THIN FILMS - Motheye surfaces reflect little light

Aug. 1, 1999
With low reflection and low absorption over wide spectral ranges, motheye-structured surfaces provide an alternative to traditional anti reflection coatings.

Bruce MacLeod and Greg Sonek

With low reflection and low absorption over wide spectral ranges, motheye-structured surfaces provide an alternative to traditional anti reflection coatings.

The optical properties of multilayer thin films and dielectric stacks are largely well known. Depending on their thickness, refractive index, and absorption coefficient, thin films can function as total-reflection, partial-reflection, or antireflection (AR) coatings on a variety of substrates. The choice of which coating material to use is often dictated by the application, the environmental conditions that the coated optic will be subjected to, and the cost of reaching a specific level of performance.


FIGURE 1. Scanning electron micrograph of the eye of a night moth reveals an array of subwavelength-sized projections covering the eye's surface. (Courtesy C. G. Bernhard: see Ref. 1)
Click here to enlarge image

The use of AR coatings can be problematic, however. Traditional single-layer AR coatings are designed to operate over a narrow, targeted wavelength band and perform poorly outside the designated range. In addition, the performance of traditional AR coatings begins to degrade at incident angles beyond 20°. Multilayer thin-film AR coatings address some of these issues with moderate success, but at a higher production cost.

Thin-film AR coatings can suffer catastrophic failure or delamination from high-energy or thermal-cycling applications. High-power laser applications require low-reflectivity lenses to limit high-energy retroreflection. The thermal performance of these AR-coated substrates is governed by the composite structure's ability to dissipate heat generated by the absorption of incident laser energy during transmission or reflection. This ability is directly related to the absorption that takes place in the substrate, coating material, and various interfaces. Surface contamination, poor adhesion, and a mismatch in thermal properties can further contribute to the creation of nonuniform temperature distributions that gradually lead to film degradation, including cracking, peeling, delamination, and surface breakdown.

Under extreme conditions, catastrophic failure can occur, such as the fracturing, melting, and ablation of both film and substrate. This can lead to a severe degradation in performance of the AR coating.

FIGURE 2. Due to its subwavelength period, a surface-relief motheye structure etched into a substrate material appears as a gradient-index film to an incident light beam, thereby serving as an impedance-matching layer that eliminates Fresnel reflections at the air-substrate interface.
Click here to enlarge image


One approach that has shown great promise for achieving the in creasingly high-performance requirements of AR surfaces is the use of motheye, or subwavelength, structures. The descriptive term motheye structures was coined in the late 1960s and early 1970s by naturalists working on relating observations in nature to real-world applications.1

These researchers noticed that the eyes of nocturnal insects such as moths reflect little or no light, regardless of the angle of incidence of the illuminating light or the light wavelength. They set about dissecting various insect eyes and found, under the high magnification afforded by an electron microscope, that the surface of a moth's eye is covered by an array of conical protuberances 200 nm high separated by 200 nm (see Fig. 1).

A motheye structure creates what is effectively a gradient-index film from a material of uniform refractive index (see Fig. 2). By itself, an optical substrate exhibits a discontinuity in refractive index at the interface between it and a surrounding medium of differing refractive index (such as air). This index mismatch is responsible for the reflected wave that is generated when a beam of light is incident on its surface. If a simple, step-like binary pattern of subwavelength period is created on the substrate surface, the binary structure behaves as if it were a thin film having the same height as that of the binary step, but with an effective index that is a spatial average of the surrounding medium and substrate refractive indexes.

A more-complex steplike structure patterned in the same substrate is equivalent to a multilayer stack of thin films, each of which has a slightly different refractive index based on the area, or fill factor, of the corresponding step. In the limit of a continuously varying surface profile, the motheye structure behaves as if it were a gradient-index film with a refractive index that varies continuously from that of the surrounding medium to that of the underlying substrate.2

This process is effectively one of impedance matching at optical wavelengths. In principle, without a discontinuity in refractive index, a light beam incident on a motheye-patterned substrate should suffer no Fresnel reflection loss. In practice, the specific spacing, depth, and cross-sectional geometry of the surface-relief structure determine the antireflective properties of the motheye surface, as well as the lower and upper cutoff wavelengths for operation.

FIGURE 3. A motheye designed for low reflection at visible wavelengths exhibits a reflection of less than 0.4% across the visible spectrum (top left). The design for the visible motheye calls for a period of 275 nm and a structure depth of greater than 280 nm (top right). A motheye in silicon (Si) designed for low reflection at midwavelength infrared shows a reflection of 2% or less for a wide range of incidence angles (bottom left). The high refractive index of Si results in a motheye design with conical features (bottom right).

