Femtosecond spectral interferometry of optical activity: Theory

Abstract

Optical activities such as circular dichroism (CD) and optical rotatory dispersion (ORD) are manifested by almost all natural products. However, the CD is an extremely weak effect so that time-resolved CD spectroscopy has been found to be experimentally difficult and even impossible for vibrational CD with current technology. Here, we show that the weak-signal and nonzero background problems can be overcome by heterodyned spectral interferometric detection of the phase and amplitude of optical activity free-induction-decay (OA FID) field. A detailed theoretical description and a cross-polarization scheme for selectively measuring the OA FID are presented and discussed. It is shown that the parallel and perpendicular electric fields when the solution sample contains chiral molecules are coupled to each other. Therefore, simultaneous spectral interferometric measurements of the parallel and perpendicular FID fields can provide the complex susceptibility, which is associated with the circular dichroism and optical rotatory dispersion as its imaginary and real parts, respectively. On the basis of the theoretical results, to examine its experimental possibility, we present numerical simulations for a model system. We anticipate the method discussed here to be a valuable tool for detecting electronic or vibrational optical activity in femtosecond time scale.

Vibrational Circular Dichroism: Time‐Domain Approaches

“…Then, the multipolar expansion form of the interaction Hamiltonian, which is valid up to the first order in the wave vector k, is [8,13,14] H I ¼ Àm Á Eðr; tÞÀM Á Bðr; tÞÀð1=2ÞQ : rEðr; tÞ ð 8:1Þ…”

“…m, M, and Q are the electric dipole, magnetic dipole, and electric quadrupole operators, respectively. Using the linear response function theory, one can find that the linear polarization is given as [8] P wherek k=jkj and r (1) (r, t) is the first-order perturbation-expanded density operator with respect to the above radiation-matter interaction Hamiltonian H I in Here, h...i denotes the trace over the bath degrees of freedom and r eq is the thermal equilibrium density operator. Note that the first term on the right-hand side of Equation 8.3 is typically two to three orders of magnitude larger than the other terms for electronic transition and four to six orders for vibrational transition.…”

“…Instead of measuring incoherent transmitted beam intensities, we have developed a chiroptical spectroscopic technique that can sensitively detect the transmitted beam at an amplitude level so that both magnitude and phase of the signal field are measured [8][9][10][11]. This additional phase information is used to simultaneously characterize the circular dichroic and birefringence effects induced by the field-chiral molecule interactions.…”

Time-Resolved Chiral Vibrational Spectroscopy

“…A related scheme for chiral mid-infrared spectroscopy was recently proposed by Cho and co-workers. [56] Here the incident linearly polarized femtosecond laser beam is completely blocked by the crossed polarizer behind the sample. Only the purely chiral, perpendicular polarized free induction decay component is transmitted and detected interferometrically after superposition with a delayed replica of the incident beam that is guided around the sample.…”

Time-domain measurement of optical activity by an ultrastable common-path interferometer

“…This yields, via a Kramers-Kronig transform, the complex chiral signal. A second measurement with analyzer aligned along the V direction produces an achiral reference signal, required to extract the CD and CB spectra [13]. The main limitation of interferometric approaches is the required high path-length stability between the two arms of the interferometer, since any vibration by a fraction of wavelength would spoil the measurement.…”