Open Access
Add to BibSonomy
Abstract
Heme is the prosthetic group for cytochrome that exists in nearly all living organisms and serves as a vital component of human red blood cells (RBCs). Tunable optical nonlinearity in suspensions of RBCs has been demonstrated previously, however, the nonlinear optical response of a pure heme (without membrane structure) solution has not been studied to our knowledge. In this work, we show optical nonlinearity in two common kinds of heme (i.e., hemin and hematin) solutions by a series of experiments and numerical simulations. We find that the mechanism of nonlinearity in heme solutions is distinct from that observed in the RBC suspensions where the nonlinearity can be easily tuned through optical power, concentration, and the solution properties. In particular, we observe an unusual phenomenon wherein the heme solution exhibits negative optical nonlinearity and render self-collimation of a focused beam at specific optical powers, enabling shape-preserving propagation of light to long distances. Our results may have potential applications in optical imaging and medical diagnosis through blood.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Abnormalities from optical imaging on blood can serve as indicators of the development of cerebrovascular diseases, such as stroke and Alzheimer's disease [1]. Over the decades, various optical examination approaches, including intrinsic signal optical imaging and optical spectroscopy have been developed for clinical diagnosis [2–4]. However, in biological suspensions, the scattering of a laser beam, especially from a continuous wave (CW) laser, can severely hinder their extensive use in light transmission and tissue imaging due to bio-particle-induced deformation in the shape and size of the laser beam at high intensities [5]. As such, a great deal of new methods and techniques have been developed to improve the transmission performance of light, like phase conjugation [6], wavefront correction [7,8], and nonlinear optics [9]. Particularly, the study of nonlinear optics in chemical and bio-matter systems may provide new fundamental understanding as well as practical applications in addressing scientific challenges in those systems [9–27].
A variety of nonlinear phenomena including optical spatial solitons, self-trapping, and self-collimation of light have been observed in dielectric [10–17], plasmonic [18–23], and biological systems [24–27], enabling efficient and distortion-free light transmission through scattering media. For instance, in the dielectric suspension where polytetrafluoroethylene (PTFE) particles are suspended in a glycerin-water solution, the gradient force gives rise to stable soliton formation and robust transmission of light over 5 mm [16]. While in food-dye solutions, the solute's particles are several nanometers, so the ubiquitous thermo-optic effects dominate, leading to the tunable self-defocusing nonlinearity and self-collimation of light [17]. Compared to the dielectric suspensions, plasmonic suspensions exhibit more extreme nonlinearities when the optical pump is near the resonant wavelength because of the enhanced field by localized surface plasmon resonance effect. Consequently, the soliton-like beam can be achieved at a lower power [18]. Furthermore, the nonlinear behavior in plasmonic suspensions can be fine-tuned by the shapes, sizes, and wavelengths of the optical pump [20,21].
More relevant to clinical and biomedical applications, Bezryadina et al. found that in natural biological suspensions of RBCs under appropriate osmotic conditions, the optical forces can pull the micron-sized cells towards the laser beam center and push forward along the beam axis, causing self-trapping and facilitating resistant propagation of light. Consequently, the shape and size of the incident beam are maintained owing to this nonlinear bio-waveguide, which may improve the optical imaging of blood and clinical diagnosis of blood diseases [25].
In RBCs, heme is an endogenous component as the precursor of hemoglobin [28]. It is one of the iron-containing groups with an iron atom located at the center of a large heterocyclic compound. Heme plays an irreplaceable role in the metabolic processes in the human body, including respiration and energy production [29,30]. Since inorganic materials such as plasmonic nanoparticles have potential cytotoxicity and immunogenicity issues, endogenous heme becomes one of the outstanding candidates for optical imaging and phototherapy [31]. The chemical structures, optical properties, and functionality of heme and its derivatives have been extensively studied [32–34]. Furthermore, some heme-based diagnoses [35,36] and heme-based therapies [31,37,38] have been investigated, such as atherosclerosis [35] and cancer combination therapy [38]. However, previous research on heme primarily focused on its optical absorption or intrinsic fluorescence properties, with its optical nonlinearity under light illumination largely unexplored.
