Non-polarizing broadband multilayer reflectors in fish

Abstract

Dielectric multilayer reflectors that are non-polarizing are an important class of optical device and have numerous applications within optical fibres [1], dielectric waveguides [2] and LEDs [3]. Here we report analyses of a biological non-polarizing optical mechanism found in the broadband guanine-cytoplasm "silver" multilayer reflectors of three species of fish. Present in the fish stratum argenteum are two populations of birefringent guanine crystal, each with their optic axes either parallel to the long axis of the crystal or perpendicular to the plane of the crystal. This arrangement neutralizes the polarization of reflection due the different interfacial Brewster's angles of each population. The fish reflective mechanism is distinct from existing non-polarizing mirror designs [4, 5, 6, 7] with the important feature that there is no refractive index contrast between the low index layers in the reflector and the external environment. It is a mechanism that could be readily manufactured and exploited in synthetic optical devices.

Figure 1. Optical reflectivity measurements

a Measurements of the degree of polarization, d(θ), at λ = 600 nm for azimuthal (dorsoventral; red cardinal crosses) and latitudinal angles of illumination (rostrocaudal; blue oblique crosses) from Clupea harengus. The black solid circles and black line represent a positive control and are experimental data and a theoretical curve for a double surface Fresnel reflection (front and back reflection) from a glass microscope slide with refractive index 1.50, in air. b, c Reflection and degree of polarization spectra at (b) 30° and (c) 60°. In (b) and (c) the black solid line is R_σ(λ), the black dashed line is R_π(λ) and the green solid line is d(λ).

Figure 2. Refractive index ratios of guanine crystals

Measurements (mean ± s.d.) of the planar refractive index ratios in Type 1 and Type 2 guanine crystals in Clupea harengus, Sardina pilchardus and Spratus spratus. The multilayers under the scales of C. harengus contained only Type 1 crystals.

Figure 3. Optical structure, modelling and parametric fit to experimental data

a Schematic diagram illustrating the multilayer model used and the two populations of guanine crystals: Type 1 crystals (purple) and Type 2 crystals (orange). The orientation of the principle refractive indices coordinate axes of each crystal layer are indicated. b Simulations of the degree of polarization, d(θ), at different angles of incidence (θ) and at λ = 600 nm for three classes of multilayer model, including a parametric fit to experimental data from Clupea harengus. The black line is for a multilayer of Type 1 crystals (f = 1), the blue line is for isotropic crystals (n_o = n_e = 1.83), the solid red line is a parametric best fit for a mixture of Type 1 and Type 2 crystals with f=0.75, and the red crosses are the mean of the azimuthal and latitudinal data from Fig. 1(a). Our model explained 95% of the variation in the data, assessed by the R² from linear regression. There was no systematic difference between model and data (mean pairwise difference and s.d. 0.0044 ± 0.0132, t = 0.7512, df = 9, p = 0.472). The best fit parameters are N=37 crystal layers in each multilayer structure, with the sampling intervals for guanine and cytoplasm thicknesses [55, 110] nm and [30, 300] nm respectively. c Simulated degree of polarization, d(λ), for the parametric best fit in Fig. 3(b) (solid black line θ = 30° and solid red line θ = 60°), and experimental d(λ) from C. harengus (dashed black line θ = 30° and dashed red line θ = 60°) as in Fig. 1(b) and 1(c).

Figure 4. A biologically inspired mechanism of polarization-neutral reflection

Simulated degree of polarization, d(θ), at different angles of incidence (θ) and λ = 600 nm for N = 20, 40, 200, 400 crystal layers (red, black, blue and green solid lines respectively) and accompanying reflection and polarization spectra at 60° for (a,b) the fish reflective structure and (c,d) a biomimetic design with 2 uniaxial populations of layers with refractive indices given by (1.83, 1.83, 1.33) and (1.33, 1.33, 1.83). N=400 in (b) and N=200 in (c). The black solid line is R_σ(λ), the black dashed line is R_π(λ) and the green solid line is d(λ). In all plots the layer thicknesses are sampled from uniform distributions on the intervals [55, 110] nm for the birefringent layers and [30, 300] nm for the isotropic layers, with f = 0.75 and the (1.83, 1.83, 1.33) layers being defined as Type 1 in the biomimetic design.