We present simple modifications of the classic Z-scan technique for the investigations of nonlinear chiroptical effects, i.e. nonlinear circular birefringence and two-photon circular dichroism. Two methods for studying these effects: a “polarimetric Z-scan” and a “polarization modulated Z-scan” are described in detail. These techniques were applied to estimate the order of magnitude of the effects for several different materials.
©2004 Optical Society of America
Optical isomers, i.e., molecules existing in two mirror image forms that cannot be superimposed by simple rotation (the phenomenon of chirality), commonly appear in all living organisms and their existence has very important consequences in biology and in biophotonics . The properties of these molecules involve a slight difference in the interaction with left and right handed circularly polarized light. Such differences should also apply to nonlinear optical processes. There is already a great body of theoretical and experimental research on second-order nonlinear optical phenomena in chiral media. The studies of the combination of chirality with third-order (cubic) optical nonlinearity can further broaden our knowledge about light-matter interaction and may be of great practical interest as third-order effects are more general, requiring no special symmetry conditions. Theoretical description of the interaction of chiral molecules with high-intensity light has been carried out for quite some time [2–4] but the experimental evidence is scarce. As early as in 1969, Kielich discussed the theory of nonlinear optical rotation  and there are indications that this phenomenon has been observed [6,7]. In 1975, Tinoco  and Power  published independent papers on two-photon circular dichroism. Later, Wagniere  predicted that optical activity of higher order should be observable in various third-order optical nonlinearity related experiments. Recently, a French group [8–11] has provided extensive experimental and theoretical treatment of the case of chiral contribution to absorption saturation which may be considered as an effective χ (3) process in the sense that it is an intensity-dependent absorption. Nonlinear circular dichroism has also been reported for lanthanides [12,13].
In principle, a multitude of nonlinear optical phenomena can arise from the handedness of light-matter interaction. We limit the scope of this paper to two phenomena which may be treated either as the chirality-induced modifications of the cubic nonlinear optical properties or, alternatively, as the nonlinear part of the usual chiroptical properties, i.e. the circular birefringence (optical activity) and circular dichroism. For fully degenerate third-order nonlinear optical phenomena defined by the nonlinear refractive index, n2, and the nonlinear absorption coefficient, β, one can introduce their chiral counterparts as δn2,c and δβc where the δ symbol stands for the difference between the value of the parameter for right- and left-handed circular polarization. On the other hand, the nonlinear circular birefringence δn2,c can be treated as derived from the optical rotation strength coefficient [α] which can be considered intensity dependent, with the coefficient d[α]/dI being a measure of the nonlinearity. One can show that d[α]/dI = π/λ. δn2,c . In a similar way, the nonlinear dichroism which is related to the imaginary part of the complex susceptibility, is δβc = d(δε)/dI, where δε is the linear circular dichroism expressed as the difference of absorption coefficients (ε) for right and left handed circularly polarized light.
The estimation of the order of magnitude of the nonlinear chiroptical effects has been attempted in several theoretical papers. Wagniere  predicted that the chiral modulation of NLO effects (i.e. the relative difference between the values of a nonlinear coefficient for the left-handed and right-handed circularly polarized light) may be of the order of 10-2. Estimates given by other authors are between 10-4 and 10-2. Thus, the effects should be measurable using standard modulation techniques. A convenient and ingeniously simple technique for measuring intensity dependent effects like nonlinear absorption and refraction is that of Z-scan . We propose here two modifications of this technique for detection of nonlinear chiroptical effects: the “polarimetric Z-scan” and the “polarization modulated Z-scan”.
2. Polarimetric Z-scan
The “polarimetric” Z-scan is presented in Fig. 1. As in a simple polarimeter, placing an optically active sample between crossed polarizers results in appearance of light transmission. By rotating the analyzer by angle ϕ one can achieve the minimum transmission condition. However, as the optically active sample is translated along the z axis, the changing light intensity leads to reappearance of the transmission which peaks at the z=0 position, i.e. where the intensity is the highest. This simple principle can be used to determine the nonlinear optical rotation, however, the appearance of increased transmission as the sample is near the focal plane of the lens may also be attributed to other effects causing depolarisation of the light transmitted through the sample. A necessary check that the light polarization plane has indeed been rotated is performing the Z-scan at analyzer positions rotated slightly off the crossing position.
