## 4 Discussion  
In the previous report [1], the broad increase in absorption over 425 nm to 505 nm was attributed to the J-aggregates formation. To explain the previous consideration, the theory of excitation energy of J-aggregates will be briefly explained. Excitation energy \(E_{k}\) of the one-dimensional aggregates composed of the molecules with excitation energy \(E_{0}\) and transition dipole moment \(M\) can be written as  
\[E_{k}=E_{0}+2J\cos(\frac{k\pi}{N+1}) \tag{4}\]  
\[J=\frac{M^{2}}{4\pi\varepsilon\epsilon^{3}}\left(1-3\cos^{2}\theta_{0}\right) \tag{5}\]  
where \(\varepsilon\) is the permittivity of the medium surrounding J-aggregates, \(N\) is the number of molecules in a single aggregate, \(r\) is the distance between the molecules and \(\theta_{0}\) is the angle between the transition dipole moment of the component TPPS molecule and the axis connecting the centers of the transition dipoles [41]. Equation (4) shows the dependence \(E_{k}\) on \(N\). In the case of TPPS, the values of \(E_{k=1}\) of dimer (\(N=2\)), trimer (\(N=3\)) and tetramer (\(N=4\)) were estimated in ref. [1; 42] to be 2.70 eV (459 nm), 2.63 eV (471 nm) and 2.60 eV (477 nm), respectively. Therefore, assuming that J-aggregates with lower \(N\) (\(N<20\)) than those observed in thermal equilibrium (\(N>20\)) was formed by light gradient force, the broad increase in absorption and the decrease in absorption at 412 nm can be explained. Furthermore, it was also explained that the broad increase in absorption of the PVA sample was smaller than the aqueous solution in the previous experiment (Figure 4b). This is because F-monomers in PVA matrix are fixed and cannot form J-aggregates by light gradient force. However, it becomes clear that the origin of the absorption change is not J-aggregates formation induced by light gradient force because the broad increase in the absorption of the PVA sample was observed in the present experiment (Figure 4a). According to the report of theoretical calculations of gradient forces applied to dye molecules, light intensities of 10 MW/cm\({}^{2}\) are required to capture a single molecule [43]. Because the laser light with an optical intensity of 1.3 kW/cm\({}^{2}\) at 808 nm or less at 532 nm was used in this experiment, the present result that the dye molecules did not form aggregates is consistent with this report. As an order-of-magnitude estimation, if the gradient force potential (\(\frac{1}{2}\alpha E^{2}\)) at \(I=\frac{\epsilon_{0}}{2}E^{2}c=1.3\) kW/cm\({}^{2}\) (\(\epsilon_{0}\): electric constant, \(E\): optical electric field, \(c\): speed of  
Figure 8: Dependence of \(F/A\) of water-MeOH mixed solution of F-monomer with [NaOH] = 1 mM (a) and 10 mM (b) on mole fraction of MeOH. The 532 nm laser was used as the pump. light) with the estimated molecular polarizability \(\alpha\) of TPPS from its polarizability volume \(V=1.46\) nm\({}^{3}\)[2] and Equation (5) of ref. [2] is compared with thermal energy \(k_{\rm B}T\) of the molecule at room temperature (\(T=300\) K) with the Boltzmann constant \(k_{\rm B}\), \(\frac{14\pi E^{2}}{k_{\rm B}T}\) is roughly evaluated to be \(10^{-7}\). It is therefore reasonable that the \(\Delta A\) signal indicating molecular aggregation beyond \(\Delta A\sim 10^{-6}\) was not observed as seen in Figure 3. To observe the capture of dye molecules, it is necessary to use a laser focused by an objective lens, for example. In fact, studies using high intensity lasers have shown results suggesting the capture of dye molecules and aggregates [44; 45; 46]. Let us discuss a possible reason why the broad increase in the absorption of the PVA sample was not observed in the previous experiment. S/N of the previously observed DAS of the PVA sample is lower than that in the present paper (Figure 4). This may be because of non-optimized sensitivity and AC gain settings of the 128-channel lock-in detector in the previous experiment. For an accurate measurement of DAS, S/N should have been improved with the optimal settings.