Mp. Rowe et al., GRADED-INDEX MODEL OF A FISH DOUBLE CONE EXHIBITS DIFFERENTIAL POLARIZATION SENSITIVITY, Journal of the Optical Society of America. A, Optics, image science,and vision., 11(1), 1994, pp. 55-70
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.