Focal Spot Optimization Using Spatial Light Modulation and a Phase Retrieval Algorithm

Abstract

Aberrations to the wavefront of a laser beam reduce the quality of the focal spot and are generally undesired. This project is aimed at determining the aberrations of laser beams by using a phase retrieval algorithm and to show that it is possible to correct the aberrations with a spatial light modulator to optimize the focal spot. In particular, a two-dimensional phase pattern is retrieved and decomposed into Zernike polynomials to generate two distinct correction patters that are applied to the spatial light modulator to increase the peak intensity and reduce the width of the focal spot. Measurements of the aberrations of a terawatt laser are performed with the phase retrieval algorithm and compared to measurements with a Shack–Hartmann wavefront sensor.

Popular Abstract

Removing the Aberrations from an Invisible Laser Beam

A laser beam can be focused to a spot to achieve an even higher intensity of the light, but aberrations of the beam increase the size of the focal spot and reduce the intensity and this project shows that the aberrations can be corrected.

A convex lens such as for example a magnifying glass can be used to focus light to
a small spot which is called the focal spot. On a sunny day a magnifying glass can
be used to burn a piece of paper by focusing the sunlight onto this paper. A larger
magnifying glass can collect more light and leads to a higher intensity of the focused sunlight. It is not possible to focus all the light into one infinitely small spot. That would result in an infinitely high intensity in this point and that is not possible due to the laws of physics. The size of the focal spot also depends on the focal length of the lens and a magnifying glass with a shorter focal length can create a smaller focal spot with a higher intensity that burns the paper better.

It is possible to calculate the size of this focal spot by using formulas, but in reality the size of the focal spot is usually larger due to aberrations of the light that gets focused. The light that comes from the sun also does not reach the magnifying glass without aberrations and the same is true during night when we look at the stars. The stars twinkle and at every moment look a little bit different due to aberrations of the light that originate from the turbulent atmosphere of the earth. Astronauts flying outside the atmosphere do not see this twinkling and could also focus the starlight better with a lens or a curved mirror. This is one of the reasons why space telescopes are launched to outer space to capture images of the universe. It is exceptionally expensive to built space telescopes and to launch them to outer space and the maximum size of space telescopes is limited by the used rocket. A technology that is used in the largest ground-based telescopes is called adaptive optics. The aberrations that originate in our atmosphere are constantly measured and corrected by deforming a mirror to counteract the effects of the atmosphere. The telescope can then see the stars without any twinkling.

A deformable mirrors is also used in the laboratory at the Lund High-Power Laser
Facility where the experimental work for this project was done. Even if the light from the infrared lasers propagate in vacuum and do do not twinkle, aberrations are still present in a laser beam. They can originate from the laser itself or be introduced by mirrors or lenses or other components in the setup that are not aligned perfectly. The aberrations do not change so quickly and if the aberrations are measured, they can be corrected with the deformable mirror. The laser beam then gets focused and the focal spot gets better if the aberrations from the beam are first removed. This focused light is used to generate high-order harmonics that create invisible pulses in the extreme ultraviolet spectrum with a duration of just a few hundred attoseconds. 100 attoseconds is an incredibly short time that is 10 quadrillion times shorter than a single second. Even light that is so fast that it could theoretically orbit the earth more than 7 times during a single second merely travels a distance that is shorter than 0.0005 times the thickness of a human hair during 100 attoseconds.

In this project, the aberrations of the infrared terawatt laser are measured with two different methods and a separate setup is built to optimize the focal spot by correcting the aberrations with a spatial light modulator which is a device that is similar to a deformable mirror with many small pixels. One method to measure the aberrations of a laser beam is to use an expensive device which is called a Shack-Hartmann wavefront sensor. It is also possible to instead focus the laser beam with a lens or a curved mirror and to capture images before and behind the focal spot and to use an algorithm on a computer to calculate the aberrations of the beam. This is a much cheaper and accessible way to determine the aberrations of a laser beam because the beam just has to get focused and just one camera is needed. This project shows that it is possible to measure the aberrations of an infrared laser beam with a camera and the phase retrieval algorithm and that the measured aberrations in the beam can be corrected with a spatial light modulator to create an improved and smaller focal spot.

• author: Petersen, Robert
• supervisor: Per Johnsson; Cord Arnold
• organization: Atomic Physics; Department of Physics
• course: PHYM03 20231
• year: 2023
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy; Technology and Engineering
• keywords: Spatial Light Modulation, Phase Retrieval Algorithm, Focal Spot Optimization, Adaptive Optics, Wavefront Sensing, Lasers
• publication/series: Lund reports on atomic physics
• report number: LRAP: 592
• language: English
• id: 9128169
• date added to LUP: 2023-06-27 11:43:53
• date last changed: 2023-06-27 11:43:53