Inspiration from the reflective sides of silvery fish
Silvery reflections from many mid-water fish, such as herring and sardines, are produced by a multilayer ‘stack’ of guanine crystals with cytoplasm gaps. Guanine is a purine base also found in the nucleic acids DNA and RNA, while cytoplasm is the substance that fills living cells and consists primarily of water. These structures act as vertical mirrors and camouflage the fish in the underwater light field.1 For optimal concealment, the reflecting structures must be able to produce high-percentage, non-polarizing reflectivity over all angles of illumination and visible wavelengths. Previous studies, for example by Rowe and Denton,2 showed that reflections from fish are only very weakly polarizing. However, optical models have until now been unable to explain this property, instead predicting that illumination by unpolarized light produces a fully polarized reflection at Brewster's angle.3, 4
Animal biophotonic structures are proving to be of great inspiration for optical technologies,5 and their investigation can offer inspiration for devices that hold significant advantages over synthetic alternatives.6 Non-polarizing dielectric multilayer reflectors, for instance, are an important class of optical device and have numerous applications within waveguides and thermoelectric devices.7 However, existing non-polarizing mirrors require a refractive index contrast with the external environment and are thus restricted by the range of suitable materials.8 This cannot be what occurs in silvery fish skin, as the cytoplasm layers have the same refractive index as water. Instead, these fish have evolved an entirely different mechanism for producing a non-polarizing reflection, which we have recently identified.9
Previous optical models of fish reflectors have assumed that the guanine crystals behave as optically isotropic layers with a refractive index of ∼1.83.3, 4 These crystals, however, are in fact highly birefringent,1 and are weakly biaxial with refractive indices 1.85, 1.81, and 1.46. It has recently been demonstrated that the relative axial growth rate of the crystals in fish is subject to biological control mechanisms, changing the optic axis of the crystal.10 This motivated us to re-examine the optical properties of individual guanine crystals, using a digital holographic transmission microscope to measure the ratio of the refractive indices along the two planar crystal axes.11
We investigated three species of silvery mid-water fish: Clupea harengus (Atlantic herring), Sardina pilchardus (European sardine) and Sprattus sprattus (European sprat). In all these species we discovered that there are two populations of guanine crystals present that are morphologically identical but have different optical properties. We classified these as Type 1 and Type 2 crystals, which have planar refractive index ratios of ∼1.025 and ∼1.250, respectively (see Figure 1). The measurements for Type 1 crystals imply that the low refractive index value of 1.46 is oriented parallel to the direction of stacking of the multilayer, while the measurements for Type 2 crystals imply that the low refractive index value is orientated in the plane of the multilayer.
To optically model the reflectivity and polarization of the guanine-cytoplasm multilayer structure, we used the 4×4 matrix method.12 This is a formalism that naturally incorporates the birefringence of the crystals and enabled us to perform a comparative analysis with reflectance spectrophotometry measurements. We found that multilayer structures that contain a mixture of the two different crystal types can well describe the experimentally observed angular dependence of polarization. A parametric fit to data from C. harengus is shown in Figure 2. This Figure also illustrates that structures with only Type 1 crystals fully polarize light at Brewster's angle, while structures with only Type 2 crystals do not well represent the experimental data.
The biological mirrors in fish skin typically have ∼30–50 crystals in the multilayer which produces maximum percentage polarization values of ∼25–35% at visible wavelengths. However, by increasing the number of layers, true non-polarizing reflection can result. This effect occurs due to the vastly different (∼30–67°) interfacial Brewster's angles of the crystals in the structure. Overall, the incident angle of light matters little. Both polarization components are always reflected from some of the layers. Unlike existing non-polarizing mirrors, a biomimetic design based on this mechanism would permit the environmental media and low-index layers to be made from the same material. This could provide an advantage in applications where the thermal and mechanical properties of the reflector benefit from being constructed with the same material externally and within the structure.
The polarization-insensitive mechanism in the skin of fish enables them to achieve high reflectivity over all angles of incidence, so it provides better camouflage in the underwater light field than a polarizing mirror would. Many aquatic animals, such as squid, cuttlefish, and mantis shrimp, are sensitive to the polarization of light and have also evolved reflective structures that control the polarization of light.13 Our Ecology of Vision research group at the University of Bristol, UK, is continuing to study the optics of these structures with a view both to understanding their role as evolutionary adaptations and exploring their optical novelty for bio-inspired devices.
The authors acknowledge support from the UK Biotechnology and Biological Sciences Research Council (NWR, grant BB/G022917/1), the UK Engineering and Physical Sciences Research Council (TMJ, grant EP/E501214/1) and the Air Force Office of Scientific Research (NWR, grant FA-9550-09-1-0149).