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Hermite–Sinusoidal-Gaussian Beams In Complex Optical Systems, Lee W. Casperson, Anthony A. Tovar
Hermite–Sinusoidal-Gaussian Beams In Complex Optical Systems, Lee W. Casperson, Anthony A. Tovar
Electrical and Computer Engineering Faculty Publications and Presentations
Sinusoidal-Gaussian beams have recently been obtained as exact solutions of the paraxial wave equation for propagation in complex optical systems. Another useful set of beam solutions for Cartesian coordinate systems is based on Hermite–Gaussian functions. A generalization of these solution sets is developed here. The new solutions are referred to as Hermite–sinusoidal-Gaussian beams, because they are in the form of a product of Hermite-polynomial functions of either complex or real argument, sinusoidal functions of complex argument, and Gaussian functions of complex argument. These beams are valid for propagation through systems that can be represented in terms of complex beam matrices, …
Generalized Sylvester Theorems For Periodic Applications In Matrix Optics, Lee W. Casperson, Anthony A. Tovar
Generalized Sylvester Theorems For Periodic Applications In Matrix Optics, Lee W. Casperson, Anthony A. Tovar
Electrical and Computer Engineering Faculty Publications and Presentations
Sylvester's theorem is often applied to problems involving light propagation through periodic optical systems represented by unimodular 2 × 2 transfer matrices. We extend this theorem to apply to broader classes of optics-related matrices. These matrices may be 2 × 2 or take on an important augmented 3 × 3 form. The results, which are summarized in tabular form, are useful for the analysis and the synthesis of a variety of optical systems, such as those that contain periodic distributed-feedback lasers, lossy birefringent filters, periodic pulse compressors, and misaligned lenses and mirrors. The results are also applicable to other types …
Synthesis Of Gaussian Beam Optical Systems, Lee W. Casperson
Synthesis Of Gaussian Beam Optical Systems, Lee W. Casperson
Electrical and Computer Engineering Faculty Publications and Presentations
Systematic procedures are presented for determining the the optical components needed to obtain an arbitrary transformation of a propagating light ray or Gaussian beam.