In order to get lasing, light has to resonate within an optical cavity, formed by mirrors or a reflective surface. The reflective surface produced by E. coli (e.g. silica and tin dioxide layer and PHB granules) is not a perfect mirror and therefore the light can only get reflected by total internal reflection When light approaches a (reflective) interface between two materials, at a large enough angle (with respect to the normal to the surface) and the refractive index on the other side is lower, all the light is reflected. This phenomenon is called total internal reflection. At which angle light gets totally reflected depends on the material characteristics (refractive indices) of both materials. when approaching the edge of the cavity at a large enough angle. When the light gets reflected by total internal reflection in a closed circular path inside a microcavity, this type of optical cavity is called a whispering gallery mode (WGM) micro-resonator (Humar et al., 2015)(figure 2). Whispering gallery modes are the phenomenon that waves are circulating in a spherical object in a closed path, that is the begin and end of one circulation is at the same point, as a result of total internal reflection at the surface (Humar et al., 2015, Wilson et al., 2012). A closed path of a an integer number of wavelengths is required so that constructive interference If we add two (or more) waves together, it results in a new wave. If the original waves have overlapping crests and valleys (are in phase), the amplitude of the resulting wave will equal the sum of the amplitudes of the original waves, a phenomenon known as constructive interference. takes place.

For the first method described above, E. coli encapsulates itself by a layer of biosilica or tin dioxide. Here we determine what the minimal size of the bacteria should be to fit light inside the encapsulated E. coli, using ray optics. We found that a biosilica covered cell should have a minimal diameter of 1-1.3 µm depending on the fluorescent proteins used. For a cell covered with tin dioxide, the minimal diameter varies between 1.5-1.7 µm depending on the fluorophore used.

We investigate the possibility of using PHB granules inside the cells as an optical cavity, as an alternative to using the whole cell as an optical cavity. In a similar method as for the encapsulated E. coli, the minimal size of the PHB granules was determined by ray optics. We found that the minimal diameter of the PHB granules is about 1.7 µm, which is larger than the small axis of E. coli. Since the PHB granules cannot reach this size inside the cell, it will not be possible to use these as an optical cavity.

The minimal sizes we calculated for an optical cavity in E. coli encapsulated by a reflective layer are comparable to the natural size of E. coli.However, this is the most optimistic model, because we computed the absolute minimum size to fit one wavelength of light between two times hitting the reflective surface. Our model thus shows that we can only trap light inside a cell in the most ideal case where we do not take losses into account.

As we need enough fluorophores in the gain medium to obtain lasing it is important to know how the concentration of fluorophores evolves over time when using specific promoters. Therefore we made a kinetic model as in figure 3. To determine the growth rate we were able to fit the measured OD values of the fluorophore expressing bacteria to a growth equation. The growth rate was used in the kinetic model to determine the promoter strength by fitting experimentally obtained data. In our case we use constitutive promoters, however it appears that this model is only applicable to inducible promoters.

To determine the intracellular concentration of the fluorophores, we made a calibration curve of EGFP. Although the fluorophores we have used in the experiments are GFPmut3b, mVenus and mCerulean. In order to determine their concentration, we used instead the calibration curve of EGFP and the relative brightness for each fluorophore compared to EGFP (Gambhir et al., 2010). The brightness of a fluorophore is the product of its quantum yield and extinction coefficient, and is proportional to the number of photons produced per molecule. Using the relative brightness we were able to determine the concentration of fluorescent molecules in the cells with the fluorophores mVenus and mCerulean. The concentration of both fluorophores is about 20mM.

In order to determine the minimal concentration of fluorophores required for lasing we made a model describing the kinetics of our biolaser. In this model we included spontaneous emission, stimulated emission and the cavity characteristics, such as mirror reflectivity and absorption by the medium. We determine the number of photons and the number of fluorophores in the excited state and solve this over time. We compared the results of our model with biolaser experiments from literature (Gather et al., 2011) and derived a threshold for lasing as a function of fluorophore concentration. We found that in a cavity the size of an E. coli cell, (1 µm in diameter), lasing can occur starting at fluorophore concentrations larger than 0.1 M. However, in our cells the maximum concentration we can achieve is about 20 mM. Since concentrations an order of magnitude higher is impossible to reach within the cell, lasing is physically not possible in our cells. Due to the small size of our cells, the mirror losses are much higher than in a large laser cavity since the photons will bounce more often to the mirrors while traveling the same distance. When we stick to the concentration of 20 mM we can determine the minimal cell size to get lasing. The minimal cell size was found to be 8 µm in diameter. We did not find a clear difference between using polysilicate and tin dioxide as a refractive layer. From our model we found that the there is no clear difference between using polysilicate or tin dioxide as a reflective surface around the cell. experiments

The quality factor (Q factor) indicates how much energy is stored in a our cavity versus how much is lost,it is defined as the energy stored divided by the energy lost in each circle times \(2 \pi\). (Cory and Chaniotakis, 2006; Kao and Santosa, 2008). As its name indicates, the Q factor is a measure of the quality of a resonator. Using COMSOL Multiphysics, we modeled the structure of the system and determined its eigenfrequencies.

Our modeling focused on finding eigenfrequencies and eigenmodes around the green light frequency to see if we can have resonation of light in our cavities. Our models showed that there are no modes of interest for the polysilicate covered cell but there are two interesting modes for the tin dioxide covered cell. An example of a mode in the tin dioxide covered cell can be seen in figure 4. This mode has the eigenfrequency of \(\omega = 6.028\times10^{14} + i\times2.3 \times 10^{11} \) Hz and results in a Q factor of \(Q=1.3109\times10^3\).