Chiroptical signal enhancement in quasi-null-polarization-detection geometry: Intrinsic limitations

Despite its unique capability of distinguishing molecular handedness, chiroptical spectroscopy suffers from the weak-signal problem, which has restricted more extensive applications. The quasi-null-polarization-detection (QNPD) method has been shown to be useful for enhancing the chiroptical signal. Here, the underlying enhancement mechanism in the QNPD method combined with a heterodyne detection scheme is elucidated. It is experimentally demonstrated that the optical rotatory dispersion signal can be amplified by a factor of ∼400, which is the maximum enhancement effect achievable with our femtosecond laser setup. The upper limit of the QNPD enhancement effect of chiroptical measurements could, in practice, be limited by imperfection of the polarizer and finite detection sensitivity. However, we show that there exists an intrinsic limit in the enhancement with the QNPD method due to the weak but finite contribution from the homodyne chiroptical signal. This is experimentally verified by measuring the optical rotation of linearly polarized light with the QNPD scheme. We further provide discussions on the connection between this intrinsic limitation in the QNPD scheme for enhanced detection of weak chiroptical signals and those in optical enantioselectivity and Raman optical activity with a structured chiral field. We anticipate that the present work could be useful in further developing time-resolved nonlinear chiroptical spectroscopy.

Figure 1

QNPD optical schemes for (a) CD and (b) ORD signal enhancement. Instead of LCP and RCP or (±45°)-rotated LP, LEP and REP with a small ellipticity of β (a) or (±)-LP beams slightly rotated by β (b) are used as incident radiation. P, polarizer; S, chiral sample; A, analyzer; D, detector. The analyzer (A) allows only the horizontal field $\left(E_{\mathrm{chiral}}^{}+E_{\mathrm{LO}}^{}\right)$ to be transmitted through while the vertical field $\left(E_V^{}\right)$ is blocked. Note that the phase differences $\left(\mathrm{\Delta }\phi \right)$ between $E_V^{}$ and $E_{\mathrm{LO}}^{}$ are ±90° for (a) CD and 0° or 180° for (b) ORD.

Figure 2

The experimental layout of the QNPD for ORD measurement. P, Glan-laser polarizer; PBS, Glan-Thomson polarizing beam splitter; CS, chiral sample; ND1 and ND 2, neutral density filters; CCD, charge-coupled device detector.

Figure 3

The enhanced ORD signal (squares) measured at 800 nm for 3 mM aqueous Ni(+) (tartrate)${}_2$. The enhancement is increased with the 1/β curve (dashed line) at large β but decreases below $\beta =0.002$ (inset).

Figure 4

The chiroptical signal enhancement for fixed average photon counts $\left(N\right)$. (a) The standard deviations $\left({\sigma }_s\right)$ of the normalized ORD signal $(g$/G) measured at 24 mM $\left(N=250\right)$ and 120 mM $\left(N=1000\right)$ concentrations of Ni(+) (tartrate)${}_2$. (b) The measured ORD dissymmetry factor $g$ (circles) from Eq. (12) together with the calculated one (dashed line) from Eqs. (26) and (27), where $\mathrm{Re}\left[x\right]=\eta L/4=-2.3\times {10}^{-3},\mathrm{Im}\left[x\right]=\delta L/2=4.6\times {10}^{-3}$ and $\left|x\right|=5.1\times {10}^{-3}$ were used in 120 mM Ni(+) (tartrate)${}_2$.

Figure 5

Numerical simulations of the chiroptical signal enhancement in the QNPD scheme. (a) The standard deviation $\left({\sigma }_s\right)$ and (b) SNR of the normalized ORD signal $(g$/G) as a function of β for three different original chiroptical strengths, $\left|x\right|=5.1\times {10}^{-3}$ (black solid line), $8.6\times {10}^{-4}$ (red dashed line), and $1.0\times {10}^{-4}$ (blue dash-dotted line). Fixed average photon counts $\left(N=1000\right)$ were used for all cases. For comparison with the experiment, the simulation results (red dotted line) at $N=250$ are plotted for $\left|x\right|=8.6\times {10}^{-4}$. The grayed square in (a) shows the measurement window in our experiment [see Fig. 4].

Figure 6

Comparison between the chiroptical enhancement effects for fixed and variable photon counts $\left(N\right)$. The (a) experimentally measured and (b) simulated standard deviations $\left({\sigma }_s\right)$ of the normalized ORD signals for weak (24 mM and $\left|x\right|=8.6\times {10}^{-4})$ and strong (120 mM and $\left|x\right|=5.1\times {10}^{-3})$ chiroptical signal intensities. Fixed $N$: $N=250$ at 24 mM and $\left|x\right|=8.6\times {10}^{-4}$ and $N=1000$ at 120 mM and $\left|x\right|=5.1\times {10}^{-3}$. Variable $N$: (a) $N=46$ 000 and (b) $N=50$ 000, respectively, at β =0.035.