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Holographic grating inscription in DR1: DNA-CTMA thin films: the puzzle of time scales

Abstract We study experimentally the dynamics of holographic inscription of gratings in DR1:DNA-CTMA thin films using a degenerate two-wave mixing (DTWM) setup in its initial phase (30 ms) and in a longer time interval (30 s). The temporal pattern of evolution of diffraction efficiency is complex, simple fitting procedures fail to reproduce the data. We point out that the complex dynamics can originate a large span of temporal scales, closely related to the microscale inhomogeneity of local free volume. Some of its hallmarks are found through Monte Carlo simulations.


Introduction
Deoxyribonucleic acid (DNA), functionalized with photoresponsive molecules, has been the subject of interest due to its potential application in nonlinear optical (NLO) effects-based devices [1]. Some of them are closely related to the dynamic holographic grating recording carried out using a degenerate two-wave mixing (DTWM) setup for DNA with cetyltrimethyl-ammonium chloride as matrix and well known photochromic molecules of Disperse Red 1 (DR1) as a dye (DR1:DNA-CTMA thin films). Under the inhomogeneous light illumination the DR1 molecules undergo multiple cycles of trans-cistrans conformational cycles which promote the build-up of a diffraction grating. The experimental results [2] of dynamic diffraction grating formation show that signal evolution is characterized by a very short time of increase and decay, full reversibility and high stability with weak dependence on wavelength and finally small diffraction efficiency which evolution can be characterized by single-exponential kinetics. Amongst those results the operational time, which can be two orders of magnitude shorter than for "traditional" host-guest gratings, e.g. those based on polystyrene matrix, are potentially attractive for non-linear optical applications.
The origin of different dynamics for the two types of systems is not known. A common opinion is that one of important factors is the nature of binding of azodyes to the DNA helix. Studies of circular dichroism [3] showed that the photochromic dye which is doped into the DNA biopolimer, can be aligned by binding in the major or minor grooves of the DNA helix or

Central European Journal of Chemistry
Holographic grating inscription in DR1: DNA-CTMA thin films: the puzzle of time scales + intercalated between the base pairs. Some arguments against this full intercalation were discussed in [4], an confirmed by You et al. [5] who has shown that the dye molecules doped to DNA-CTMA probably do not interact directly with DNA helix and that the CTMA acts as a kind of an interface between DNA double helix and DR1 molecule. A similar physical picture, in what follows referred to as a semi-intercalation hypothesis (cf. Section 3.1), was earlier formulated by some of us on purely theoretical grounds [6,7]. Monte Carlo simulations of the semi-intercalation model combined with analytical arguments [8] have reproduced the main experimental data of [2] (see Sections 3.2 and 3.3 for more details), and provided a strong support to semi-intercalation approach. On the other hand, the theoretical analysis predicted that the dynamics of the grating inscription should have, in general, a more complex pattern than a single-exponential one. Quite recently, we have reported first experimental results [9] which show that a non-exponential dynamics set in on much longer time scales than those of experiments reported in [2]. We conclude that the topic of the temporal patterns of both short-time and long-time dynamics of the inscription of the gratings in DNA biopolymer remains open. The aim of this paper is twofold: (i), to present new measurements of the dynamics of grating inscription in DR1:DNA-CTMA system in short and long intervals of time and to analyze the emerging temporal patterns; (ii), to formulate, on theoretical grounds, a hypothesis concerning their origin and to present Monte Carlo simulations in its support. Fig. 1 shows the experimental configuration schematically, which was used for the study of the inscription of diffraction grating using the degenerate two-wave mixing (DTWM) technique. Two s-polarized beams -I and I' -generated by the Ar + laser (cw, P = 300 mW of total laser power, λ = 514.5 nm) were crossing at 2θ angle and interfering in the sample, generating local changes in refractive index of the medium, consistent with the interference pattern. The dynamics of the process of diffraction grating generation, represented by the temporal evolution of the signal power diffracted in the first order of diffraction, was measured with the high-speed photodetector (Thorlabs) connected to a digital oscilloscope (Tektronix, TDS 220). Additionally, a chopper positioned on I' beam was used in order to study an optical erasure dynamics in a short time scale (milliseconds).

Sample preparation
To prepare a biopolymeric matrix we used a commercially available purified salmon roe DNA (Sigma -D1626) and complexed it with a cationic surfactant CTMA (cetyltrimethyl-ammonium chloride) replacing all Na + ions of DNA salt. This complex is soluble in many organic solvents including alcohols and can be processed into good optical quality thin films by casting and spin-coating deposition. The conversion of pure DNA material into DNA:CTMA complex was done according to procedure described elsewhere [10,11]. We have prepared butanol solutions of DNA-CTMA and Disperse Red 1 separately and mixed them in order to obtain 2% DR1 in DNA-CTMA w/w in the dry mass. The DR1:DNA-CTMA solution was cast onto glass plates and dried 24 hours in air at room temperature. Thickness of the layer amounted to 4 µm which guarantee measurable diffraction efficiency [2].

Experimental results and discussion
The example of dynamic diffraction grating inscription and erasing in DR1:DNA-CTMA film with Ar + laser (s-s recording polarization configuration, I = I' = 470 mW cm -2 , 2θ = 6 0 ) and chopper working with frequency of f = 40 Hz is presented in Fig. 2. The dependence of the diffraction efficiency on time was satisfactorily fitted using a singleexponential function which has a rise constant τ r ≈ 4 ms, after which the inscription is practically completed. The decay of the grating which occurs after the laser light was turned off is also very steep reflecting the same type of dynamics as in the recording process, but this effect is not the objective of the current study.