Generalized beam matrices: Gaussian beam propagation in misaligned complex optical systems

Abstract

A novel 3 X 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 merna, and amplifiers are included; and a new beam transformation is found. In addition, a novel exponential variable-reflectivity mirror, which displaces a Gaussianbeam without changing its spot size, and a complex prismlike medium are introduced.

Reflection and Transmission of Light Beams at a Curved Interface: Coherent State Approach

“…Unlike the superposition of off-axis Gaussian function components used in [14], CS decomposition represents the superposition of linearly shifted and spatially rotated beams, forming the full set of functions. Transfer-matrix method [15] can be used to calculate the propagation of off-axis Gaussian beams in optical systems with tilted, displaced and curved optical elements.…”

Beam propagation in a uniaxial crystal under small angle to the optical axis and arrays of bottle beams

“…To calculate positions of two focuses, we used rough ABCD model, described in [13] for the case of misaligned complex optical systems, i.e. when axis of the beam and axis of the optical element are not coincide.…”

Beam Modes of Lasers with Misaligned Complex Optical Elements

“…In the appendix of Ref. 138 it is shown that when the generalized beam matrix elements are purely real (i.e. for lossless optical systems), the propagation characteristics may be described in terms of a generalized ray matrix.…”

“…Gaussian transmission filters (and Gaussian variable reflectivity mirrors) [22] [153] [155]- [159], exponential transmission filters (and exponential variable reflectivity mirrors) [138], homogeneous amplifiers and absorbers [134], amplifiers (and absorbers) with a linear gain (loss) profile [17] [138], and amplifiers (and absorbers) with a quadratic gain (loss) profile [I] [14] [145] are all complex optical elements. Amplifiers and absorbers may be in the shape of a wedge or lens [138]. A medium which may have both a quadratic gain and refractive index profile is known as a complex lenslike medium [I] while a similar linearly profiled medium is a complex prismlike medium [138].…”

“…Amplifiers and absorbers may be in the shape of a wedge or lens [138]. A medium which may have both a quadratic gain and refractive index profile is known as a complex lenslike medium [I] while a similar linearly profiled medium is a complex prismlike medium [138].…”