Figure 2 shows an example of such a set of results obtained using 100 fs pulses at 650 nm (1 kHz repetition rate) and a solution of sucrose as a sample. The existence of the intensity dependent rotation of the polarization plane is confirmed by the characteristic “heterodyne” effect which is due to the light transmitted through the analyzer acting as a local oscillator when mixing with the transmission due to the nonlinear polarization rotation. The theoretical lines in the figures were calculated using the Malus law
where PT and P0 are the transmitted and incident power, Ω is the angle of rotation of the analyzer from the low intensity minimum position, dϕ/dI is the nonlinearity of the optical rotation strength of the substance in the cell, and I(z) is the cell-position-dependent intensity calculated knowing the Rayleigh length of the beam, zR A small background transmitted power PS is due to scattering. Depending on whether the signs of Ω and dϕ/dI are the same or opposite, the nonlinear effect will result in a Z-scan curve with either a peak or a dip at z=0.
From results in Fig. 2 we determine for sucrose d[α]/dI=5×10-12 deg cm/W at 650 nm. This value can be compared with the results of Cameron and Tabisz  who investigated sucrose with nanosecond pulses at 308 nm and quoted the two-photon specific rotation as -0.16 ± 0.05 at the intensity of 7.2×1012 W/m2. Converting to the same units as used by us, this corresponds to d[α]/dI=-2.2×10-11 deg cm/W. Our result is smaller and positive, but this may be understandable in view of the difference in the wavelength of the measurement which is likely to lead to dispersion and change of sign of the effect at two-photon absorption wavelength. One should note here that our application of the polarimetric Z-scan does not take into account possible appearance of ellipticity due to the presence of nonlinear dichroism. However, samples exhibiting nonlinear absorption can also, in principle, be investigated by the same technique. Limiting factors of the technique are the presence of analyzer leakage Ps (typically 10-4 - 10-3P0) and the onset of hyper-Raman and other additional NLO effects, typically at intensities of a few hundreds of GW/cm2.
3. Polarization-modulated Z-scan
The principle of a “polarization-modulated Z-scan” measurement is shown in Fig. 3. A quarter-wave plate rotating at the frequency f2 provides a time-dependent modulation of polarization of the laser light. One should note that rotation of a quarter-wave plate gives a polarization that changes between linear and both senses of circular polarization. The repetition rate of the change between two senses of the circular polarization is 2f2. As in the classical Z-scan technique, the sample is translated through the focus of a lens and the change of intensity may lead to both distortion of the phase front due to self-focusing and to change of the total intensity due to nonlinear absorption. Both effects can be detected by simply measuring either the total intensity (“open aperture” scan), or intensity in the central part of the beam after passing it through an aperture (“closed aperture” scan). In both cases one can expect that the existence of a difference between the nonlinear parameters for the left-handed and right-handed circular polarizations will lead to the appearance of an intensity dependent (that is z-dependent) signal at the frequency of 2f2. Alongside with the usual Z-scan signals that can be detected in this system by monitoring the signal component at the frequency of the chopper, f1, the chiral modulation signals allow one to determine the nonlinear circular birefringence and the nonlinear circular dichroism.
A typical “closed aperture” transmission as a function of z would exhibit a minimum followed by a maximum with the amplitude of the signal approximately proportional to the nonlinear phase shift and thus to the value of n2 (averaged over all polarizations) whereas the modulation signal should give the difference of Z-scans for the two opposite senses of the circular polarization, thus the amplitude of the signal being proportional to δn2,c. A similar principle applies to the open aperture Z-scans where the nonlinear absorption signal exhibits a dip in the total transmission vs. z curve, the depth of which is approximately proportional to β, and the chiral modulation of the dip depth should be proportional to δβc. Thus, in both cases, the amplitudes of the respective signals can be used to determine the respective chiralities:
where ∆I stands for the appropriate signal amplitude and we use the averaged values of n2 and β because of the difference between these parameters for linear and circular polarized light. The averaging is over the changing polarizations as the quarter-wave plate rotates.
