Universal description of geometric phases in higher-order optical modes bearing orbital angular momentum

We study geometric phases that arise from (cyclic) transformations of the transverse spatial structure of paraxial optical modes. Our approach involves bosonic ladder operators that, in the spirit of the quantum-mechanical harmonic oscillator, generate sets of transverse optical modes. It applies to modes of all orders in a very natural way and provides a universal geometric interpretation of the phase shifts acquired by nonastigmatic modes under typical experimental conditions.