The Motheye Antireflection Device

James Cowan, Ph.D.
President, Aztec Systems, Inc., &
Chief Technical Officer, Holographix, Inc.

One of the persistent problems in optics is the reduction of unwanted reflections from optical surfaces. At a glass-air interface, for example, about four percent of the incident light is reflected, a result that occurs because of the abrupt change in the index of refraction when light passes from air to glass.

A common method of reducing the reflectivity is to coat the glass surface, which could be, for example, a lens, with a thin film antireflection coating. The coating could be, typically, a single layer, or more effectively, a multi-layer of such materials that the index change is gradual rather than abrupt. Thin film coated optics are quite efficient in achieving antireflection characteristics, but they have several serious drawbacks. Probably the most serious disadvantage of thin film coatings is their high expense, because the coatings have to be done by vacuum evaporation of often exotic materials. But also the coatings can be fragile, unstable, and suffer deterioration from moisture and heat.

An alternative to the use of thin films is a phenomenon that was discovered many years ago in nature, the so-called motheye structure. The name comes from the eye of the night flying moth, which achieves antireflection by means of a unique surface relief structure consisting of a close-packed hexagonal array of tiny protuberances. Their dimensions are small compared to the wavelength of light, typically 200 to 300 nanometers, with a corresponding depth. Antireflection is achieved because incoming light sees a surface that does not change abruptly, but rather gradually, in going from air to the material of the eye. This sub-wavelength structure is as effective as multi-layers in reducing the reflection of light from surfaces, a fact that has led many researchers in recent years to find means of somehow utilizing and incorporating it as an alternative to thin films.

Advances in lithographic and optical interference techniques for the fabrication of sub-wavelength structures, combined with new methods of replication, have allowed the ability to simulate the motheye structure in photo-resist and to mass produce it thus enabling the motheye to be a commercially viable alternative to multi-layer coatings. The technique is an extension of the method used to make holographic diffraction gratings, namely, the interference of two beams of laser light in a layer of photoresist. When exposed and developed, the photoresist layer forms a surface relief structure whose dimensions reflect the variation in intensity distribution of the interference pattern across the surface. Depending on the angle between the interfering beams, a diffraction grating is formed whose spacing, or pitch, can be varied from several micrometers down to about half the wavelength of the interfering light. Since the interference intensity varies sinusoidally, the corresponding surface relief pattern that results also shows a sinusoidal, or wavelike, distribution. The grating that is formed in this way is a so-called linear grating, which, when viewed from above consists of an array of straight lines, and viewed from the edge displays the wavelike pattern.

The extension of this technique to form a motheye structure consists of making a so-called crossed grating, which involves doing a first exposure to a two-beam interference pattern, rotating the recording surface by 90 degrees, and then doing a second exposure. The resulting developed surface shows an undulating surface in two dimensions, a checkerboard pattern of hills and valleys. This is a rough simulation of the actual motheye pattern in that the protuberances are submicron in spacing, and that they are rounded at top and bottom and are gradually tapering. The difference is that the pattern formed in this way is a square array, while the real motheye is a hexagonal close-packed array.

Because any regular array of this type forms a diffractive structure, care must be taken to insure that there are no visible diffractive orders that would remove light from the main transmitted beam and also be an annoying distraction. This places a limit on the periodicity of the array, which for visible light in the 400 to 700 nanometer range means that the spacing cannot be larger than the shortest wavelength in the observed spectrum, or 400 nanometers. Furthermore, if light is emerging from a high index material like glass into air, this spacing must be reduced by the index of the material. For glass, with an index of 1.5, the maximum spacing is thus 400/1.5, or 267 nanometers. A further consideration is that even with a spacing this small, there exists the possibility of annoying diffracted light appearing at extremely large angles of incidence, which requires a further reduction of the periodicity to closer to 200 nanometers.

The next consideration has to do with the depth of the protuberances, or the aspect ratio (depth to periodicity). The aim of any antireflection surface is to achieve minimum reflectivity while at the same time insuring maximum transmissivity. Simple scalar diffraction theory shows in general that the greater the depth, or aspect ratio, the better are these properties achieved. At the same time there is a practical limit to this depth in terms of actually being able to fabricate and to replicate the pattern. Generally, a 1:1 aspect ratio is satisfactory, and for the small spacings involved this can usually be achieved. This means that the aim would be a 200 nanometer pitch array with a depth between 200 and 300 nanometers.

As a final consideration, the shape and distribution of the protuberances must be taken into account. As mentioned, the profile should be smoothly tapered in order to prevent any abrupt changes in index of refraction. But diffraction theory further states that the degree of taper is important, particularly for high index materials. This means that the amount of curvature of the profile must be adjusted in order to achieve the maximum antireflection behavior. The distribution of the protuberances is also important, and it is significant to note that nature has chosen a hexagonal close-packed array for the motheye.

The foregoing considerations have stimulated research aimed at improving the basic surface relief structure. Improved and innovative methods of laser interferometry, recording geometries, types of photoresist, and development procedures have yielded profiles that even more closely simulate what is found in nature. Experiments on the reflectivity of this improved surface in photoresist indicate that with proper exposure and processing, high transmission can be obtained with negligible reflectivity.

Perhaps the greatest advantage of the motheye structure is the ease and low cost with which it can be replicated. Current techniques allow for the creation of an optimized photoresist profile. This “master” structure can then be transformed into a stamper capable of producing thousands of replica motheyes using photopolymer replication, embossing or injection molding techniques. These replicas can be produced at very attractive prices when compared to multi-layer coatings.