Second-harmonic generation with Bessel beams

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