Design and fabrication

Motheye structures can be designed for a variety of ultraviolet (UV), visible, and infrared (IR) materials by following several simple design rules. First, to avoid significant diffraction and surface-scatter effects, the periodicity of the surface-relief structures must be smaller than the shortest wavelength of operation divided by the index of refraction of the substrate. This is equivalent to having only the zeroth order reflected and transmitted waves propagate, without aberration or distortion, through the substrate. Otherwise, the motheye structure will function like a conventional diffraction grating, with most of the light scattered into higher diffraction orders.

Second, for optimal performance the height of the structures should be at least 40% of the longest operating wavelength.3 Third, the optimal profile to be achieved should closely approximate a pyramid with straight or tapered (curved) sidewalls and should assume a greater taper as the index of the underlying substrate increases.4

The basic process that Holographic Lithography Systems (Bedford, MA) and others have developed for fabricating motheye structures is based on holographic (interference) lithography and reactive ion etching. Holographic lithography is the process of recording, in a photosensitive film, a periodic pattern resulting from the interference of two coherent laser beams. The interfering beams produce an optical standing wave with a period equal to l/(2n sinq), where l is the laser wavelength, n is the refractive index of the medium in which the exposure is made, and q is the half-angle of the interfering beams.

Based on the choice of l and q, structures having periods between 200 nm and 4 µm with critical dimensions as small as 100 nm and as large as several microns can be generated. The exposure process is inherently maskless, has an extremely large depth of field, and can produce a variety of uniform periodic patterns (for example, gratings, lines, holes, cones, tips, and posts) over large areas.

To make a motheye surface, the substrate to be patterned is coated with a film that is photosensitive to the specific laser wavelength being used. After the exposure and development of the motheye pattern in the photosensitive film, the pattern must be transferred to the underlying substrate using an etching process. Reactive ion etching is the preferred method, because it is capable of producing high-aspect-ratio structures through both physical ion bombardment and chemical etching of the substrate surface.

By using replication techniques, including UV curing, injection molding, and embossing, it is possible to form motheyes in many materials used in visible-wavelength applications-for example, UV-curable photopolymers, acrylics, and polycarbonates. These techniques have proven to have the high fidelity required to reproduce features down to 193-nm periods while maintaining the highest levels of performance.5 To effectively generate motheye "master" tools for these replication efforts, the photoresist patterned master alone can be made durable enough to withstand the replication process. Although most infrared materials such as zinc selenide (ZnSe) and germanium cannot be replicated into, replication-when possible-can offer substantial cost savings in any volume production because the etching step will not longer be required.

Successful application

To date, these techniques have been successfully used to produce motheye patterns for the visible, midwavelength IR, and long-wavelength IR in glass, silicon (Si), and ZnSe substrates (see Fig. 3). An unpatterned glass surface in air has a nearly constant reflectance of 4.2% over the visible wavelength range from 400 to 700 nm. When that same surface is patterned with motheye structures with the appropriate spacing and profile, reflection losses are reduced to less than 0.4% across the visible spectrum. For a silicon surface patterned with an 800-nm-period motheye designed for midwavelength IR, sample reflectance is reduced to below 2% over the 1.5-5.5-µm band. The data show that motheye surfaces are capable of maintaining low reflectance, even as the incident angle is increase to 50°. Hence, unlike conventional thin-film coatings, motheye-structured surfaces have a large acceptance angle and can perform well over a broad wavelength range and at high incident angles. Motheye AR applications include lenses and optics for use throughout the UV, visible, and IR spectral regions.


  1. C. G. Bernhard, Endeavour, 26, 79 (1967).
  2. D. H. Raguin and G. H. Morris, Appl. Opt. 32(7), 1154 (March 1, 1993).
  3. S. J. Wilson and M. C. Hutley, Optica Acta 29(7), 993 (1982).
  4. W. H. Southwell, J. Opt. Soc. Am. A,8(3), 549 (March 1991).
  5. J. Anagnostis, S. Payette, and D. Rowe, "Replication of High Fidelity Surface Relief Structures," ASPE 1999 Spring Topical Meeting, Chapel Hill, NC (April 12, 1999).

BRUCE MACLEOD is vice president of manufacturing and GREG SONEK is manager of optical products at Holographic Lithography Systems Inc., Three Preston Court, Bedford, MA 01730; e-mail: [email protected] and [email protected].

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