Artifact-free balanced detection for the measurement of circular dichroism with a sub-picosecond time resolution

We present the development of a subpicosecond spectropolarimeter enabling high sensitivity balanced detection of time-resolved circular dichroism (TRCD) signals from chiral sample in solution. The signals are measured with a conventional femtosecond pump-probe set-up using the combination of a quarter-waveplate and a Wollaston prism. This simple and robust method allows access to TRCD signals with improved signal-to-noise ratio and very short acquisition times. We provide a theoretical analysis of the artifacts of such detection geometry and the strategy to eliminate them. We illustrate the potential of this new detection with the study of the [Ru(phen)3]·2PF6 complexes in acetonitrile.


INTRODUCTION
Circular dichroism (CD), the difference in absorption for a left or right-circularly polarized light, is commonly used to access information on the conformation of chiral molecules.It can be particularly useful to study biological molecules such as proteins or DNA which have characteristic CD spectra in the UV range between 200 and 300 nm that can be phenomenologically or theoretically related to their secondary structures. 1 In this context, transposition of CD measurements to the time domain (TRCD), in the UV-visible spectral domain, is a very promising strategy to access the conformational dynamics of proteins and oligonucleotides outside equilibrium that play a key role in their function.
Few attempts to implement TRCD in a femtosecond pump-probe experiments have been proposed [2][3][4][5][6] , but all those experiments that want to measure extremely weak signals (around 10 -5 -10 -3 in differential absorbance) suffer from many polarization artifacts 7 .Here, we specifically address these main drawbacks with the development of an alternative detection method based on the balanced detection of the pump-induced ellipticity changes of the probe linear polarization by chiral samples.The principle relies on the full characterization of the probe elliptic polarization with a single laser shot by using the combination of a broadband quarter-waveplate (QWP) and a Wollaston prism.We perform a theoretical analysis of the artifacts for such detection geometry and provide a strategy to perform artifact-free TRCD measurements.We then illustrate the performances of our new set-up with the experimental study of [Ru(phen)3]•2PF6 complexes in acetonitrile.

BASIC PRINCIPLE 2.1 Ideal case
The principle of the technique to measure the sample CD with a unique beam is described in figure 1.A linearlypolarized beam is successively sent through the sample and a quarter-wave plate whose axes are oriented at 45°.The two linear (parallel and perpendicular) polarizations are then separated by a Wollaston prism and separately measured by two detectors.In order to understand this optical system, we use the Jones formalism.The Jones vector for the horizontally polarized incoming probe light along the (Ox) axis is given by: (1) The outcoming probe laser field reads as: ( Each optical element is described by (2×2) matrix.The Jones matrix associated with the QWP, for an orientation at an angle of +45° (clockwise) with respect to its fast axis oriented along (Ox), is expressed as follows: (3) Chiral samples exhibiting small optical activity can be described with the Jones matrix (4)   where L is the sample thickness, n, the refractive index and α, the sample absorption coefficient.4γ corresponds to the sample CD and θ to sample circular birefringence (CB), respectively defined as: (5) (6)   where AL,R and nL,R are the sample absorbance and refractive index for left-and right-circularly polarized light.
From the above equations, it is straightforward to calculate the CD as 8 where the I's denote the intensity measured in detectors 1 and 2. This possibility to measure the CD with a unique pulse allows one to get a much better signal-to-noise ratio compared to technique that make successive measurements.
In order to access TRCD, one can use the same set-up in a pump-probe configuration as depicted in figure1.The chopper synchronized at half the repetition rate of the laser allows one to measure the CD with and without the pump and hence the pump-induced CD.

Polarization artifacts
The ideal case depicted so far is unfortunately very easily polluted by pump-induced artifacts.To examine those artefacts, we follow the calculation of Xie et al 9 and introduce the following matrix for the sample that takes into account pump-induced linear birefringence (β) and dichroism (g).Full calculation 8 yields for the pumpinduced CD : , showing that TRCD is insensitive to linear dichroism, but not to linear birefringence.It is therefore important to align very precisely the pump and the probe polarization to get rid of this artifact.An experimental demonstration will be given below.

Unbalanced probe transmission artifact
Another source of artifact is the fact that it is in practice impossible to obtain a perfectly balanced detection between the two detectors 1 and 2 due to subtle differences between the two optical paths or to slight differences between the detectors.Actually, such problem is known to occur in ROA or CPL measurements and the proposed solution is to make two consecutive measurements with the QWP oriented at ±45°. 10 We propose to use the same trick to overcome this problem.Actually, carrying out the calculation with the Jones matrix formalism, one can show that changing the QWP angle yields a change of sign of the measured CD, but not the sign of the offset due to the unbalanced detection.
Averaging the results obtained for the ±45° orientations of the QWP therefore allows one to get rid of this artifact.

EXPERIMENTAL DEMONSTRATIONS
The experimental demonstrations are carried out with a single-wavelength detection pump-probe set-up using an amplified 1 kHz Ti:sapphire laser system (Spectra-Physics, Solstice), delivering 100-fs pulses at 800 nm with an energy of 3 mJ.The 400-nm pump pulses are obtained from the second harmonic of the fundamental pulses.Their energy is set to 0.37 µJ to avoid photo-degradation during experiments.Probe pulses at 270 nm with an energy of 12 nJ are generated by parametric amplification of a white light continuum and second harmonic generation.Experiments are carried out on solutions of [Ru(phen)3]•2PF6 complexes for which we have two enantiomers and their racemic mixture at the same concentrations.Figure 2 illustrates the commonly-encountered artifacts.In figure 2(a), the peak around zero delay is due to the misalignment of the pump polarization with respect to the probe one, it impairs strongly the short-time measurements Therefore a very fine adjustment of the pump polarization (better than 0.1°) is required to get rid of the artifact as exemplified in the curve "0°" in figure 2(a).Figure 2(b) shows unbalanced probe transmission artifact that translates into an undue pump-induced CD signal in the racemic mixture.The origin of this effect is unfortunately too subtle to be corrected in a simple alignment procedure.However, in agreement with the Jones matrix calculations, one clearly sees that changing the QWP angle from +45° to -45° does not change the sign of the artifact.It is thus possible to make an average of the two curves to suppress the offset, be it due to the pump or not.This procedure is applied in figure 3 and one can see that the signals are perfectly symmetrical for the two enantiomers and zero for the racemic mixture, certifying that what is measured is the genuine pump-induced chiral signal.

CONCLUSION
We have described a new measurement method of CD based on the balanced detection of the pump-induced ellipticity changes of the probe linear polarization in chiral samples.Thanks to the rigorous control of the pump and probe linear polarizations, we demonstrated the feasibility of artifact-free TRCD measurements in regular quartz spectroscopic cells.Experimental demonstrations are given in a chiral Ru(phen)3 salt.These improvements represent an important technical progress opening the way for the development of more amenable TRCD detections on ultrafast pump-probe setups.