We outline a theory for the calculation of the beam quality factor of an aberrated laser beam. We provide closedform equations that show that the beam quality factor of an aberrated Gaussian beam depends on all primary aberrations except tilt, defocus, and x-astigmatism. The model is verified experimentally by implementing aberrations as digital holograms in the laboratory.
If a heated pipe is rotated about its axis, a density gradient is formed which results in the pipe acting as a graded index lens. In this study we revisit the concept of a spinning pipe gas lens and for the first time analyse both the wave propagation of optical fields through the lens, and determine the optical aberrations introduced by the lens to the laser beam. We show that such lenses are highly aberrated, thus having a deleterious effect on the laser beam quality.
The concept of orthonormal polynomials is revisited by developing a Zernike-based orthonormal set for a non-circular pupil that is transmitting an aberrated, non-uniform field. We refer to this pupil as a general pupil. The process is achieved by using the QR form of the Gram Schmidt procedure on Zernike circle polynomials and is interpreted as a process of balancing each Zernike circle polynomial by adding those of lower order in the general pupil, a procedure which was previously performed using classical aberrations. We numerically demonstrate this concept by comparing the representation of phase in a square-Gaussian pupil using the Zernike-Gauss square and Zernike-circle polynomials. As expected, using the Strehl ratio, we show that only specific lower-order aberrations can be used to balance specific aberrations, for example, tilt cannot be used to balance spherical aberration. In the process, we present a possible definition of the Maréchal criterion for the analysis of the tolerance of systems with apodized pupils.
We outline an approach for the calculation of the mean focal length of an aberrated lens and provide closed-form solutions that show that the focal length of the lens is dependent on the presence of defocus, x-astigmatism, and spherical aberration. The results are applicable to Gaussian beams in the presence of arbitrary-sized apertures. The theoretical results are confirmed experimentally, showing excellent agreement. As the final results are in algebraic form, the theory may readily be applied in the laboratory if the aberration coefficients of the lens are known.
The orbital angular momentum of light has been suggested as a means of information transfer over free-space, yet the detected optical vortex is known to be sensitive to perturbation. Such effects have been studied theoretically, in particular through turbulence. Here we demonstrate a simple apparatus to introduce turbulence-like distortions to optical fields propagating over a long path. We create vortex beams and observe their propagation through a heated spinning pipe, known to mimic the two primary atmospheric aberrations, namely tip-tilt and defocus. We use a digital decomposition tool to modally resolve the distorted vortex beam into its azimuthal components to observe the impact of the medium on the detection of the encoded vortex charge. Such techniques are useful in studies of free-space optical communication with orbital angular momentum.
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