We present the results of a numerical simulation tool for modeling the second-harmonic generation (SHG) interaction experienced by a diffracting beam. This code is used to study the simultaneous frequency and spatial profile conversion of a truncated Bessel beam that closely resembles a higher-order mode (HOM) of an optical fiber. SHG with Bessel beams has been investigated in the past and was determined have limited value because it is less efficient than SHG with a Gaussian beam in the undepleted pump regime. This thesis considers, for the first time to the best of our knowledge, whether most of the power from a Bessel-like beam could be converted into a second-harmonic beam (full depletion), as is the case with a Gaussian beam. We study this problem because using HOMs for fiber lasers and amplifiers allows reduced optical intensities, which mitigates nonlinearities, and is one possible way to increase the available output powers of fiber laser systems. The chief disadvantage of using HOM fiber amplifiers is the spatial profile of the output, but this can be transformed as part of the SHG interaction, most notably to a quasi-Gaussian profile when the phase mismatch meets the noncollinear criteria. We predict, based on numerical simulation, that noncollinear SHG (NC-SHG) can simultaneously perform highly efficient (90%) wavelength conversion from 1064 nm to 532 nm, as well as concurrent mode transformation from a truncated Bessel beam to a Gaussian-like beam (94% overlap with a Gaussian) at modest input powers (250 W, peak power or continuous-wave operation). These simulated results reveal two attractive features – the feasibility of efficiently converting HOMs of fibers into Gaussian-like beams, and the ability to simultaneously perform frequency conversion. Combining the high powers that are possible with HOM fiber amplifiers with access to non-traditional wavelengths may offer significant advantages over the state of the art for many important applications, including underwater communications, laser guide stars, and theater projectors.

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Higher order modes (HOM) are electromagnetic resonant fields. They can be excited by an electron beam entering an accelerating cavity, and constitute a component of the wakefield. This wakefield has the potential to dilute the beam quality and, in the worst case, result in a beam-break-up instability. It is therefore important to ensure that these fields are well suppressed by extracting energy through special couplers. In addition, the effect of the transverse wakefield can be reduced by aligning the beam on the cavity axis. This is due to their strength depending on the transverse offset of the excitation beam. For suitably small offsets the dominant components of the transverse wakefield are dipole modes, with a linear dependence on the transverse offset of the excitation bunch. This fact enables the transverse beam position inside the cavity to be determined by measuring the dipole modes extracted from the couplers, similar to a cavity beam position monitor (BPM), but requires no additional vacuum instrumentation.At the FLASH facility in DESY, 1.3 GHz (known as TESLA) and 3.9 GHz (third harmonic) cavities are installed. Wakefields in 3.9 GHz cavities are significantly larger than in the 1.3 GHz cavities. It is therefore important to mitigate the adverse effects of HOMs to the beam by aligning the beam on the electric axis of the cavities. This alignment requires an accurate beam position diagnostics inside the 3.9 GHz cavities. It is this aspect that is focused on in this thesis. Although the principle of beam diagnostics with HOM has been demonstrated on 1.3 GHz cavities, the realization in 3.9 GHz cavities is considerably more challenging. This is due to the dense HOM spectrum and the relatively strong coupling of most HOMs amongst the four cavities in the third harmonic cryo-module. A comprehensive series of simulations and HOM spectra measurements have been performed in order to study the modal band structure of the 3.9 GHz cavities. The dependencies of various dipole modes on the offset of the excitation beam were subsequently studied using a spectrum analyzer. Various data analysis methods were used: modal identification, direct linear regression, singular value decomposition and k-means clustering. These studies lead to three modal options promising for beam position diagnostics, upon which a set of test electronics has been built. The experiments with these electronics suggest a resolution of 50 micron accuracy in predicting local beam position in the cavity and a global resolution of 20 micron over the complete module. This constitutes the first demonstration of HOM-based beam diagnostics in a third harmonic 3.9 GHz superconducting cavity module. These studies have finalized the design of the online HOM-BPM for 3.9 GHz cavities at FLASH.

Práce se zabývá buzením vyšších módů v kvádrových a válcových dielektrických rezonátorových anténách pro účely zvýšení zisku. Pomocí numerických simulací jsou studovány vlastnosti a limity anténních prvků. Je zkoumáná vzájemní vazba mezi dielektrickými rezonátorovými anténami pracujícími s vyššími vidy a na základě výsledků je možno usuzovat o vhodnosti těchto prvků k popužití v anténních řadách. V práci je popsán analytický model efektivní permitivity perforovaných dielektrik, který respektuje anizotropní povahu tohoto materiálu. Model je založen na Maxwell Garnettové aproximácií nehomogenních materiálů. Dále jsou studovány povrchové vlny na perforovaných substrátech a je ověřena použitelnost teoretického modelu i v tomto případě. Nakonec jsou studovány dielektrické rezonátorové antény vytvořené pomocí perforací v dielektrickém substrátu a je demonstrováno zhoršení určitých vlastností takových antén.