The difference between the nonlinear parameters, n2 and β, for the linearly and circularly polarized light is also an important property of a nonlinear medium and it can be measured in the same polarization modulated Z-scan experiment by a simple change to the detection of the fourth harmonic of the frequency of rotation of the quarter-wave plate. Considerations of the polarization changes on quarter-wave plate rotation indicate that the fourth-harmonic (measured at 4f2) signal is a measure of n2,lin-n2,c for the closed aperture case and βlin-βc for the open aperture case. We have measured such signals for many substances and will report on the results elsewhere.
Table 1 shows an example of the estimation of the nonlinear chiral effect: the nonlinear circular birefringence from closed-aperture polarization modulated Z-scans. We provide here results obtained on two isomers of pinene: (+)α-pinene ([α]= +42°, Sigma Aldrich) and (-)α-pinene ([α]= -41°, Sigma Aldrich). The signals measured at f1 in a 1 cm cell with both types of α-pinene display a characteristic S-shape indicating a positive n2, which gives a nonlinear absorption-free, self-focussing effect (Fig. 4). A comparison with nonlinearity of silica glass (assumed to be 3×10-16 cm2/W) gives n2 ≈ 1.5×10-15 cm2/W for both forms of pinene at 775 nm.
The ratio of the signal modulated at 2f2 to that detected at f1 gives δn2,c/n2.av which, after suitable conversions results in d[α]/dI ≈ 1×10-11 deg cm/W for both types of pinene, with the expected inversion of sign of the effect for samples of the opposite optical rotation strengths (the absolute signs of the effects not determined in these measurements). In view of relatively high noise of the measurement, these results should be regarded as estimates of the upper limit of the effect. One notes that this technique yields the same order of magnitude estimates for the nonlinear optical rotation as the polarimetric Z-scan.
To establish the possibility of detecting two-photon nonlinear circular dichroism we have investigated several systems which were expected to show such an effect. The systems were of two types: either containing a two-photon chromophore in a chiral (but not two-photon absorbing by itself) medium or a chiral two-photon chromophore dissolved in a non-chiral solvent. In several cases we have seen modulation of the nonlinear absorption signal in open aperture Z-scans which could be attributed to the presence of two-photon NLCD. A more detailed description of these cases will be published elsewhere. We present here one example of the open aperture scan performed on a two-photon absorbing sample. The sample used in our experiment is the (R)-enantiomer of (1R-4-nitrophenylethyl)-5‶-thiooctadecyl-[2,2‵:5‵,2‶]terthien-5-ylmethylidene amine, with higher than 99% enantiomeric excess, dissolved in chloroform. The molecular structure of this chromophore and its linear absorption spectrum as well as linear chiroptical properties are described in Ref. . Our studies show that the chromophore exhibits a significant two-photon absorption, when excited at a wavelength of ~775nm, and they also indicate the presence of two-photon circular dichroism. Modulation of the nonlinear absorption signal reaching 3×10-3 has been measured in this experiment while no signal was detected in a racemic mixture. In view of uncertainties discussed in Section 5, these numbers again represent the upper limit of the two-photon dichroism observed.
4. Two-photon fluorescence detection of polarization modulation in Z-scan
For fluorescent substances it is common to investigate their nonlinear absorption properties through the measurements of multiphoton induced fluorescence. This principle can be combined with that of polarization-modulated Z-scan. Such a technique is a simple extension of fluorescence detected circular dichroism  and the principle has already been used in the investigations of two-photon circular dichroism of lanthanides . A simple modification of the experiment shown in Fig. 3 is the addition of a detector which is sensitive to the multiphoton induced fluorescence in the cell as it is scanned along the z direction. We used a fibre mounted on the cell or a detector positioned at the side of the scanning stage on which the cell was imaged with a lens. Initial experiments have shown that modulation signals can be readily detected. This method is therefore promising for the investigation of polarization dependent nonlinearities, especially since the signals are measured against zero background, unlike the usual refractive and absorptive Z-scan signals. However, the interpretation of our preliminary data is hampered by the fact that the fluorescence detection involves several effects including not only polarization dependences of the nonlinear absorption itself but also consecutive relaxation and emission processes.