In this work, we present an experimental study of nonlinear optical response and beam propagation dynamics in two different types of heme solutions. Through a series of Z-scan and nonlinear beam propagation experiments, we show that the optical nonlinearity can be tuned by changing the optical powers, concentration, and solute properties. The nonlinearity leads to the self-collimation of an initially focused beam, preserving its size and shape when propagating through the heme solutions. To understand these effects, we perform numerical simulations using the nonlinear Schrödinger equation (NLSE) and the thermal convection equations. Our results confirm that the observed phenomenon is largely due to absorption-induced thermal-optic and thermal-convection effects. Furthermore, we also discuss the difference between such effects and the nonlinearity observed in membrane structure RBC suspensions. Our findings highlight the potential use of thermal effects in maintaining laser beam quality in heme solutions, which may find potential applications in the development of imaging techniques for biological samples in scattering media.
2. Materials and experimental setup
We use two kinds of heme solutions as nonlinear materials to investigate the nonlinear transmission. Hemin and hematin are two common and stable forms of heme, both belonging to the ion-porphyrin compounds with a porphyrin macrocycle, as shown in Fig. 1(a). The primary distinction between the two lies in the axial ligand attached to the central iron atom: hemin features a chloride ion, while hematin has a hydroxide ion. The different microscopic chemical structures may be responsible for different degrees of macroscopic optical nonlinearity as we shall present below.
Fig. 1. Schematic of the experimental setup and two typical heme structures. (a) Two distinct molecular structures of the heme are used as solutes for two different nonlinear solutions. Left: hematin; Right: hemin. (b) A simple setup is used for nonlinear propagation experiments, where L1 and L2 form a beam expander; L3 is the focusing lens, and L4 is the imaging lens. CCD: charge-coupled device used as a beam analyzer together with the BeamView software.
To study the nonlinear transmission of light in heme solutions, the main experimental configuration depicted in Fig. 1(b) is adopted. A CW laser beam with a Gaussian profile is expanded using a telescope (consisting of lenses L1, f = 100 mm and L2, f = 150 mm) before being focused by a convex lens (L3, f = 120 mm). A 30-mm-long quartz cuvette is located after L3, with the anterior face located 10 mm away from the focal point (denoted by the brown cube). The excellent transparency of quartz makes it possible to neglect its absorption of light. To observe the output pattern of the beam, an imaging lens (L4, f = 120 mm) and CCD camera are used. For convenience, a half-wave-plate is also used to control the optical power. An independent closed-aperture Z-scan experiment is carried out to measure the nonlinear refractive index of the heme solutions using a 1-mm-long cuvette.
3. Experimental results
3.1 Negative nonlinearity in heme solutions revealed by Z-scan experiments
To measure the nonlinear refractive index of two types of heme solutions, we employed the closed-aperture Z-scan technique [39,40].The setup is consistent with our previous work [17], and the wavelength light source for Z-scan experiment is 532 nm and the optical power is 50 mW. The cuvette is limited to 1-mm-thick, and is moved by a 1D translation stage, with the moving range from -20 mm to +20 mm on each side of the focus. The normalized power transmittance is presented in Fig. 2. During the experiment, we found that hemin is more difficult to dissolve in water and ethanol than hematin does, especially in water. Hemin-water solutions cannot present a homogeneously dispersed phase under our experimental conditions. Therefore, the relevant result in the hemin-water solutions is not presented. Besides, the transmission curves in three different solutions (hematin-ethanol, hematin-water, and hemin-ethanol) show similar trends at a specific concentration. As a typical example, we show the results from the Z-scan experiments of these three solutions at a concentration of 1.8 × 10−4 g/mL in Fig. 2.
Fig. 2. Closed-aperture Z-scan measurements for the nonlinear refractive index coefficient of different types of heme solutions. Blue and red dotted lines are for hematin-ethanol and hematin-water solutions, and the gray dotted line is for hemin-ethanol solution. The relevant result of hemin-water solution is not presented, because of poor transmittance (hemin is difficult to dissolve in water). The concentration of hematin/ hemin in these three solutions is at the same value of 1.8 × 10−4 g/mL.
