Most of us are familiar with the term laser, you have probably seen one or used one as a pointer in a presentation, in a computer mouse or to measure a distance. What makes a laser different from other light sources is its coherence, meaning that it produces a narrow beam that doesn’t disperse over long distances, and that all the light particles, photons, in the beam have identical properties.

The word laser is an acronym for Light Amplification by Stimulated Emission of Radiation. This acronym describes the working principles of a laser. The main parts of a laser are the energy pumping source, the gain medium and two mirrors, typically one with a reflectivity of 100% and one with a reflectivity close to 100%. The lasing process starts when a light pumping source is used to excite the gain medium. When the gain medium is excited due to the pumped energy the electrons of its atoms jump to a specific higher energy state due to the energy they absorbed and after a while they drop down to their initial equilibrium position. The energy difference from the specific higher position to the equilibrium is emitted in the form of a photon with exactly that amount of energy, so we can see that the color of the light depends only on the active region’s material. Those produced photons are now leaving the atoms in random directions but some of them bounce back from the two mirrors and are trapped in the device. When those photons meet other excited atoms they make them release the extra energy in the form of a photon and the produced photon moves in the same direction as them. This process is called stimulated emission, so instead of one photon bouncing back and forth now we have two, which is how the light is amplified in the direction perpendicular to the two parallel mirrors. Finally, when the light is amplified enough it leaves the device from the partially reflective mirror as a laser beam. Figure 1 below shows all the basic components of a laser we have discussed.

Video explaining the lasing principle (LASER, 2016):

The three main ways to handle particle light interactions are Rayleigh scattering, Mie theory and Ray optics. The Mie theory is the most complete and reliable model, and applicable in a big range of particle sizes (Pecina, 1978). Mie scattering is the Mie solution to the Maxwell’s equations and it describes the scattering of an incoming continuous plane wave of a sphere of arbitrary radius (Zijlstra, 2005; Bohren and Huffman, 1983). In general, it is used in cases where the size of a particles is comparable to the wavelength of the incoming light, to calculate the electric- and magnetic fields in and out of the sphere and the scattering amount (Mie scattering, 2016).

The size of a scattering particle can be represented with the non-dimensional parameter χ:

Three main scattering regimes exist for different particle sizes (Pecina, 1978; Kostylev, 2007) :

• \( \chi \ll 1\) : Rayleigh scattering
• \( \chi \approx 1 \) : Mie scattering
• \( \chi \gg 1\): Geometric Scattering

As can be seen from equation 1 the regime that needs to be considered depends on both the particle size and the wavelength. Depending of those two parameters Geometric optics, Mie Scattering, Rayleigh Scattering or no scattering can be considered as shown in figure 1 below.

A comprehensive view on the Mie theory and its solution for two concentric spheres (similar to our lenses) can be found in (Aden and Kerker, 1951).

Mie theory in the modeling.

Mie theory was used in the modeling of biolenses. As Mie theory is a solution of Maxwell’s equations it is very hard to develop numerical solutions from scratch. The COMSOL models created to investigate the interaction of light with the silica covered cells are using the Mie theory to compute the results.