Phase Retrieval and Gaussian Beam Mode Decomposition of Gyrotron Beams

In this dissertation, we have developed the necessary basis for the characterization of the RF output of a gyrotron. The characterization includes the phase reconstruction and Gaussian beam mode decomposition. In order to analyze the phase reconstruction in detail, we have developed an accurate field propagation method using the complete Rayleigh-Sommerfeld scalar diffraction integral (RSDI) and the Huygens-Fresnel diffraction integral (HFDI), using a fast Fourier Transform (FFT) based approach. The discretization of the two diffraction integrals is analyzed analytically and numerically. In the case of the HFDI, a condition on the distance of propagation, where aliasing and replication are completely removed, is found. It relates the distance of propagation Δz, the number of sampling points M, the grid cell size Δx and the wavelength λ as: Δz = M(Δx)2 · 1/λ. The two formalisms are also studied using a zero-padding technique, which can be used to propagate the field to any arbitrary distance. These propagation methods are then used in the Iterative Phase Retrieval Algorithm (IPRA) for phase reconstruction. The effects of several parameters on the IPRA (the number of planes, the measurement plane size, the distance of propagation, the number of sampling points and the grid cell size, the misalignment along the optical axis, etc.) are then analyzed. For the theoretical field profiles used in this dissertation, the misalignment along the optical axis in the form of a transverse shift affects the IPRA most severely. The experimental procedure to measure the beam intensity patterns using infrared (IR) thermography is explored extensively. Out of the many target materials used, Robax is the most appropriate in terms of dynamic range, temperature linearity and for the possibility to perform measurements from the front side and the back side. Further, infrared image data processing is investigated for intensity pattern enhancement. This includes various steps: Fixed Pattern Noise (FPN) correction by subtracting the background image of the target taken before the microwave irradiation, defective pixels correction, perspective correction, image pattern enhancement by filtering and denoising. Further, the intermodal decomposition of the reconstructed phase and amplitude is analyzed in detail using two methods, in order to extract the Gaussian content: Finding a set of Gaussian beam parameters and a mode content matrix which maximizes the power in the fundamental mode |C00|2. This method is commonly used by the gyrotron tube developers. Finding a set of Gaussian beam parameters and a mode content matrix which minimizes the error between the corresponding reconstructed field and the input (theoretical and/or experimental) field. It is found that, the two methods may give significantly different results. As a general rule, the second method gives more precise and more reliable results, but the solution is unfortunately not unique and depends both on the measured profile and the measurement parameters. Therefore, the concept of Gaussian content adopted by the community seems to be incomplete, and the corresponding optimized parameters should be associated to it. The definition of Gaussian content should then be reexamined, and completed by an analysis of the power coupling coefficient of the microwave beam to the transmission line (corrugated waveguide or a quasi-optical line).


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