From the findings presented in Fig. 2, it is evident that both types of heme exhibit a peak-valley pattern in their normalized transmittance, which is indicative of their negative nonlinearity characterized by a negative Kerr coefficient [40,41]. It is worth noting that the hematin solution exhibits a stronger nonlinearity compared to the hemin solution, as evidenced by its higher peak value in the normalized transmittance curve. Given this, we focus on hematin-ethanol and hematin-water solutions in the following. To further investigate the solvent-dependent nonlinearity, we conduct a comparison between hematin-ethanol and hematin-water solutions. Noticeably, at equivalent concentrations, hematin in ethanol exhibits a higher strength of nonlinearity than that in water. For subsequent calculations, we employ the approach outlined in [42] to determine the nonlinear coefficient of the hematin-ethanol solution, which is determined to be n2 = -1.78 × 10−7cm2/W as a representative value. According to the results obtained from these Z-scan experiments, it is expected that both types of heme solutions exhibit tunable self-defocusing nonlinearity. Furthermore, the absence of significant asymmetry between the peaks and valleys in the Z-scan curves reveals a weak nonlinear absorption in the heme solutions. It is worth mentioning that the nonlinear transmission phenomena here is related mostly to self-focusing and self-defocusing, not significantly correlated with nonlinear absorption. As a result, in our subsequent experiments, we have disregarded the impact of nonlinear absorption on the beam propagation.
3.2 Solvent- and concentration-dependent nonlinear propagation of light
In natural situations, it is not feasible to confine the solutions within 1 mm, as observed in the Z-scan analysis. Therefore, we employ the optical setup depicted in Fig. 1(b) to investigate the long-distance propagation of light through the prepared solutions of different concentrations. To explore the influence of colvent and concentration, hematin-ethanol and hematin-water solutions are both prepared at concentrations 1.8 × 10−4 g/mL, 3 × 10−4 g/mL, and 3.75 × 10−4 g/mL. After being heated (40°C) and stirred for 30 minutes, they form brownish solutions. It is important to mention that the heating process during dissolution aims to achieve a more homogeneous solution without affecting the molecular structure of hemin and hematin. After propagating through a distance of 30 mm, we measure the size of the output beam at the output plane, as shown in Figs. 3(a)-3(b). We find that, with the increase of optical power, the diameter of the beam (full width at 1/e2-intensity) decreases initially and then increases. This change in the size of the output beam is attributed to the giant negative nonlinearity that acts like a concave lens, shifting the beam's focal point forward gradually. From Figs. 3(a) and 3(b), one can find that the output beam sizes in high-concentration solutions (blue lines) change more acutely than that in lower-concentration solutions (red and orange lines), which are consistent with the Z-scan experiment. Moreover, the solvent used in our experiments also has a significant influence. A comparison between Figs. 3(a) and 3(b) shows that hematin requires a higher power to exhibit appreciable nonlinearity in water than in ethanol. Therefore, the nonlinear propagation dynamics of light in solutions are solvent- and concentration-dependent. For solutions with low concentrations of hematin-ethanol, as well as other solution types like hematin-water and hemin-ethanol, their nonlinearities exhibit a smaller strength. Consequently, a higher optical power is necessary during the transmission process in order to observe changes in the output beam profile, in comparison to linear conditions. Likewise, generating the self-collimation effect and producing ring-shaped patterns also requires a higher power. For instance, in the case of a hematin-water solution with a concentration of 3 × 10−4 g/mL, the diameter noticeably decreases at 192 mW.
Fig. 3. (a) Measured output beam diameter as a function of optical powers, after propagation over 30 mm in hematin-ethanol solutions of different concentrations. (b) The same as (a) but for hematin-water solutions. (c) Intensity pattern of the beam at the input facet of the cuvette. (d1-d4) Output patterns at different optical powers in hematin-ethanol solutions with 3.75 × 10−4 g/mL. (e1-e4) Side-views of beam propagations corresponding to (d1-d4). It is noted that the full width at 1/e2 of the ring pattern at the high-power region is meaningless, so it does not appear in (a) and (b).
3.3 Self-collimation and deep penetration of light
Based on these solvent- and concentration-dependent negative nonlineaities, we now proceed to discuss the process of beam propagation through heme solutions, which facilitates deep penetration while preserving the shape of the beam. To illustrate this phenomenon, we utilize the hematin-ethanol solutions with the highest nonlinearity as an example.
