Beams

As mentioned in the Rays section, a beam within the context of this package serves as a data structure for storing collections of rays, forming the backbone of the simulation framework. Beams are intended to be designed as AbstractTrees to allow for ray bifurcations, e.g. in the case of optical elements such as beamsplitters. The solve_system! function relies on this data structure to perform ray tracing computations within optical systems.

To ensure compatibility and extensibility, beam types must adhere to the BeamletOptics.AbstractBeam interface. Refer to its documentation for more information.

Basic beam

A minimal implementation of the BeamletOptics.AbstractBeam type is provided by the Beam. It can be used to store a light path through an optical system. If the beam is split, its children will be recursively traced until all paths are solved.

Beam{T, R <: AbstractRay{T}} <: AbstractBeam{T, R}

A ray tracing example through an arbitrary system using a Beam is shown below. Individual Ray segments are marked by their starting position and direction. The Beam expander and Miniature microscope tutorial covers the use of the Beam in more detail.

Beam groups

For convenience, the BeamletOptics.AbstractBeamGroup offers a container-like interface for groups of Beams as commonly used in other software packages. The following concrete implementations are currently provided:

julia> BeamletOptics.list_subtypes(BeamletOptics.AbstractBeamGroup);└── BeamletOptics.AbstractBeamGroup
    ├── CollimatedSource{T, R} where {T<:Real, R<:BeamletOptics.AbstractRay{T}}
    └── PointSource{T, R} where {T<:Real, R<:BeamletOptics.AbstractRay{T}}

At least 2 types have been found.

Refer to the following sections for convenience constructors to generate the sources listed above.

Collimated beam source

The collimated beam source is ideal to model light coming from a focal plane at infinity. This is useful for simulating plane wavefronts. You can define a collimated monochromatic Beam source as follows:

CollimatedSource(pos, dir, diameter, λ; num_rings, num_rays)

A special constructor called UniformDiscSource is available, which offers an equal-area sampling (Fibonnaci-pattern) sampling and is thus favorable in situations where the weighting of the individual beams becomes important, e.g. for calculating a point spread function using PSFDetector.

UniformDiscSource(pos, dir, diameter, λ; num_rays=1_000)

Point beam source

The PointSource type is used to model emission from a spatially localized source that radiates Beams in a range of directions. This is commonly used to simulate conical emission patterns, such as light emerging from a fiber tip or a light source for a lens objective with a known focal distance. You can specify the origin and a propagation direction, which are then used to construct the monochromatic PointSource.

PointSource(pos, dir, θ, λ; num_rings, num_rays)

Below you can find an exemplary illustration of a PointSource.

Gaussian beamlet

Lasers are common devices in modern optical laboratories. Modeling their propagation through an optical setup can be of interest when planning new experiments. Geometrical ray tracing struggles to capture the propagation of a laser beam correctly, since it can not inherently capture the wave nature of e.g. the Gaussian beam.

The electric field of the $\text{TEM}_{00}$ spatial Gaussian mode can be calculated analytically using the BeamletOptics.electric_field function:

electric_field(r, z, E0, w0, w, k, ψ, R) -> ComplexF64

The evolution of this field through an optical system can be modeled e.g. by the ray transfer matrix formalism using the complex $q$-factor [7, pp. 27]. A Julia-based implementation of this approach can be found in ABCDMatrixOptics.jl. However, in the case of this package another approach will be used.

Complex ray tracing

In 1968 an internal publication at Bell Labs by J. Arnaud introduced the concept of complex rays wherein three geometrical beams can be used to model the propagation of a Gaussian in fundamental mode through a symmetric optical system, i.e. without the Gaussian obtaining astigmatism and/or higher-order abberations. This method is analoguos to the ray transfer matrix based $q$-method [8].

Without extensions of the original method, the following key assumptions must be met such that this method can be applied

• all (complex) beams of the Gaussian in question must intersect the same optical elements
• the optical elements are large compared to the beam (waist)
• the paraxial approximation must hold for each beam
• the Gaussian may not be clipped by hard apertures
• Lagrange invariant must be fulfilled

Various versions of this approach have been implemented under different names in commercial software, most notably FRED and Code V, as well as in open source software, e.g.

• Raypier - based on Cython, maintenance status not known
• Poke - based on Zemax API and Python, maintained by J. Ashcraft et al. [9]
• IfoCAD - maintenance status not known, refer to Wanner et al. [10]

This package implements the above method via the GaussianBeamlet and the BeamletOptics.AstigmaticGaussianBeamlet (Work in progress).

Stigmatic Beamlets

The GaussianBeamlet implements the BeamletOptics.AbstractBeam interface and can be used to model the propagation of a monochromatic Gaussian ($\text{TEM}_{00}$-mode) through optical system where all optics lie on the optical axis, e.g. no tip and/or tilt dealignment, and abberations can be neglected. It is represented by a chief (red), waist (blue) and divergence (green) beam. See below how these beans are placed in relation to the envelope of the Gaussian beam.

GaussianBeamlet{T} <: AbstractBeam{T, Ray{T}}

A GaussianBeamlet can be constructed via:

GaussianBeamlet(position, direction, λ, w0; kwargs...)

Obtaining the beam parameters

Once a GaussianBeamlet has been traced through an optical system, several parameters might be of interest for further analysis. In order to relate the traced geometrical beams/rays to the Gaussian parameters, the publications of Arnaud, Herloski et al. and DeJager et al. are used [8, 11, 12]. Consider the following system where a Gaussian beam with arbitrary parameters has been traced through a lens using the approach outlined in the Complex ray tracing section.

The user can obtain parameters such as the beam waist radius, the radius of curvature and more using the BeamletOptics.gauss_parameters function. Below the local waist radius and curvature $R = r^{-1}$ have been calculated for the example above.

Astigmatic Polarized Beamlets

• Assumptions
  • homogeneous polarization distribution across waist
  • Lagrange invariant