**Abstract**

Chiroptics is the study of the changes in circular polarization states of light transmitted through analytes typically dissolved in isotropic solutions. However, experimental challenges have long prevented chiroptical measurements of anisotropic media such as single crystals of low symmetry, liquid crystals, or structured films. The high accuracy universal polarimeter (HAUP) was introduced in 1983 to investigate the differential refraction of left and right circular polarization states, circular birefringence (CB), and even in anisotropic media that are dominated by the differential refraction of orthogonal linear polarization states, linear birefringence (LB). In this century, the HAUP was extended to also measure not only the dispersive optical effects (CB and LB) but also the corresponding dissipative effects, circular dichroism (CD) and linear dichroism (LD), differences in light absorption. The improved device is the generalized-HAUP (G-HAUP). Not only can it deliver all the linear optical properties of dissymmetric, anisotropic, and absorbing media, but it can also do so in the ultraviolet as well as the visible part of the electromagnetic spectrum. In this review, characteristic features of the G-HAUP and its applications to crystals of photomechanical salicylidenephenylethylamines, alanine, benzil, and magneto-optical CeF3 are described.

**Keywords:** chiroptical properties, circular birefringence, optical activity, circular dichroism, linear birefringence, linear dichroism, chirality, high accuracy universal polarimeter (HAUP), generalized-HAUP (G-HAUP)

### **1. Introduction**

Chiroptics is the study of the transmission of circularly polarized light through transparent analytes. Linear chiroptical effects are circular birefringence (CB), more colloquially know as optical rotation (OR) or optical activity (OA), sometimes described by gyration of magneto-optical tensors, and circular dichroism (CD). Besides the proliferation of near-synonymous terms, *chiroptics* is itself a misnomer. While chirality is a necessary condition for measurement of CB and CD of molecules rapidly, randomly reorienting in isotropic media, chirality is not necessary when measurements are extended to anisotropic media such as single crystals. Molecules in solution must be chiral, characterized by a pure rotational group (*Cn*, *Dn*,*T*, *O*, *I*), to be optically active, but some achiral crystals can also be optically active in some directions, in particular those belonging to non-enantiomorphous crystallographic point groups (*Cs*, *C*2*v*, *S*4, *D*2*d*) [1]. Thus, the *chiro* prefix is a linguistic infelicity that arose from the historical difficulty of measuring CB and CD in low symmetry crystals, dominated as they are by LB and LD, which can typically be 10**<sup>2</sup>** –10**<sup>4</sup>** times larger than the former. Molecules are small compared with the wavelength of radiation used in spectropolarimetric measurements; thus, CB and CD are small; molecules of 1–2 nm barely feel the sense of the twist of the electric field of circularly polarized light with a pitch of *ca*. 500 nm. By comparison, it is easy to detect small changes in polarization in isotropic media in normal incidence, which are otherwise indifferent to linearly polarized light. However, in solids with much larger competing perturbations to the state of polarization, chiroptical effects can fall within the experimental noise.

OA was evidenced by Arago in 1811 when he passed linearly polarized light along the high-symmetry *c*-axis of quartz [2]. However, the determination of the anisotropy of OA by making off-axis measurements was a challenging area of research as late as 1988 [3]. The minor dissymmetry-induced perturbations to the polarization state of light in anisotropic media is of the same order of magnitude as parasitic ellipticities from imperfect samples and the polarimeter optical components. Consequently, we know comparatively little about the orientational dependence of CB in molecules, a considerable hole in the science of molecular chirality. A strategy for filling this hole is to characterize the chiroptical properties and to understand what responses contribute to the orientational averages measured in solution.

The *intensity* of light passing through a polarizer, chiral anisotropic sample, and analyzer, contains all the necessary information, in principle, for extracting CB even in the presence of dominating LB. However, the implementation of this extraction was only achieved after the invention of electrophotometry and stable, high-intensity light sources. In 1983, Kobayashi and Uesu used photon-counting techniques, lasers, and computerized modulation of polarizer and the analyzer orientations (*θ* and *Υ*; see **Figure 1a**) to determine OA in crystals for directions off the optic axes. This so-called HAUP (high accuracy universal polarimeter) [4–6] was a watershed that gave researchers some confidence after almost two centuries that OA could be measured in crystals generally.

Curiously, the acronym *HAUP* itself is also a slight misnomer. While the HAUP was *universal* in tackling circular and linear anisotropies simultaneously, it could not be considered truly universal until it could function as a complete polarimeter, thus delivering CD and LD as well. For this reason, the extended HAUP method and its associated optical analysis were developed to deliver all four optical effects simultaneously: CB, LB, CD, and LD [6, 7]. Moreover, generalized-HAUP (G-HAUP) has now been extended into the ultraviolet part of the electromagnetic spectrum [8].

*Chiroptical Studies on Anisotropic Condensed Matter: Principle and Recent Applications… DOI: http://dx.doi.org/10.5772/intechopen.108721*

#### **Figure 1.**

*(a) Schematic representation of the conventional HAUP optics with optical chopper (Ch), lock-in amplifier (LIA), linear polarizer (*P*), sample stage with a temperature control unit and a pinhole (*S*), linear analyzer (*a*), and detector (*D*).* θ *and* Υ *are the azimuth angle of* P *from an extinction position of a crystalline sample and the deflecting angle* a *from the crossed Nicols position, respectively. (b) Photograph of the G-HAUP apparatus developed by authors.*

In addition to the HAUP [4–9], other strategies have arisen to measure CB and CD in crystals using modulation of light polarization states photoelastically. These include universal chiroptical spectrophotometer (UCS) [10] and the 4 photo-elastic modulator (4PEM) polarimeter [11]. The UCS relies on the fact that the contributions to a timevarying intensity signal have different frequency dependencies and can be isolated with lock-in amplifiers. 4PEM is a complete polarimeter configured to deliver the whole polarization transfer or Mueller matrix and without any moving optical components to minimize errors. In the 4-PEM polarimeter, all the Mueller matrix elements are simultaneously obtained from 16 frequencies in a Fourier analysis of time-dependent light intensity. The 4-PEM polarimeter can also be operated at oblique angles of incidence so as also to obtain data in reflection like an ellipsometer [12].

This review consists of the following seven sections. Section 2 briefly explains the optical system and characteristic features of the G-HAUP. Sections 3, 4, 5, and 6 describe the recent applications of G-HAUP to salicylidenephenylethylamines [13], alanine [14], benzil [15], and CeF3 crystals [9]. Finally, Section 7 presents conclusions and future directions for the G-HAUP.
