Optical force-induced nonlinearity and self-guiding of light in human red blood cell suspensions

Osmotic conditions play an important role in the cell properties of human red blood cells (RBCs), which are crucial for the pathological analysis of some blood diseases such as malaria. Over the past decades, numerous efforts have mainly focused on the study of the RBC biomechanical properties that arise from the unique deformability of erythrocytes. Here, we demonstrate nonlinear optical effects from human RBCs suspended in different osmotic solutions. Specifically, we observe self-trapping and scattering-resistant nonlinear propagation of a laser beam through RBC suspensions under all three osmotic conditions, where the strength of the optical nonlinearity increases with osmotic pressure on the cells. This tunable nonlinearity is attributed to optical forces, particularly the forward-scattering and gradient forces. Interestingly, in aged blood samples (with lysed cells), a notably different nonlinear behavior is observed due to the presence of free hemoglobin. We use a theoretical model with an optical force-mediated nonlocal nonlinearity to explain the experimental observations. Our work on light self-guiding through scattering bio-soft-matter may introduce new photonic tools for noninvasive biomedical imaging and medical diagnosis.


Animation and videos:
Illustration of optical self-trapping by means of red blood cells (RBCs)

Absorption spectra of human RBC suspensions:
RBCs in buffer media have a strong Soret band at 416 nm and weak absorption bands at 543 nm and 578 nm (Fig. S2). The measured data for three different buffers were normalized via dividing the spectra by their norms. RBCs have relatively low absorption at 532 nm, the wavelength used in our nonlinear self-trapping experiment. A slight variation in absorption under different buffers can be seen in the zoom-in inset of Fig. S2: the absorbance increases in RBC suspensions when ranging from hypotonic, then isotonic and finally hypertonic buffer conditions. Meanwhile, due to the change of RBC size/shape, the Hb concentration increases within the cell from hypotonic to hypertonic via isotonic buffer conditions, which leads to an increase in the effective index of refraction 22,42 .

Transmission measurements in human RBC suspensions:
We performed a series of experiments to measure the normalized transmission of light through the RBC suspensions as a function of input power, under different osmotic conditions. In addition to the summarized results depicted in Fig

Viability assessment of RBCs:
In this study, a light beam was focused using a normal lens (f = 125 mm) which generates a much lower photon density compared to the high numerical aperture objective (NA ≥ 1.3) used for our optical tweezers setting. Even with an incident power as high as 700 mW, we estimated that the power density (<1 mWμm -2 ) is still below the threshold for radiation damage 27 . In the nonlinear propagation experiment, the measurements were performed in 4 mL volume suspensions, which further minimizes the local heating and photodamage effects.
In particular, to check for possible photodamage, the suspended RBCs in all three used buffers were spun down after illumination with the 532 nm laser for several minutes at the power of about 450 mW (higher than the value used for the nonlinear self-trapping experiments of Fig. 1 in different buffer solutions). No pink coloration in the supernatant solution was observed, thus indicating that there is no hemolysis due to the laser illumination. This was verified by recording absorption spectra of the supernatant obtained from the suspensions with and without laser exposure, where no absorption was observed. In addition, to examine possible damage of individual cells due to laser illumination, a high concentration of RBCs (suspended in the hypotonic buffer) were casted on a thin glass slide chamber made of coverslips and exposed to the focused laser beam at 450 mW. White light images were recorded before and after exposure using a 100x oil immersion microscope objective and a CCD camera (Fig. S4). The experiment was repeated three times, and no significant changes in cell shape or damage of the RBCs was observed under the microscope. Supplementary Fig. S4: White-light images of RBCs (a) before and (b) after illumination with a 532 nm laser beam at 450 mW power. Images were recorded using a 100x oil immersion microscope objective. No significant changes in shape or damage of the RBCs were observed.

Theoretical model:
To numerically simulate the nonlinear beam propagation through different suspensions of RBCs, we employed an extension of our non-local theoretical model (previously described in Ref. 21). It is a diffractive nonlinear Schrödinger-type equation: where is the electric field envelope, = 2 / denotes the vacuum wavenumber, and is the scattering cross-section for the absorption losses. Meanwhile, represents the volume of an individual particle and its refractive index, stands for the refractive index of the background medium, and denotes the time and intensity-dependent particle concentration. The evolution of the latter is determined by coupling Eq.
(1) to a diffusion-advection equation: where is the diffusion coefficient, is time, = (| | ) is a velocity field determined by the optical forces and is the particle mobility. The intensity dependent optical forces acting on the particles are modeled as ( = | | ) = ∇ + , which includes contributions from both an optical gradient force with polarizability coefficient and a forward-scattering force with coefficient along the longitudinal direction . In our simulations, we used = 1.2 · 10 m 2 .s and = 1.2 · 10 m.s , which results in a proportionality of / consistent (i.e., in the same order of magnitude) with Rayleigh predictions. The variation in osmotic conditions for the different RBC suspensions is taken into account within the model by changing the particle volume and refractive index, and also by rescaling the magnitude of the optical forces with the assumption of a similar proportionality dependence on size and refractive index as for dielectric spheres in the Rayleigh scattering approximation 51 .
To numerically solve Eq. (1), we used a (2+1)D split-step Fourier algorithm that also includes additional scattering effects to model the random fluctuations of the refractive index. To obtain a self-consistent solution, we repeatedly propagate the field through the entire medium and calculate the particle distribution after a short time-step for the corresponding optical force. The new particle distribution is then used in the next iteration to propagate the field again, and the process is repeated until no significant modification of either the field or the particle distribution is observed.