Tool for simulating the focusing of arbitrary vector beams in free-space and stratified media

Abstract

Vectorial models of focused beams are important to a variety of fields including microscopy, lithography, optical physics, and biomedical imaging. This has led to many models being developed, which calculate how beams of various profiles are focused both in free space and in the presence of stratified media. The majority of existing models begin with a vectorial diffraction formula, often referred to as the Debye-Wolf integral, which must be evaluated partially analytically and partially numerically. The complexity of both the analytic and numerical evaluations increases significantly when exotic beams are modeled, or, a stratified medium is located in the focal region. However, modern-day computing resources permit this integral to be evaluated entirely numerically for most applications. This allows for the development of a vectorial model of focusing in which the focusing itself, interaction with a stratified medium, and incident beam specification are independent, allowing for a model of unprecedented flexibility. We outline the theory upon which this model is developed and show examples of how the model can be used in applications including optical coherence tomography, high numerical aperture microscopy, and the properties of cylindrical vector beams. We have made the computer code freely available.

Optical Time-Resolved Microscopy on Few-Atoms-Thick Materials

“…Also, we have to take into account the distortions of femtosecond pulses when focusing through dielectric slabs. , When focusing a beam of light on a thin film sample through a dielectric slab, as illustrated in Figure b, cases 5–7, the objective focal spot can undergo deformations due to the refractive index contrast between the slab and the surrounding medium. This effect is caused by the spatial variation of the phase shift induced by the slab on the transmitted beam, leading to distortions of the focused spot shape.…”

“…In Figure , an example demonstrates the focusing of light with a wavelength of 800 nm through a standard 170 μm thick glass cover slide used in microscopy. The vectorial simulation, relative to a dry objective with a numerical aperture of 0.55, is based on the work of ref . The focus position of the free beam (no glass slide) is located at the axis origin, as shown by the red line.…”

TDMS: An open source Time Domain Maxwell Solver for simulations in biomedical optics

“…The comple amplitude of the illumination uses open source software to compute the Debye-Wolf integral, 5 which means that the illumination satisfies Maxwell's equations. Using this formulation also allows for realistic parameters such as aperture sizes, aberrations, arbitrary polarisation, bespoke optical fiber modes, etc., to be included in the model.…”

Manipulating the transverse spin angular momentum and Belinfante momentum of spin-polarized light by a tilted stratified medium in optical tweezers

“…Also, due to the coupled nature of spin and polarization properties in SOI, the change in polarization needs to be continuously tracked for the propagation of all the plane waves. Since this formalism depicts the field as a vectorial superposition of plane waves, focusing and propagation through stratified medium gets decoupled [22], and one can find field components relatively easily. Such decoupling of a single problem into two independent problems allows us to numerically find the optical fields for the tilted interface structure for an incident beam with an arbitrary field profile.…”

“…In what follows, we follow Ref. [22] to present the basic steps and generalize the approach for the case of a tilted stratified medium. We start our theoretical model with a lens system of arbitrary NA and focal length f , with its axis along ẑ, as shown in Fig.…”