Higher-order fractal laser modes

Abstract

Our recent unexpected discovery that fractal pattern formation occurs in the modes of unstable optical resonators has opened up a new area in laser science. In this paper, we present recent results on the generation of higher-order fractal modes in unstable cavity lasers. Our initial work was performed in cavities with only one transverse dimension; this was then generalised to encompass resonators with fully 2D transverse characteristics. The mode profiles in this case are of such complexity that we have called the device the kaleidoscope laser. Excellent agreement between experiment and theory has been obtained in regard to the detailed properties of 2D modes. Moreover, the fractal topology of unstable cavity eigenmodes becomes at once apparent when they are represented in a 2D phase space (the transverse plane) since their fractal dimension lies between 1 and 2. However, even though higher-order modes are routinely generated in experiments, theoretical work has to date been limited to only lowest-loss 2D modes. In this paper, we consider two different ways of removing this restriction. Firstly, we generalise the virtual source method to the case of a fully 2D transverse geometry. Secondly, we discuss a computational approach that mimics the standard experimental solution to the generation of higher-order modes in which a narrow-band spectral filter is included in the cavity.