Upper limits of dielectric permittivity modulation in bacteriorhodopsin films

A theoretical study of light-induced modulation of the dielectric permittivity in bacteriorhodopsin films has been done (including $B\to M$ and $B\to Q$ transitions). Analysis of dielectric permittivity modulation enables us to determine the fundamental limits of BR to be used in a holographic data storage system, together with the optimum experimental and material conditions. In order to carry out this analysis, the macroscopic dielectric permittivity was related to the microscopic polarizability of the three states of BR considered ($B$, $M$ and $Q$). This parameter was calculated using a modelization procedure that includes the effect of ASP85, TRP86, and TYR185 aminoacid residues (the $\mathrm{B}3\mathrm{LYP}∕6\text{−}31+{\mathrm{G}}^{*}$ method was used for the calculations). Good concordance between theoretical calculations and experimental data was found for the linear optical properties (absorption wavelength, transition dipole moment, and dielectric permittivity modulation). The theoretical upper limits of $\Delta ϵ$ at $750\mathrm{nm}$ (far from the resonance of the molecule) in a randomly oriented material are about 0.01 and 0.012 for $B\to M$ and $B\to Q$ transitions, respectively. The values of $\Delta ϵ$ obtained were used to simulate diffraction efficiencies $\left(\eta \right)$ of a volume phase hologram recorded in a BR film. The high absorptive losses at low wavelengths (about $625\mathrm{nm}$) cause an interesting behavior, since the highest $\Delta ϵ$ do not produce the greatest $\eta$. The highest $\eta$ is produced for a hologram thickness in the range of $900–1000\mu \mathrm{m}$ and working wavelength of $700–750\mathrm{nm}$.

Figure 1

Schematic representation of the bacteriorhodopsin structure and its photocycles.

Figure 2

Schematic representation of the procedure used to calculate the optical properties.

Figure 3

Projection onto the $xy$ plane of the transition densities between ground and first excited state calculated with the $\mathrm{B}3\mathrm{LYP}∕6\text{−}31+{\mathrm{G}}^{*}$ method (white and black colors denote positive and negative values, respectively).

Figure 4

Theoretical upper limits of the dielectric permittivity modulation of BR for $B\to M$ (black lines) and $B\to Q$ (dashed lines) transitions versus the working wavelength $(\varphi =0.65,N={10}^{25})$.

Figure 5

Simulations of diffraction efficiency $\left(\eta \right)$ for $B\to M$ and $B\to Q$ transitions of BR versus the reading wavelength $\left(\lambda \right)$ for various hologram thicknesses (left part, gray level and line thickness increases with $d$) and the hologram thickness $\left(d\right)$ for various $\lambda$ (right part, gray level and line thickness increases with $\lambda$). The values of the other variables used are ${\zeta }_i=1∕3$, $N=8.77\times {10}^{23}\text{molecules}∕{\mathrm{m}}^3$, $\varphi =0.65$, $\mathrm{B}3\mathrm{LYP}∕6\text{−}31+{\mathrm{G}}^{*}$ values of microscopic properties and $\theta =13.8$, which was the same as in the experimental setup of Ref. 33.