Abstract
Applications that envisage utilizing the orbital angular momentum (OAM) at the single photon level assume that the OAM degrees of freedom of the photons are orthogonal. To test this critical assumption, we quantize the beam-like solutions of the vector Helmholtz equation from first principles. We show that although the photon operators of a diffracting monochromatic beam do not in general satisfy the canonical commutation relations, implying that the photon states in Fock space are not orthogonal, the states are bona fide eigenstates of the number and Hamiltonian operators. As a result, the representation for the photon operators presented in this work form a natural basis to study structured monochromatic light at the single photon level.
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