Figure 3(c) shows the intensity pattern of the input beam at the input facet of the cuvette. Figures 3(d1)-3(d4) are the output patterns after 30 mm propagation at three different powers (1.2 mW, 50 mW, 200 mW, and 700 mW), and Figs. 3(e1)-3(e4) are the corresponding side-views. We see that at 1.2 mW, the propagation of light exhibits linear diffraction, with the focal point located 10 mm away from the input facet [Figs. 3(d1) and 3(e1)]. The pattern of output is much larger than input, with the energy spreading into a larger space. When the power reaches 50 mW, the beam exhibits a reduced pattern compared with that observed in the linear regime propagation [Fig. 3(d2)] exhibiting a similar in size and shape to that injected into the input facet. From the side view of Fig. 3(e2), we can see clearly that the beam propagation is more robust, and the energy content is more localized than in the linear case. Experimental results demonstrate that, by increasing the average power, the beam undergoes self-collimation and energy concentration during propagation, decreasing the beam waist at the output facet of the cuvette when compared with the one observed in the linear regime. The reason behind this deep penetration of light is mostly the thermal-optics effect, which induces the focal point to shift forward and form the self-collimated beam over a distance [17,21], localizing the energy and achieving deep penetration in the medium which will be verified by the simulation results presented below.
However, when the power increases into 200 mW, as illustrated in Fig. 3(d3) and 3(e3), the optical power exceeds a certain threshold, and the thermo-optic effects become stronger, causing the beam to diverge. Meanwhile, this divergence is accompanied by a pronounced thermal convection effect, leading to alterations in the shape of the output pattern of the beam. In this regard, as shown in Fig. 3(d4) and Fig. 3(e4), for high average powers [700 mW], the output intensity profile tends to reshape into a deformed asymmetric ring-shaped pattern,which is like a “Mexican hat”.
In addition, from Fig. 3(e4), We have noticed that when the input beam passes through this medium, it undergoes broadening in a curved trajectory and exhibits asymmetry along the propagation axis (see dashed line in Fig. 3(e1)-3(e4)). This is quite different from the symmetrical diffraction observed in conventional linear media. This intriguing phenomenon arises from the interaction between light and particles, as well as the presence of strong convections at high powers. Under the combined action of these two effects, solute particles diffuse to regions farther away from and slightly below the center of the beam. As a result, an asymmetric distribution of refractive index is formed along the y-axis. Consequently, the beam widens, and a more significant portion of energy propagates through the region where y < 0, giving rise to a curved trajectory.
For low concentrations of hematin-ethanol solutions and other kinds of solutions (hematin-water and hemin-ethanol), their nonlinearities are weaker. Consequently, a higher optical power is required during the transmission process for changes in the output beam profile to occur compared to linear conditions. Similarly, generating the self-collimation effect and producing circular ring-shaped patterns also necessitates higher power.
4. Simulation results
In this section, we carry out NLSE simulations to mimic the propagation dynamic of an initial Gaussian beam (which is focused on a specific average power) when traveling in a negative nonlinear medium, whose nonlinear action is initiated by the thermo-optic effects. The thermal convection equation is also accounted for in order to describe the formation of the diffractive ring-shaped pattern occurring to high-power values. We show that numerical results provide a suitable theoretical tool for corroborating the above experimental observations. The analysis starts with the intensity of a Gaussian field, expressed as
In Eqs. (3) and (4), $\alpha _0 = 1$ cm-1 is the absorption coefficient, which is calculated from the experimental result of the absorption spectrum of hematin-ethanol solution using the Bill-Lambert's Law: A = α0bc, and here A = 0.5 from Y-coordinates in the absorption spectrum, b = 1.36 cm is the optical path length, and c = 3.75 × 10−4 g/mL is the concentration. Then, cP = 2.4 × 103 J/(Kg °C) is the specific heat, $\rho = 0.78$ g/cm3 is the density, $D = {\rm K/}\left( {\rho \cdot c_p} \right)$ is the thermal diffusivity of the medium, with K = 0.16 W/(m·K) being the thermal conductivity of the sample, n0 = 1.36 is the refractive index of solvent, and dn/dT is the thermo-optics coefficient. It is noted that, in Eq. (4), the dn/dT is derived from the Z-scan experiment through $\Delta n = \frac{{dn}}{{dT}}\frac{{{I_0}\alpha \omega _0^2}}{{4K}}.$ The detailed method is described in [44], which we do not elaborate here. Since the thermal effect establishes within times of about 1s, it is necessary to carry out an integration over the time t. In simulations, t = 1.0 s, and the characteristic diffusion time t’ = 0.16 s, which is defined by $t^{\prime} = \frac{{{\omega _0}^2}}{{4D}}$. Specifically, numerical simulations are performed via the split-step Fourier method applied to the following NLSE, which governs the paraxial propagation of the light in the nonlinear medium to a certain range of distance z [12]
Fig. 4. Simulation results. (a) Input beam. (b)-(c) Output patterns at different (lower) powers. (d) and (e) are output patterns at severely high powers, with severe convection. (f) is the optical pattern, which is cut at the position of the orange frame in (i) during propagation. (g)-(i) Side views of beam propagation.