5. Discussion and conclusions
We have shown here that simple modifications of the Z-scan technique may be useful in investigations of polarization-dependent nonlinear optical effects and we have detected signals which can be ascribed to nonlinear chiroptical properties. A necessary warning is, however, that the presence of light-induced linear birefringence and dichroism due to the light induced orientation of molecules may interfere in getting a correct estimation of the magnitudes of the nonlinear chiroptical processes . Moreover, the nonlinear circular birefringence and nonlinear circular dichroism of a liquid cannot be considered simple averages of the respective molecular properties. As comes from Ref. , these effects have components due to both the nonlinear gyration of the molecules themselves, and to the intensity-dependent reorientation of chiral molecules. Thus, detailed studies are needed to understand the contribution of various microscopic mechanisms to the observed macroscopic effects. It is worth noting that the various polarization-dependent nonlinear effects that can be detected by the techniques proposed by us may be of use e.g. in nonlinear microscopy.
This work was supported by the Chemistry and Life Sciences Directorate of the Air Force Office of Scientific Research, Grant No. FA9550-04-1-0158.
1. P. N. Prasad. Introduction to biophotonics (Wiley & Sons, Hoboken, New Jersey, 2003). [CrossRef]
2. I. Tinoco Jr., “Two-photon circular dichroism,” J. Chem. Phys. 62, 1006–1009 (1975). [CrossRef]
3. E. A. Power, “Two-photon circular dichroism,” J. Chem. Phys. 63, 1348–1350 (1975). [CrossRef]
4. G. Wagniere, “Optical-activity of higher-order in a medium of randomly oriented molecules,” J. Chem. Phys. 77, 2786–2792 (1982). [CrossRef]
5. S. Kielich, “Nonlinear optical activity in liquids,” Acta Physica Polonica 35, 861–862 (1969).
6. D. V. Vlasov and V. P. Zaitsev, “Experimental observation of nonlinear optical activity,” Pis’ma Zh. Eksp. Teor. Fiz. 14, 171–175 (1971).
7. R. Cameron and G. C. Tabisz, “Observation of two-photon optical rotation by molecules,” Mol. Phys. 90, 159–164 (1997).
8. F. Hache, H. Mesnil, and M. C. Schanne-Klein, “Nonlinear circular dichroism in a liquid of chiral molecules: A theoretical investigation,” Phys. Rev. B 60, 6405–6411 (1999). [CrossRef]
10. H. Mesnil, M. C. Schanne-Klein, F. Hache, M. Alexandre, G. Lemercier, and C. Andraud, “Experimental observation of nonlinear circular dichroism in a pump-probe experiment,” Chem. Phys. Lett. 338, 269–276 (2001). [CrossRef]
11. H. Mesnil, M. C. Schanne-Klein, F. Hache, M. Alexandre, G. Lemercier, and C. Andraud, “Wavelength dependence of nonlinear circular dichroism in a chiral ruthenium-tris(bipyridyl) solution,” Phys. Rev. A 66, 013802 (2002). [CrossRef]
12. J. Sztucki and W. Strek, “Two-photon circular dichroism in lanthanide(III) complexes,” J. Chem. Phys. 85, 5547–5550 (1986). [CrossRef]
13. K. E. Gunde and F. S. Richardson, “Fluorescence-detected two-photon circular dichroism of Gd3+ in trigonal Na3[Gd(C4H4O5)3].2NaClO4.6H2O,” Chem. Phys. 194, 195–206 (1995). [CrossRef]
14. M. Sheikh-bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. v. Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990). [CrossRef]
15. A. Pucci, S. Nannizzi, G. Pescitelli, L. D. Bari, and G. Ruggeri, “Chiroptical properties of terthiophene chromophores dispersed in oriented and unoriented polyethylene films,” Macrom. Chemistry and Physics 205, 786–794 (2004). [CrossRef]
16. D. H. Turner, I. Tinoco, and M. Maestre, “Fluorescence detected circular-dichroism,” J. Am. Chem. Soc. 96, 4340–4342 (1974). [CrossRef]
17. X. Xie and J. D. Simon, “Picosecond circular dichroism spectroscopy: A Jones matrix analysis,” J. Opt. Soc. Am. B 7, 1673–1684 (1990). [CrossRef]