Full-wave simulation of focusing light through scattering layers using the T-matrix method

Optical wavefront shaping (WFS) is a method of controlling the propagation of light through scattering media by spatially modulating the incident wavefront. This allows light to constructively interfere to produce an optical focus at depth or to image through turbid media and around corners. Experimental investigation of WFS can be complemented by computational approaches. This is because computational methods can easily resolve both amplitude and phase information, can directly evaluate the field inside a given medium, and are able to comprehensively and dynamically control the domain with respect to optical properties or geometry. However, current simulation methods are either too computationally challenging to model volumes of at least a transport mean free path (where light propagation becomes diffuse and WFS has the greatest potential benefit), or too incomplete to model the underlying deterministic scattering and interference processes that characterise physically realistic light transport.

To address the challenge of designing a computationally efficient yet physically rigorous simulation of WFS we have coupled the T-matrix method with a discrete particle model of turbid media. This full-wave method directly solves Maxwell’s equations (and as such can accurately simulate the physics of light scattering) but does not require a computationally expensive subwavelength discretisation of the simulation domain. Instead, the T-matrix method works by propagating light through a medium of scattering particles (most commonly spheres) such that the total field is a superposition of the scattered fields associated with each sphere. This field is calculated by solving a linear system governing how each sphere interacts with every other sphere. The angular spectrum method is then used to simulate the complex beams found in WFS by decomposing the incident light into a spectrum of plane waves, which can be simulated sequentially.

To demonstrate the technique, the seminal Vellekoop and Mosk WFS experiment is replicated in silico by simulating the generation of an optical focus through a titanium dioxide (TiO2) scattering layer using a full-phase stepwise sequential algorithm. A 30x30x10µm3 domain was constructed comprised of TiO2 scattering spheres with a radius of 1µm and refractive index of 2.6 at a concentration of 0.26 by volume. The background refractive index was set to 1.33 and 441 different plane waves (λ=633nm) were simulated propagating through the medium using the CELES software, with the polar and azimuthal angles of the incident waves varying from -10 to 10°. Mie theory was used to design this domain such that it has a transport mean free path of ∼5µm, which ensures that there is no correlation between the input and output fields.