From a physical viewpoint, as the optical power increases, the temperature difference across the light beam also increases. This, in turn, leads to a more pronounced particle diffusion towards the areas far from the beam's center. Consequently, self-defocusing nonlinearity becomes more prominent, resulting in a significant broadening of the beam. Meanwhile, the influence of gravity contributes to a noticeable decrease in the refractive index in the regions located around and above y = 0 in comparison to the region below y = 0 (due to the thermal-convection effect). As a result, the beam undergoes a shift towards the y < 0 direction, forming a fan-like pattern. Interestingly, it is also noticed the emergence of a bulb-shaped intensity pattern at a distance of 5 mm away from the input surface during propagation. These findings provide valuable insight into the heme-light interaction in the nonlinear domain, as well as the potential applications of beams with unique shapes for heme detection.
5. Conclusion
In conclusion, we have presented an experimental study of tunable nonlinear response in two kinds of heme (hematin and hemin) solutions prepared in different solvents (ethanol and water). The nonlinearity observed in pure heme samples differs from that exhibited by the RBCs with complex of hemin bound to proteins and surrounded by cell membranes. In the RBC suspensions, the nonlinearity is mediated mainly by the optical gradient and scattering forces, where the soft-matter system exhibits altogether a positive nonlinearity that counteracts the spreading of the beam. However, we measured the particles’ size of heme through dynamic light scattering (Malvern-2000). The maximum signal obtained from two different heme solutions indicates that the particles in these solutions are smaller than 10 nm. In the Rayleigh regime, the gradient force can be calculated by Eqs. (1) and (2) in [9]. The refractive indices of the particles and the background medium are 1.48 and 1.36, respectively. Additionally, the particle radius (R) used in our numerical calculation is 10 nm. The estimated maximum force is approximately 10−21 N, which falls far below the typical range of optical trapping forces. Therefore, individual heme particles in pure heme solutions alone are too small to be trapped by optical forces, resulting in a dominating thermal effect that leads to negative nonlinearity in the medium. Nevertheless, both soft-matter media can be employed to enhance beam propagation, even though the mechanism varies depending on the specific scenarios. Corroborated by both numerical simulations and experiments, the results of our study reveal that these nonlinear effects can be effectively utilized to mitigate diffraction and scattering of a focused optical beam, which enables long-distance-diffraction-resistant propagation through the otherwise scattering media. Furthermore, we have also observed the formation of asymmetric patterns at high-power levels,which can be attributed to thermal convection effects. We believe that these findings may enhance our understanding of light-matter interactions in blood-containing soft-matter environments, which may be useful for potential applications in heme-related biomedical research.
Funding
National Key Research and Development Program of China (2022YFA1404800); National Natural Science Foundation of China (12134006, 12250410236, 12274242, 12374309); Natural Science Foundation of Tianjin City (21JCJQJC00050, 21JCYBJC00060); 111 Project (B23045).
Disclosures
The authors declare no conflicts of interest.
