Applications of digital holograms for the selection and detection of transverse laser modes.
The transverse mode of generally available commercial lasers in most instances is not suitable for desired applications. Shaping the laser beam either extra-cavity, that is outside the laser resonator, or intra-cavity, which is inside the laser resonator, is required to force the laser beam or cavity to oscillate on a selected desirable single laser mode. The shaped laser beam’s spatial intensity profile and propagation properties would then be suitable for the desired application. The crux of the work presented in this thesis involves intra-cavity beam shaping where we generate desirable transverse modes from inside the laser resonator and detecting such mode using digital holograms. In Chapter 1 we discuss a novel technique of modal decomposition of an arbitrary optical light field into underlying superposition of modes. We show that it can be used to extract physical properties associated with the initial light field such as the intensity, the phase and M2, etc. We show that this novel modal decomposition approach that requires no a priori knowledge of the spatial scale of the modes which lead to an optimised modal expansion. We tested the new technique by decomposing arbitrary modes of a diode-pumped solid-state laser to demonstrate its versatility. In Chapter 2 we experimentally demonstrate selective generation of Laguerre-Gaussian (LG) modes of variable radial order from 0 to 5, with zero azimuthal order. To generate these customised LG modes from within the laser resonator we show that a specialised optical element in a form of an amplitude mask is required to be inserted inside the laser resonator. The amplitude mask is designed and fabricated to contain absorbing rings which are immutably connected to the desired LG mode. The geometry of the absorbing ring radii are selected to match and coincide with the location of the selected LG mode zero intensity parts inside the cavity. We show for the first time that the generated LG modes using this method are of high mode purity and a gain mode volume similar to the desired LG mode. The results provide a possible alternative route to high brightness diode pumped solid state laser sources. In Chapter 3 we show that we can overcome the disadvantage of the specialised optical element being immutably connected to the selection of a particular mode by experimentally demonstrating a novel digital laser capable of generating arbitrary laser modes inside the laser resonator. The digital laser is realised by intra-cavity replacing an end-mirror of the resonator with a rewritable holographic mirror which is an electrically addressed reflective phase-only spatial light modulator (SLM). We show that by calculating a new computer-generated holographic gray-scale image on the SLM representing the desired customized laser mode digitally, the digital laser resonator is capable of generating the desired laser modes on demand. The results provide a new laser that can generate customized laser modes. In Chapter 4 we show that the digital laser can be used as a test bed for conceptualizing, testing, and proving ideas. We experimentally demonstrate this by using a simple laser cavity that contains an opaque ring which is digitally programmed on the SLM and an adjustable circular aperture on the output coupler mirror. We show that by manually varying the diameter of the aperture without realignment of the laser, the generated laser modes can be tuned from a Gaussian mode to a Flat-top mode. This opens up new digital methods that can be used to test laser beam shaping techniques. In Chapter 5 we outline a simple laser cavity comprising an opaque ring and a circular aperture that is capable of producing spatially tuneable laser modes, from a Gaussian beam to a Flat-top beam. The tuneability is achieved by varying the diameter of the aperture and thus requires no realignment of the cavity. We demonstrate this principle using a digital laser with an intracavity spatial light modulator, and confirm the predicted properties of the resonator experimentally. In Chapter 6 we discuss the techniques used to intra-cavity generate and detect LG beams with a non-zero azimuthal index since they are known to carry orbital angular momentum (OAM), and have been routinely created external to laser cavities. We show that the few reports of obtaining such beams from laser cavities suffer from inconclusive evidence of the real electromagnetic field. In this Chapter we revisit this question and show that an observed doughnut beam from a laser cavity may not be a pure Laguerre–Gaussian azimuthal mode but can be an incoherent sum of petal modes, which do not carry OAM. We point out the requirements for future analysis of such fields from laser resonators. In Chapter 7 we conclude and discuss future work.