Theory of Apparent Circular Dichroism Reveals the Origin of Inverted and Noninverted Chiroptical Response under Sample Flipping

Abstract

Circular dichroism (CD) finds widespread application as an optical probe for the structure of molecules and supramolecular assemblies. Its underlying chiral light−matter interactions effectively couple between photonic spin states and select quantum-mechanical degrees of freedom in a sample, implying an intricate connection with photon-to-matter quantum transduction. However, effective transduction implementations likely require interactions that are antisymmetric with respect to the direction of light propagation through the sample, yielding an inversion of the chiroptical response upon sample flipping, which is uncommon for CD. Recent experiments on organic thin films have demonstrated such chiroptical behavior, which was attributed to "apparent CD" resulting from an interference between the sample's linear birefringence and linear dichroism. However, a theory connecting the underlying optical selection rules to the microscopic electronic structure of the constituent molecules remains to be formulated. Here, we present such a theory based on a combination of Mueller calculus and a Lorentz oscillator model. The theory reaches good agreement with experimental CD spectra and allows for establishing the (supra)molecular design rules for maximizing or minimizing this chiroptical effect. It furthermore highlights that, in addition to antisymmetrically, it can manifest symmetrically such that no chiroptical response inversion occurs, which is a consequence of a helical stacking of molecules in the light propagation direction.

Reciprocal and Non‐reciprocal Chiroptical Features in Thin Films of Organic Dyes

“…In particular, two of these thin films were overlapped with their dipping directions at various tilt angles φ: with φ=+45°, the ECD spectrum showed a significant CP absorption between 400 and 470 nm (Figure 6, blue line), while by overlapping them at φ=−45° a mirror‐image ECD spectrum was recorded (Figure 6, red line); at φ=0° or 90°, no CP absorption was detected in the ECD spectrum. This simple expedient of layers tilted at ±45° well revealed the essence of non‐reciprocal LDLB contribution in the ECD spectra of anisotropic thin film samples: the LDLB effect may arise from a number of linearly birefringent and linearly dichroic layers helically overlapped [29] . This experiment clearly highlights the possible macroscopic source of the LDLB effect.…”

“…This simple expedient of layers tilted at � 45°w ell revealed the essence of non-reciprocal LDLB contribution in the ECD spectra of anisotropic thin film samples: the LDLB effect may arise from a number of linearly birefringent and linearly dichroic layers helically overlapped. [29] This experiment clearly highlights the possible macroscopic source of the LDLB effect.…”

“…The non‐reciprocal CP absorption is invariant upon sample rotation around the instrumental optical axis, but it inverts its sign by sample flipping: in other words, it consists in the inversion of the handedness of CP light component which is preferentially transmitted or emitted by the two opposite faces of the same thin film sample. This non‐reciprocal behavior has not to be confused with a breaking of Lorentz reciprocity, which is not violated by the LDLB term [29] . It must also be stressed that this term of the experimental CP absorption of thin films is not an artifact: it is a real and perfectly reproducible contribution, completely independent of instrumental faults and of the intrinsic technical limitation of polarization‐modulation instruments, unlike the two following terms in equation (4).…”

“…This non-reciprocal behavior has not to be confused with a breaking of Lorentz reciprocity, which is not violated by the LDLB term. [29] It must also be stressed that this term of the experimental CP absorption of thin films is not an artifact: it is a real and perfectly reproducible contribution, completely independent of instrumental faults and of the intrinsic technical limitation of polarization-modulation instruments, unlike the two following terms in equation (4).…”

“…Very recently, Tempelaar et al proposed a fascinating theory, based on a combination of the Mueller matrix theory and a Lorentz oscillator model, to interpret non-reciprocal chiroptical properties of thin films. [29] This theory offers insight into the supramolecular arrangement of π-conjugated dyes able to generate LDLB effects. The authors considered parallel layers of molecules undergoing two or more nondegenerate electric-dipole allowed transitions whose transition dipole moments lie at an acute angle β.…”