Data availability
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
References
1. N. Korte, R. Nortley, and D. Attwell, “Cerebral blood flow decrease as an early pathological mechanism in Alzheimer's disease,” Acta Neuropathol. 140(6), 793–810 (2020). [CrossRef]
2. D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23, S275–S288 (2004). [CrossRef]
3. I. Georgakoudi, W. L. Rice, M. Hronik-Tupaj, et al., “Optical spectroscopy and imaging for the noninvasive evaluation of engineered tissues,” Tissue Eng. Part B-Re. 14(4), 321–340 (2008). [CrossRef]
4. T. Pan, D. Lu, H. Xin, et al., “Biophotonic probes for bio-detection and imaging,” Light Sci. Appl. 10(1), 124 (2021). [CrossRef]
5. Y. C. Chen and X. Fan, “Biological Lasers for Biomedical Applications,” Adv. Opt. Mater. 7(17), 1900377 (2019). [CrossRef]
6. Z. Yaqoob, D. Psaltis, M. S. Feld, et al., “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2(2), 110–115 (2008). [CrossRef]
7. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010). [CrossRef]
8. R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics. 9(9), 563–571 (2015). [CrossRef]
9. R. Gautam, A. Bezryadina, Y. Xiang, et al., “Nonlinear optical response and self-trapping of light in biological suspensions,” Adv. Phys.- X 5(1), 1778526 (2020).
10. P. W. Smith, A. Ashkin, J. E. Bjorkholm, et al., “Studies of self-focusing bistable devices using liquid suspensions of dielectric particles,” Opt. Lett. 9(4), 131–133 (1984). [CrossRef]
11. C. Conti, G. Ruocco, and S. Trillo, “Optical Spatial Solitons in Soft Matter,” Phys. Rev. Lett. 95(18), 183902 (2005). [CrossRef]
12. R. El-Ganainy, D. N. Christodoulides, C. Rotschild, et al., “Soliton dynamics and self-induced transparency in nonlinear nanosuspensions,” Opt. Express 15(16), 10207–10218 (2007). [CrossRef]
13. P. J. Reece, E. M. Wright, and K. Dholakia, “Experimental observation of modulation instability optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98(20), 203902 (2007). [CrossRef]
14. M. Matuszewski, W. Krolikowski, and Y. S. Kivshar, “Spatial solitons and light-induced instabilities in colloidal media,” Opt. Express 16(2), 1371–1376 (2008). [CrossRef]
15. Y. Lamhot, A. Barak, O. Peleg, et al., “Self-trapping of optical beams through thermophoresis,” Phys. Rev. Lett. 105(16), 163906 (2010). [CrossRef]
16. W. Man, S. Fardad, Z. Zhang, et al., “Optical Nonlinearities and Enhanced Light Transmission in Soft-Matter Systems with Tunable Polarizabilities,” Phys. Rev. Lett. 111(21), 218302 (2013). [CrossRef]
17. Y. Zhang, G. Liang, L. Tang, et al., “Tunable optical nonlinearity and self-collimation of light in food dye solutions,” Opt. Commun. 528, 129010 (2023). [CrossRef]
18. S. Fardad, A. Salandrino, M. Heinrich, et al., “Plasmonic Resonant Solitons in Metallic Nanosuspensions,” Nano Lett. 14(5), 2498–2504 (2014). [CrossRef]
19. T. S. Kelly, Y. X. Ren, A. Samadi, et al., “Guiding and nonlinear coupling of light in plasmonic nanosuspensions,” Opt. Lett. 41(16), 3817–3820 (2016). [CrossRef]
20. H. Xu, P. Alvaro, Y. Xiang, et al., “Plasmonic resonant nonlinearity and synthetic optical properties in gold nanorod suspensions,” Photon. Res. 7(1), 28–35 (2019). [CrossRef]
21. A. B. Ortega, E. C. Brambila, V. López Gayou, et al., “Light control through a nonlinear lensing effect in a colloid of biosynthesized gold nanoparticles,” J. Mod. Optic. 66(5), 502–511 (2019). [CrossRef]
22. Y. Xiang, G. Liang, P. Alvaro, et al., “Resonant optical nonlinearity and fluorescence enhancement in electrically tuned plasmonic nanosuspensions,” Adv. Photonics Res. 2(5), 2000060 (2021). [CrossRef]
23. J. Zhan, D. Li, D. Bongiovanni, et al., “Nonlinear generation of hollow beams in tunable plasmonic nanosuspensions,” APL Photonics 8(7), 076102 (2023). [CrossRef]
