GRADED-INDEX MODEL OF A FISH DOUBLE CONE EXHIBITS DIFFERENTIAL POLARIZATION SENSITIVITY

The close apposition of the inner segments of the two cones that combi ne to form a double cone causes the pair of cone inner segments to gui de light as a unitary structure whose transverse sections are roughly elliptical. Electron micrographs of the photoreceptors of a green sunf ish (Lepomis cyanellus) retina provide evidence that the refractive in dex in the ellipsoid region of the inner segments of the double cones is higher in the center than at the perimeter. The hypothesis that the shape and refractive-index gradient could confer differential polariz ation sensitivity on double cones is examined with a two-dimensional w aveguide model of a double-cone inner segment. The model has a dielect ric constant that varies parabolically along the narrowest (x) dimensi on, leading to the index profile: n(x) = n(max)[1 - (x/x(o))(2)](1/2), where n(max) is the peak value of the index and x(o) is a parameter s pecifying the rate at which the index decreases with increasing \x\. A quantity, the polarization contrast, is introduced as a measure of th e differential polarization sensitivity of adjacent receptors in the s quare mosaic of double cones in the sunfish retina. Polarization contr ast is proportional to the relative difference in power absorbed by tw o double cones oriented with their shortest axes orthogonal to each ot her and stimulated by a field of uniform polarization. Polarization co ntrast is computed as a function of wavelength for appropriate values of n(max) and x(o). For normally incident light polarized parallel to one of the two axes of the double cones' cross sections, the polarizat ion contrast is generally between 1% and 5% for wavelengths ranging fr om 550 to 750 nm. Over most of those wavelengths the polarization cont rast of the graded-index-model double cone is approximately five times as large as that of a homogeneous-slab model of the same size and ave rage refractive index. Additional benefits of a graded index, optical isolation of adjacent photoreceptors and antireflection at the photore ceptor entrance, are also discussed.