Customizing the output beam shape from a laser invariably involves specialized optical elements in the form of apertures, diffractive optics and free-form mirrors. Such optics require considerable design and fabrication effort and suffer from the further disadvantage of being immutably connected to the selection of a particular spatial mode. Here we overcome these limitations with the first digital laser comprising an electrically addressed reflective phaseonly spatial light modulator as an intra-cavity digitally addressed holographic mirror. The phase and amplitude of the holographic mirror may be controlled simply by writing a computer-generated hologram in the form of a grey-scale image to the device, for on-demand laser modes. We show that we can digitally control the laser modes with ease, and demonstrate real-time switching between spatial modes in an otherwise standard solid-state laser resonator. Our work opens new possibilities for the customizing of laser modes at source.

The modal decomposition of an arbitrary optical field may be done without regard to the spatial scale of the chosen basis functions, but this generally leads to a large number of modes in the expansion. While this may be considered as mathematically correct, it is not efficient and not physically representative of the underlying field. Here we demonstrate a modal decomposition approach that requires no a priori knowledge of the spatial scale of the modes, but nevertheless leads to an optimised modal expansion. We illustrate the power of the method by successfully decomposing beams from a diode-pumped solid state laser resonator into an optimised Laguerre-Gaussian mode set. Our experimental results, which are in agreement with theory, illustrate the versatility of the approach.

Laguerre-Gaussian beams with a nonzero azimuthal index are known to carry orbital angular momentum (OAM), and are routinely created external to laser cavities. The few reports of obtaining such beams from laser cavities suffer from inconclusive evidence of the real electromagnetic field. In this Letter 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 this paper we experimentally demonstrate the intracavity generation of selected Laguerre-Gaussian modes of variable radial order, from 0 to 5. Our technique requires only an amplitude mask made up of absorbing rings to be placed inside the cavity, with the ring radii selected to coincide with the zeros of the desired Laguerre-Gaussian mode. We demonstrate high mode purity and a mode volume proportional to the order of the mode. Our results suggest a possible route to high brightness diode-pumped solid-state laser sources.