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• 1. [Article] Generalized Beam Matrices. III. Application to Diffraction Analysis

  In analogy with Huygen’s wavelets a new method based on Gaussian beamlets is used to develop a conventional diffraction integral formalism for paraxial optical systems representable by complex 2×2 ABCD ...

  Citation × Citation Citation Abstract Copy Title: Generalized Beam Matrices. III. Application to Diffraction Analysis Author: Casperson, Lee W., Tovar, Anthony A. Year: 1996 In analogy with Huygen’s wavelets a new method based on Gaussian beamlets is used to develop a conventional diffraction integral formalism for paraxial optical systems representable by complex 2×2 ABCD Gaussian beam matrices. This method, along with a new phase parameter transformation, is then used to produce a new diffraction integral for studying the propagation of light beams with arbitrary spatial profiles through much more general misaligned complex optical systems representable by 3×3 ABCDGH beam matrices. Title: Generalized Beam Matrices. III. Application to Diffraction Analysis Author: Casperson, Lee W., Tovar, Anthony A. Year: 1996 In analogy with Huygen’s wavelets a new method based on Gaussian beamlets is used to develop a conventional diffraction integral formalism for paraxial optical systems representable by complex 2×2 ABCD Gaussian beam matrices. This method, along with a new phase parameter transformation, is then used to produce a new diffraction integral for studying the propagation of light beams with arbitrary spatial profiles through much more general misaligned complex optical systems representable by 3×3 ABCDGH beam matrices. Close

• 2. [Article] Generalized Beam Matrices. II. Mode Selection in Lasers and Periodic Misaligned Complex Optical Systems

  A generalized beam matrix method is used to investigate the mode structure of astigmatic misaligned optical systems with loss or gain. In these optical systems the usual real-argument polynomial-Gaussian ...

  Citation × Citation Citation Abstract Copy Title: Generalized Beam Matrices. II. Mode Selection in Lasers and Periodic Misaligned Complex Optical Systems Author: Casperson, Lee W., Tovar, Anthony A. Year: 1996 A generalized beam matrix method is used to investigate the mode structure of astigmatic misaligned optical systems with loss or gain. In these optical systems the usual real-argument polynomial-Gaussian beams are not eigenfunctions, and off-axis complex-argument polynomial beams must be used. New beam transformations for these complex-argument modes are reported. Stability criteria are developed, and mode selection in laser resonators that contain tilted, displaced, or curved complex optical elements is discussed. Title: Generalized Beam Matrices. II. Mode Selection in Lasers and Periodic Misaligned Complex Optical Systems Author: Casperson, Lee W., Tovar, Anthony A. Year: 1996 A generalized beam matrix method is used to investigate the mode structure of astigmatic misaligned optical systems with loss or gain. In these optical systems the usual real-argument polynomial-Gaussian beams are not eigenfunctions, and off-axis complex-argument polynomial beams must be used. New beam transformations for these complex-argument modes are reported. Stability criteria are developed, and mode selection in laser resonators that contain tilted, displaced, or curved complex optical elements is discussed. Close

• 3. [Article] Generalized Beam Matrices: Gaussian Beam Propagation in Misaligned Complex Optical Systems

  A novel 3 × 3 transfer-matrix method is developed to propagate off-axis Gaussian beams in astigmatic optical systems that may include tilted, displaced, or curved optical elements. Unlike in a previous ...

  Citation × Citation Citation Abstract Copy Title: Generalized Beam Matrices: Gaussian Beam Propagation in Misaligned Complex Optical Systems Author: Tovar, Anthony A., Casperson, Lee W. Year: 1995 A novel 3 × 3 transfer-matrix method is developed to propagate off-axis Gaussian beams in astigmatic optical systems that may include tilted, displaced, or curved optical elements. Unlike in a previous generalized ray matrix formalism, optical elements that possess gain or loss such as Gaussian apertures, complex lenslike media, and amplifiers are included; and a new beam transformation is found. In addition, a novel exponential variable-reflectivity mirror, which displaces a Gaussian beam without changing its spot size, and a complex prismlike medium are introduced. Title: Generalized Beam Matrices: Gaussian Beam Propagation in Misaligned Complex Optical Systems Author: Tovar, Anthony A., Casperson, Lee W. Year: 1995 A novel 3 × 3 transfer-matrix method is developed to propagate off-axis Gaussian beams in astigmatic optical systems that may include tilted, displaced, or curved optical elements. Unlike in a previous generalized ray matrix formalism, optical elements that possess gain or loss such as Gaussian apertures, complex lenslike media, and amplifiers are included; and a new beam transformation is found. In addition, a novel exponential variable-reflectivity mirror, which displaces a Gaussian beam without changing its spot size, and a complex prismlike medium are introduced. Close

• 4. [Article] Hermite–Sinusoidal-Gaussian Beams in Complex Optical Systems

  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 ...

  Citation × Citation Citation Abstract Copy Title: Hermite–Sinusoidal-Gaussian Beams in Complex Optical Systems Author: Casperson, Lee W., Tovar, Anthony A. Year: 1998 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, and the previous beam solution sets are special cases of these more general results. Propagation characteristics and applications of these beams are discussed, including their use as a basis set for propagation of arbitrary electromagnetic beams. Title: Hermite–Sinusoidal-Gaussian Beams in Complex Optical Systems Author: Casperson, Lee W., Tovar, Anthony A. Year: 1998 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, and the previous beam solution sets are special cases of these more general results. Propagation characteristics and applications of these beams are discussed, including their use as a basis set for propagation of arbitrary electromagnetic beams. Close