The Introduction
Motivation
Orbital Angular Momentum beam
Laguerre Gaussian beam
Gyrotron
Theoretical & Mathematical Development
Laguerre Gaussian beam generation
- Spiral Phase Plate
- Hologram
- Mode converters
The differences between the two beams are in the shape of the phase and the shape of the intensity donut, so most of the method uses the Gaussian beam to LG beam conversion process. The simplest way to create an LG beam is to use a Spiral Phase Plate (SPP). Plane waves such as a Gaussian beam pass through the SPP and the input beam is converted into an LG beam.
For this reason, the use of this SPP is the best way to generate the LG beam with high power. The shape of the SPP is a disk, which is a dielectric material, and the front side is flat, and the other side is staircase shape, the stars gradually increase along the azimuth angle. If the beam wavelength is not very short, the fabrication of SPP is not complicated.
In case of increasing topological load, the total height also increases because the azimuthal angle is set by the equation. However, the increase in total height can occur with the transmission speed, reflection and power loss problem. This new form of SPP has a benefit for generating high-order LG modes theoretically, but generating the LG020 mode is impossible due to manufacturing limitation.
This method is a general technique potentially applicable to all types of complex beams or the superposition of those beams. Moreover, the far field of the hologram, which comes from the Fourier transform, is a close approximation of the target beam. In these direct converting optical devices, a helix phase dislocation is introduced at the center of the beam, which causes destructive interference upon propagation, leading to the characteristic donut shape intensity pattern.
The mode converter is based on cylindrical lenses and converts HG modes of all types into corresponding Laguerre Gaussian modes. They realized that the particular design of the cylindrical lens telescope would transform between the HG and the Laguerre Gaussian mode. Unlike SPP or hologram, this mode converter can theoretically produce pure Laguerre Gaussian modes [17].
High power Laguerre Gaussian beam detection
- Reference beam
- Young’s double slit experiment
- Phase retrieval
- Aperture shape
As a result, the topological charge of the LG beam can be known by observing the number of points. The CST result of LG beams which are topological load one and two are illustrated in Fig. 3-4, the spiral line numbers are two because the LG beam has a topological charge of two.
We also noticed that the diameter of the LG beam is slightly increased instead of the single beam topological charge. The result of the intensity and phase patterns of the low power experiment, topological charge one and two, is shown in the figure. In addition, the SPP is rotated by 90 degrees to generate the LG beam of topological charge two.
In particular, the LG beam intensity of topological charge 2 is not perfectly aligned with the CST simulation case, but the strong intensity position and phase patterns are almost the same. The SPP makes a Gaussian transformation to the LG beam, which has a topological charge of one or two. Therefore, the double slit cannot use the whole LG beam to identify the topological charge, and part of the LG beam is distinguishable in one double slit.
We focus on a high-power LG beam in azimuthal numbers one and two, so that the double slit is also optimized at topological charges one and two. However, the LG beam of topological charge two is not clear because the center intensity is much weak. According to the topological charge of a beam, the interference patterns give a different intensity shape in high-power experiments.
In our analysis, the low-order topological charge of the LG beam is identified by a double-slit experiment. Using the double-slit experimental method, we successfully identified the topological charge of the LG beam. In the case of the LG beam it has a topological charge value of two, the phase beam has two spiral lines as theory.
Experimental Method & Materials
Spiral Phase Plate Design and experiment
- Low power experiment
- High power experiment
Compared with the hologram method, the SPP can give a high power LG beam without highly energy loss. The reason of diameter difference is for safety because the SPP for generating the topological charge two beam has longer total height than topological charge one case. The intensity patterns clearly show donut shapes and the phase of the beam also gives spiral lines which are the same as our expectation according to the topological charge.
A simulation of LG beams with topological charge one and two is performed, and the SPP specifications are the same as in Table 3-1. The intensity of the donut shape is clearly shown on the generated LG beam, and the phase of the LG beam gives a spiral line. Therefore, these results show that this SPP generates a LG beam having a topological charge of one successfully in the CST simulation environment.
Generally in CST simulation, the spiral lines show that the generated beam is obviously LG beam. In low-power experiments, we focus on LG beam generation in the actual experimental environment and control the beam intensity and phase. After passing through the SPP, the Gaussian beam is transferred to the LG beam whose azimuth index is determined by SPPs.
On the other hand, the phase patterns of the LG beam are the same as the CST simulation. These unmatched intensities may be from the SPP fabrication problem because the second-generation topological load SPP was not fabricated at a 1 mm interval. Therefore, the shape of the fabricated SPP affects the LG beam shape, but may not be critical with a 95 GHz beam.
The result of the figure clearly shows that the vortex lines correspond to the number of topological charges in both simulation and experiment. From these two results we can conclude that the second result has a higher topological charge than the first result. No direct phase measurement is performed, but based on intensity information, the LG beam, whose topological charge one and two are successfully generated in a high-power system.
Phase detection Young’s Double slit experiment
- Low power experiment
- High power experiment
SPP is placed 1mm after the Gaussian beam and then a double slit is placed 40mm from SPP. However, when the beam has a topological l, there is a phase difference between the top and bottom of the beam, so that the interference patterns give a tilted intensity after passing through the double slit. These interference patterns allow the topological charge of the LG beam to be identified by observing the tilt direction and angle.
In order to obtain a better result, the flat hole surface is essential, so we produce the double slit using a Nano CNC machine which can make flat surface, the error rate is in the range of Nano scale. 3-15 is an experimental setup for measuring interference patterns of a low power LG beam when the beam passes through the double slit. The double slit is an aluminum plate so there is a lot of diffraction going on around the slit.
As you can see, we can indirectly infer the topological charge from the tilt degree. However, if we imagine that there is an apparent connecting line, the ray of topological charge could be identified by comparing the amount of tilt with the topological charge. The twisted beam is created by transforming a high-power Gaussian beam from the 95 GHz Gyrotron into an LG beam.
The interference pattern measurement methods are the same as the LG beam generation by SPP in the high-power experiment, except for the size of the observation plane. In a power experiment, especially when the beam has a topological charge of two, the interference of an unrelated form is at the center of the plot, such as the low power experiment. This phenomenon could be due to the imperfect shape of the LG beam and an alignment problem, but the connected line would indicate that it is a topological charge beam of two LG beams.
To identify the topological charge of the beam more precisely, the tilted angle of interference patterns with respect to the topological charge graph is shown in Fig. calculated value of the angle is shown in table 3-3. The objective of this study is to understand the characteristics of LG beam in high power mode.
In addition, the generated LG modes were identified through Young's double-slit experiment under both conditions. In double slit experiment, LG beams which are topological charge one and two show tilted interference patterns after passing through the double slit.
Summary & Conclusion
