You are perhaps not so willing to play fetch in Auntie Gertrude’s antique store, but once you reach an open field – you almost have to resist throwing the ball.

There are equations that allow for the simulation of this atomic scenario and also for much more interesting questions to be asked. You might think that the way to ensure your loyal companion sounds like she's imbibed helium is simply to throw it as hard as you can. This would be true if she were incapable of tiring. In reality, if you throw it too hard (but still inside the park) then your companion might return to you at a walking pace, sounding like a deflating balloon.

One of the unanswered (or rather unmeasured) questions in the field that studies this, is based upon the premise that your dog physically “misses you” (think of it as running in-between your legs by accident) when she tries to return the ball to you. Upon passing you, she’ll turn and come back -- and when she does successfully return the ball to you, her speed will still be measurable, and it is guaranteed to be a speed that could have been measured had she not missed you the first time. The problem is – such an event has not yet been experimentally observed; the dog always seems to be successful in returning the ball the first pass despite the theory pointing out that the miss scenario should be possible.

The subject of my thesis is to simulate your visit to the park with the dog and investigate the ways in which we might be able to make your dog run past you instead of returning the ball directly to you.

• author: Causer, Tom
• supervisor: Johan Mauritsson; Samuel Bengtsson
• organization: Atomic Physics; Department of Physics
• course: FYSK02 20211
• year: 2021
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: hhg, high harmonic generation, trajectories, xuv, semi-classical, multiple, third trajectory, further, matlab, hhg approximation, simulation, far-field, near-field, fourier transform
• language: English
• additional info: The purpose of this thesis is to investigate the High-Harmonic Generation (HHG) process by simulating electron trajectories, and their resulting Extreme Ultra Violet (XUV) output. The HHG process is one in which a focused beam of infrared (IR) light can rival (in terms of intensity) the potentials of atoms, which makes tunnelling likely -- this sets off a chain of events resulting in an XUV pulse.; The thesis utilises a semi-classical method in order to predict where one might look for further trajectories. This method is programmed into MATLAB in order to run simulations and investigate the results.; The code allows for a deep-dive into different aspects of the process, including laser profile shape, laser properties (wavelength and intensity) and number of atoms within the beam.; One of the conclusions of the thesis is the reaffirmation that finding the third trajectory is not simply a case of knowing what settings to apply, but moreso the principle that trajectories past the second are much less likely to be taken by electrons (even in a purely classical regime, before taking into account phenomena like Electron Wave Packet (EWP) spreading). The thesis also demonstrates an approximation of the HHG process to the tenth trajectory, where usually only up to the second is shown, which provides an interesting insight into how they are grouped around certain harmonics.
• id: 9047901
• date added to LUP: 2021-06-03 08:55:57
• date last changed: 2023-01-18 12:02:25