Dichroism

Dichroism is polarization-dependent absorption. A linearly dichroic material absorbs light polarized along one axis more strongly than light polarized along the perpendicular axis; a circularly dichroic material absorbs left- and right-circularly polarized light by different amounts. Linear dichroism is the working principle of most sheet polarizers: stretched polyvinyl alcohol film doped with iodine absorbs light polarized along the aligned polymer chains and transmits the orthogonal polarization. Circular dichroism is a small effect, usually well below 1 % of the total absorbance, produced by chiral molecules and used routinely to determine the secondary structure of proteins.

The word also has a separate use for materials or filters that show one colour in transmission and another in reflection, or whose colour depends on thickness, and "dichroic" filters and mirrors are named after it; these separate wavelengths by thin-film interference and are covered under dichroic mirror.

Relation to birefringence

In an anisotropic medium the complex refractive index $n + i\kappa$ has different values for the two eigenpolarizations. A difference in the real part, $\Delta n$, is birefringence and produces retardance; a difference in the imaginary part, $\Delta\kappa$, is dichroism and produces a difference in transmitted intensity. The two are linked by the Kramers-Kronig relations, so a material with a dichroic absorption band is also birefringent near that band. For circular polarizations the pair is circular dichroism and optical rotation (circular birefringence); their combined spectral signature near an absorption band is the Cotton effect.

Linear dichroism and polarizer performance

Linear dichroism is quantified by the difference in absorbance for light polarized parallel and perpendicular to a reference axis,

$$\mathrm{LD} = A_\parallel - A_\perp,$$

or by the dichroic ratio $A_\parallel / A_\perp$. Each absorbance follows the Beer-Lambert law for its own polarization, with transmittance $T = 10^{-A}$. For a polarizer film with $A_\parallel = 3.0$ along its absorbing axis and $A_\perp = 0.1$ along its transmitting axis,

$$T_\parallel = 10^{-3.0} = 0.10\ \%,$$ $$T_\perp = 10^{-0.1} = 79.4\ \%.$$

The dichroic ratio is 30, and the polarization extinction ratio is 794:1, or 29.0 dB. Doubling the film thickness doubles both absorbances: the extinction ratio rises to about 630,000:1 while transmission falls to 63 %, which is the basic trade-off in designing absorbing polarizers.

Natural linear dichroism occurs in crystals such as tourmaline, one of the earliest polarizing materials, and in many minerals, where colour changes with the direction of polarization; geologists call the effect pleochroism and use it to identify minerals in thin sections. Oriented molecules in stretched films, liquid crystals, membranes and DNA fibres show it as well, and linear dichroism spectroscopy uses it to determine the orientation of chromophores relative to an alignment axis.

Circular dichroism

Circular dichroism is defined as

$$\Delta A = A_L - A_R,$$

the difference in absorbance for left- and right-circularly polarized light. It is often reported as ellipticity: after passing through the sample, initially linear light becomes slightly elliptical, and for small $\Delta A$ the ellipticity in degrees is

$$\theta = \frac{\ln 10}{4}\,\frac{180}{\pi}\,\Delta A = 32.98\,\Delta A.$$

A sample with $\Delta A = 10^{-4}$ therefore has an ellipticity of 3.3 millidegrees, a typical order of magnitude in protein spectroscopy. In the far ultraviolet, an α-helical protein shows negative bands near 222 and 208 nm and a positive band near 192 nm, while β-sheet structures give a negative band near 218 nm and a positive band near 195 nm; fitting a measured spectrum to reference spectra estimates the fraction of each structure. Circular dichroism is also used to assign the absolute configuration of chiral molecules and to follow folding and binding.

Measurement

A linear dichroism spectrum is measured by recording absorbance with the incident polarization set parallel and then perpendicular to the sample axis, or by modulating the polarization and detecting the difference directly. Circular dichroism spectrometers switch the light between left and right circular polarization with a photoelastic modulator at around 50 kHz and recover the small modulated component of the detector signal with a lock-in amplifier, which is necessary because $\Delta A$ is thousands of times smaller than $A$.

Pitfalls

In oriented or scattering samples, linear dichroism and linear birefringence combine to produce spurious circular dichroism signals, so CD measurements on films, fibres or crystals need correction or a full Mueller-matrix measurement. High total absorbance leaves too little light to measure a small difference, so CD samples are usually prepared with a total absorbance of about 1 or less. Sheet polarizers lose dichroic ratio at the ends of their design band and degrade under heat and intense light; for near-infrared or high-power use, crystal or nanoparticle-glass polarizers are used instead.

Common questions

What is the difference between dichroism and birefringence?

Dichroism is polarization-dependent absorption, a difference in the imaginary part of the refractive index; birefringence is polarization-dependent phase velocity, a difference in the real part. Dichroism changes the transmitted intensity of each polarization, and birefringence changes their relative phase.

Why is circular dichroism used for proteins?

The peptide backbone in α-helices, β-sheets and disordered regions produces distinct far-ultraviolet CD spectra, so a spectrum recorded with a fraction of a milligram of protein in solution gives a rapid estimate of secondary structure without a crystal.

Is a dichroic mirror dichroic?

Only in the separate, colour-splitting sense of the word. A dichroic mirror separates colours by interference in a thin-film stack and does not rely on polarization-dependent absorption.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 8; C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983); M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Ch. 15; N. J. Greenfield, Nature Protocols 1, 2876 (2006).