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Ultrafast X-Rays Imaging For Medical Physics

Ultrafast X-Rays Imaging For Medical Physics

ABSTRACT

In this thesis we explored the production of highly coherent and energetic extreme ultra violet(XUV) radiation through the process of high harmonic generation(HHG).

HHG is a process by which a ultrashort laser pulse interact with and plucks an electron from an atom, coherently accelerates it away from and back to the ion core, emits a high energy photon with frequency been equal to an odd integer multiples of the laser frequency. For its complete description, we consider a one-dimensional Hydrogen atom interacting with a 50 fs laser pulse which can be described by the time dependent Schrodinger equation (TDSE). The TDSE is solve by the Fast Fourier Split Operator method. Firstly, both the ground state and the energy of the system are obtained by imaginary time propagating any arbitrary wave-function taken as the initial state. Secondly, by real time propagating the wave-function of the obtained ground state, the time dependent wave-function of the system, its energy, and the probity in density could be determined.

TABLE OF CONTENTS

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
1 Introduction 1
2 X-Ray Imaging Theory And Applications 2
2.1 History Of X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 History Of Electromagnetic Radiation . . . . . . . . . . . . . . 3
2.3 X-rays Physics And Generation . . . . . . . . . . . . . . . . . . 4
2.3.1 X-ray Generation . . . . . . . . . . . . . . . . . . . . . . . 4
2.3.2 X-rays Physics . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4 Interaction Of X-Rays . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4.1 Photoelectric Absorption . . . . . . . . . . . . . . . . . . . 7
2.4.2 Rayleigh Scattering . . . . . . . . . . . . . . . . . . . . . . 7
2.4.3 Compton Scattering . . . . . . . . . . . . . . . . . . . . . 9
2.4.4 Pair Production . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4.5 Relative Predominance Of Individual Effects . . . . . . 10
2.5 Medical Application Of X-Rays . . . . . . . . . . . . . . . . . . . 11
2.5.1 General Radiography . . . . . . . . . . . . . . . . . . . . . 12
2.5.2 Mammography . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.3 Fluoroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.4 Computed Tomography . . . . . . . . . . . . . . . . . . . . 13
2.6 Radiation Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6.1 Radiometric Quantities . . . . . . . . . . . . . . . . . . . . 14
2.6.2 Dosimetric Quantities . . . . . . . . . . . . . . . . . . . . . 15
2.7 Radiation Protection . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.7.1 Nonstochastic Effect . . . . . . . . . . . . . . . . . . . . . . 16
2.7.2 Stochastic Effects . . . . . . . . . . . . . . . . . . . . . . . 16
2.7.3 National Council On Radiation Protection Recommendations . . . . . . . . 17
2.7.4 Three Cardinal Principles Of Radiation Protection . . 17
3 Optical Production Of X-rays 18
3.1 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.1 Principles of laser oscillation . . . . . . . . . . . . . . . . 18
3.2 Atoms In Strong Laser Fields . . . . . . . . . . . . . . . . . . . . 21
3.2.1 Strong-Field Approximation (SFA) . . . . . . . . . . . . 22
3.2.2 High Harmonic Generation . . . . . . . . . . . . . . . . . 23
4 Model And Methodology 27
4.1 Model Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.1 1D Hydrogen Atom In A Linearly Polarized Laser Field 27
4.2 Dipole Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Emission Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.4 Numerical Solution Of The Time-Dependent
Schrodinger Equation . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4.1 Split Operator Method . . . . . . . . . . . . . . . . . . . . 31
4.4.2 Computation Of The Energy . . . . . . . . . . . . . . . . 32
4.5 Absorbing Boundaries . . . . . . . . . . . . . . . . . . . . . . . . 33
5 Result And Conclusion 34
5.1 Computation Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.2 Time Depended Coulombic Potential . . . . . . . . . . . . . . . 34
5.3 Generating A Ground State Through Imaginary Time Propagation . . . . . . . . 34
5.4 Evolution Of The System . . . . . . . . . . . . . . . . . . . . . . 35
5.5 Conclusion . . . . . . . . . . . . 38
APPENDICES 38
A Python Code 39

CHAPTER ONE

Introduction

X-Rays, discovered by Rontgen in 1895, are still considered as the most important modern discovery due to their basic applications in numerous areas of science including Physics, Chemistry, Material Science, Geology, Biology, Security, and Medicine.

This revolution found an alternative to the electron tube of Rontgen, since the invention of the rst laser by T Maiman in 1960 [18]. Consequently, contributions in producing coherent beams at shorter wavelengths within the spectrum region of X-rays have been continuously encouraged. The goal is to provide highly brilliant X-rays for a host of applications ranging from medical imaging [21] to attosecond spectroscopy.

The technique behind this optical source is the so-called High Harmonic Generation (HHG) [20]. HHG is a coherent, directional, and short-pulsed source of extreme ultraviolet(XUV) radiation, whose applications include the time-dependent attosecond probes of electron dynamics, nanoscale imaging, and the investigation of electromagnetic
nonlinearity in the XUV regime.

The main goal of this thesis is to essentially explore the optical production of X-rays using the High Harmonic Generation (HHG) process. The work is organized as follows:

Chapter 2 discusses the history of X-rays, followed by a physical understanding of how they are created, captured, and used to create images. It continues with a discussion on dosimetry and radiation protection. Chapter 3 discusses the optical production of X-rays within the HHG process together with some basic concepts of light (absorption, spontaneous emission, and stimulated emission) and laser principles.

Chapter 4 discusses a full description of the HHG by solving the time dependent Schrodinger equation (TDSE) of our model, a 1D Hydrogen atom in a strong laser eld. With the time dependent on wave function; obtained by solving the TDSE by means of the Split Operator method, one can compute all desired observables of the system.



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