24. A. Bezryadina, T. Hansson, R. Gautam, et al., “Nonlinear self-action of light through biological suspensions,” Phys. Rev. Lett. 119(5), 058101 (2017). [CrossRef]
25. R. Gautam, Y. Xiang, J. Lamstein, et al., “Optical force-induced nonlinearity and self-guiding of light in human red blood cell suspensionsm,” Light Sci. Appl. 8(1), 31 (2019). [CrossRef]
26. N. Perez, J. Chambers, Z. Chen, et al., “Nonlinear self-trapping and guiding of light at different wavelengths with sheep blood,” Opt. Lett. 46(3), 629–632 (2021). [CrossRef]
27. R. Sipen and A. Bezryadina, “Light propagation in DNA suspensions,” Proc. SPIE PC12212, Molecular and Nano Machines V, PC122120C (26 September 2022). [CrossRef]
28. D. Chiabrando, S. Mercurio, and E. Tolosano, “Heme and erythropoieis: more than a structural role,” Haematologica 99(6), 973–983 (2014). [CrossRef]
29. S. Severance and I. Hamza, “Trafficking of heme and porphyrins in metazoan,” Chem. Rev. 109(10), 4596–4616 (2009). [CrossRef]
30. P. Ponka, “Cell biology of hemem,” Am. J. Med. Sci. 318(4), 241–256 (1999). [CrossRef]
31. H. Keum, D. Yoo, and S. Jon, “Photomedicine based on heme-derived compounds,” Adv. Drug Delivery Rev. 182, 114134 (2022). [CrossRef]
32. J. W. Petrich, C. Poyart, and J. L. Martin, “Photophysics and reactivity of heme proteins: a femtosecond absorption study of hemoglobin, myoglobin, and protoheme,” Biochemistry 27(11), 4049–4060 (1988). [CrossRef]
33. A. Nath, J. A. Dharmadhikari, A. K. Dharmadhikari, et al., “Ultrafast dynamics of hemin aggregates,” Phys. Chem. Chem. Phys. 19(39), 26862–26869 (2017). [CrossRef]
34. A. M. Alsharabasy, A. Pandit, and P. Farràs, “Recent advances in the design and sensing applications of hemin/coordination polymer-based nanocomposites,” Adv. Mater. 33(2), 2003883 (2021). [CrossRef]
35. V. Jeney, G. Balla, and J. Balla, “Red blood cell, hemoglobin and heme in the progression of atherosclerosis,” Front. Physiol. 5, 379 (2014). [CrossRef]
36. F. R. de Oliveira Silva, M. H. Bellini, V. R. Tristão, et al., “Intrinsic Fluorescence of Protoporphyrin IX from Blood Samples Can Yield Information on the Growth of Prostate,” J. Fluoresc. 20(6), 1159–1165 (2010). [CrossRef]
37. M. Shayeghi, G. O. Latunde-Dada, J. S. Okahill, et al., “Identification of an Intestinal Heme Transporter,” Cell 122(5), 789–801 (2005). [CrossRef]
38. J. Lee, A. E. Yesilkanal, J. P. Wynne, et al., “Effective breast cancer combination therapy targeting BACH1 and mitochondrial metabolism,” Nature 568(7751), 254–258 (2019). [CrossRef]
39. T. Geethakrishnan and P. K. Palanisamy, “Z-scan determination of the third-order optical nonlinearity of a triphenylmethane dye using 633 nm He–Ne laser,” Opt. Commun. 270(2), 424–428 (2007). [CrossRef]
40. P. B. Chapple, J. Staromlynska, J. A. Hermann, et al., “Single-Beam Z-Scan: Measurement Techniques and Analysis,” J. Nonlinear Opt. Phys. 06(03), 251–293 (1997). [CrossRef]
41. E. W. V. Stryland and M. Sheik-Bahae, “Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials,” Routledge 671–708 (2018).
42. M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, “High-sensitivity, single-beam n_2 measurements,” Opt. Lett. 14(17), 955–957 (1989). [CrossRef]
43. R. Karimzadeh, “Spatial self-phase modulation of a laser beam propagating through liquids with self-induced natural convection flow,” J. Opt. 14(9), 095701 (2012). [CrossRef]
44. H. A. Badran, “Z-Scan Measurement For The Thermo-Optic Coefficient and Transmitted Beam Profile Of 1.8-Dihydroxy-Naphthalin-3, 6 Disulfonic Acid-[2-(4-azo)]-N-(5-Methyl-3-Isoxazolyl)-Benzene Sulfonamide,” Advances in Physics Theories and Applications 26, 36–44 (2013).
