Low Refractive Index

November 16, 2015

I just got a new pair of eyeglasses. Unlike my old pair, which used lenses ground from glass, this new pair has plastic lenses. Although I don't know the specific plastic used for the lenses, polycarbonate is representative of such materials, and it has a low density (1.22 g/cc) with a high refractive index (1.585) that makes it easier to figure a lens.

Optical crown glass, a traditional lens material, also has a high refractive index (1.523), but it's much heavier, having a density of 2.55 g/cc. My new eyeglasses are much lighter than the old, since the density of the plastic is half that of glass. My new eyeglasses have progressive lenses, a bifocal lens technology with a smooth transition between distance and reading aspects.

Optical lenses have been known from antiquity, but the apparent first mention of their use as a corrective lens is in Pliny the Elder's description of an emerald as a vision aid.[1] (The Glasses Apostle, a 1403 painting by Conrad von Soest (c. 1730 - c. 1422), considered to be the oldest depiction of eyeglasses north of the alps, via Wikimedia Commons.)

While high refractive index is useful for lens making, low refractive index optical materials are also useful. Optical fiber is an example of an optical element combining a low refractive index material with high refractive index material. Two useful optical elements making use of both low and high refractive index materials are the dielectric mirror and the dichroic filter.

Whenever light passes through an interface of one refractive index to another, a portion of the light will be reflected, and the rest will be transmitted. By selecting the thickness of multiple refractive layers, the reflected rays can be selected to interfere constructively or destructively at certain wavelengths. This is an optical manifestation of Bragg's law.

Modern material deposition techniques make it easy to produce optical films of many layers. I designed a bandpass filter for the helium-neon laser wavelength (632.8 nm) using alternating layers of materials with refractive indices of 1.49 and 2.38. This filter has 40 double layers with a layer thickness of 106.17 nm for the lower refractive index and 66.47 nm for the higher refractive index. The filter response at normal incidence is shown below.

Optical response of a bandpass filter designed for the 632.8 nm helium-neon laser wavelength. This filter has eighty layers of alternating low and high refractive index. (Graphed using Gnumeric.)

The lowest refractive index is 1.0, the refractive index of the vacuum, but the refractive index of air, about 1.0003, is close enough to one that 1.0 is often used in calculations. When an air gap is formed between two parallel plates of high refractive index, this Fabry–Pérot etalon will cause an interference pattern through constructive and destructive interference of light waves of a particular wavelength. Although any interface between media of different refractive indices will lead to reflection (4% in the case of window glass), such etalons perform best with partially-transmitting mirrors (see figure).

A Fabry–Pérot etalon and its interference pattern.(Created using Inkscape.)

Construction of an air gap between parallel plates is easy when the plates are thick, like microscope slides. Thin plates would likely deform, so the parallelism is destroyed. It would be far easier to work with an optical material with a refractive index very close to 1.0.

That was the motivation for recent research by scientists from North Carolina State University (NCSU, Raleigh, North Carolina) and the Air Force Research Laboratory (Dayton, Ohio). In a recent paper in Advanced Functional Materials, they describe a nanolattice material with a refractive index as low as 1.025.[2-3] As is typical in science, this recent advance is built on a previous process, developed by the NCSU scientists last year.[4-5]

The NCSU process creates a sea of self-assembled colloidal particles on surfaces. In last year's study, such an assemblage was placed on a photosensitive layer to act as lenses for selective exposure.[4-5] Says Chih-Hao Chang, an assistant professor of mechanical and aerospace engineering at NCSU,

"We are using the nanosphere to shape the pattern of light, which gives us the ability to shape the resulting nanostructure in three dimensions without using the expensive equipment required by conventional techniques... and it allows us to create 3-D structures all at once, without having to make layer after layer of 2-D patterns."[5]

An example of an asymmetric hollow-core three-dimensional nanostructure fabricated by shining light through a surface nanoparticle lens array. (NCSU image by Xu Zhang.)[5]

The surface nanoparticles were used to create ordered nanostructured layers in a different way to create the low refractive index films. The surface array acts as a template for formation of a thin layer of aluminum oxide by atomic layer deposition (ALD). The polymer surface array is then burned off, and a three-dimensional aluminum oxide coating is left behind.[3]

Explains Xu Zhang, lead author of the recent paper and a Ph.D. student at NCSU,

"The key to the film's performance is the highly-ordered spacing of the pores, which gives it a more mechanically robust structure without impairing the refractive index. We are able to control the thickness of the aluminum oxide, creating a coating between two nanometers and 20 nanometers thick... Using zinc oxide in the same process, we can create a thicker coating. And the thickness of the coating controls and allows us to design the refractive index of the film."[3]

The structure of a nanostructured dielectric film at the micrometer scale. (NCSU image by Chih-Hao Chang.)

The research team has developed a mechanically stiff aluminum oxide film with a refractive index of 1.025.[3] Aside from optical applications, these films can serve as electrical insulators in high speed interconnections in integrated circuits. Says Chang, "The steps in the process are potentially scalable, and are compatible with existing chip manufacturing processes... Our next steps include integrating these materials into functional optical and electronic devices."[3]

This photograph compares the transparency of the low refractive index films (NM) with glass. (NCSU image by Chih-Hao Chang.)

References:

1. Pliny the Elder, "The Natural History," John Bostock, Trans., Book 37, Chap. 16 ("Smaragdus"), via Project Perseus.
2. Xu A. Zhang, Abhijeet Bagal, Erinn C. Dandley, Junjie Zhao, Chrisopher J. Oldham, Gregory N. Parsons and Chih-Hao Chang, "Ordered Three-Dimensional Thin-Shell Nanolattice Materials with Near-Unity Refractive Indices," Advanced Functional Materials, October 12, 2015, doi: 10.1002/adfm.201502854.
3. Matt Shipman, "Dielectric Film Has Refractive Index Close to Air for Photonics Applications," North Carolina State University Press Release, October 12, 2015.
4. Xu A. Zhang, Bin Dai, Zhiyuan Xu and Chih-Hao Chang, "Sculpting Asymmetric Hollow-Core Three-Dimensional Nanostructures Using Colloidal Particles," Small, December 8, 2015, DOI: 10.1002/smll.201402750.
5. Matt Shipman, "Nanoparticle Allows Low-Cost Creation of 3-D Nanostructures," North Carolina State University Press Release, December 8, 2014.