Faster and more accurate geometrical-optics optical force calculation using neural networks
David Bronte Ciriza, Alessandro Magazzù, Agnese Callegari, Gunther Barbosa, Antonio A. R. Neves, Maria A. Iatì, Giovanni Volpe, Onofrio M. Maragò
arXiv: 2209.04032

Optical forces are often calculated by discretizing the trapping light beam into a set of rays and using geometrical optics to compute the exchange of momentum. However, the number of rays sets a trade-off between calculation speed and accuracy. Here, we show that using neural networks permits one to overcome this limitation, obtaining not only faster but also more accurate simulations. We demonstrate this using an optically trapped spherical particle for which we obtain an analytical solution to use as ground truth. Then, we take advantage of the acceleration provided by neural networks to study the dynamics of an ellipsoidal particle in a double trap, which would be computationally impossible otherwise.

Machine learning to enhance the calculation of optical forces in the geometrical optics approximation David Bronte Ciriza, Alessandro Magazzù, Agnese Callegari, Maria A. Iatì, Giovanni Volpe, Onofrio M. Maragò Submitted to: OSA-OMA-2021, AF2D.2 Contribution Date: 16 April Time: 17:00 CEST

Short Abstract: We show how machine learning can improve the speed and accuracy of the optical force calculations in the geometrical optics approximation

Extended Abstract: Light can exert forces by exchanging momentum with particles. Since the pioneering work by Ashkin in the 1970’s, optical forces have played a fundamental role in fields like biology, nanotechnology, or atomic physics. Optical tweezers, which are instruments that, by tightly focusing a laser beam, are capable of confining particles in three dimensions, have become a common tool for manipulation of micro- and nano- particles, as well as a force and torque transducer with sensing capabilities at the femtonewton level. Optical tweezers have also been successfully employed to explore novel phenomena, including protein folding and molecular motors, or the optical forces and Brownian motion of 1D and 2D materials.

Numerical simulations play a fundamental role in the planning of experiments and in the interpretation of the results. In some basic cases for optical tweezers, the optical trap can be approximated by a harmonic potential. However, there are many situations where this approximation is insufficient, for example in the case of a particle escaping an optical trap, or for particles that are moving on an optical landscape but are not trapped. In these cases, a more complex treatment of the light-matter interaction is required for a more accurate calculation of the forces. This calculation is computationally expensive and prohibitively slow for numerical simulations when the forces need to be calculated many times in a sequential way. Recently, machine learning has been demonstrated to be a promising approach to improve the speed of these calculations and therefore, to expand the applicability of numerical simulations for experimental design and analysis.

In this work, we explore the geometrical optics regime, valid when the particles are significantly bigger than the wavelength of the incident light. This is typically the case in experiments with micrometer-size particles. The optical field is described by a collection of N light rays and the momentum exchange between the rays and the particle is calculated employing the tools of geometrical optics. The limitation of considering a discrete N number of light rays introduces artifacts in the force calculation. We show that machine learning can be used to improve not only the speed but also the accuracy of the force calculation. This is first demonstrated by training a neural network for the case of a spherical particle with 3 degrees of freedom accounting for the position of the particle. We show how the neural network improves the prediction of the force with respect to the initial training data that has been generated through the geometrical optics approach.

Starting from these results for 3 degrees of freedom, the work has been expanded to 9 degrees of freedom by including all the relevant parameters for the calculation of the optical forces considering also different refractive indexes, shapes, sizes, positions, and orientations of the particle besides different numerical apertures of the objective that focuses the light.

This work proves machine learning as a compact, accurate, and fast approach for optical forces calculation and presents a tool that can be used to study systems that, due to computation limitations, were out of the scope of the traditional ray optics approach.