Mode interference patterns in retinal receptor outer segments

Abstract

Abstract-Some calculated interference patterns of electromagnetic modes are given for a dielectric waveguide representative for the receptor outer segment. The results are qualitatively in accordance with observations of Enoch.Retinal receptors are lightguiding structures of relatively small dia, in which the energy is guided in patterns called modes (Enoch, 1963). These modes have a definite phasevelocity. However, generally some modes with d&rent phaseveloeities occur inside the receptor outer segment. In this case the modes interfere with a different phase at different levels along the outer segment.For some cases interference patterns of guided modes were calculated. Results qualitatively in aceordante with some observations of Enoch (1963) were obtained. THEORYThe receptor outer segment was approximated by a homogeneous isotropic circular cylindrical dielectric rod (Fig. 1). Apart from guided modes there are unguided modes which are not bound to the receptor. These unguided modes wig not be considered here. The characteristics of the guided modes are determined by the normalized frequency u = (Znpn,/l,,)JG and 8. Here d = 1 -(n:/n:); n, and n2 are the refractive indices of the inside and outside medium respectively, p is the radius of the rod and )LnC is the vacuum wavelength of the incident light. For retinal receptors the parameter S is of the order of @l, therefore the approx results for 6-0 may be used for the field of the modes (Snyder, 1969a). The amplitude with which a mode is excited may be calculated neglecting the reflected light (Snyder, 1969b). In this approximation when the light incident on the outer segment is plane polar&d, plane polarized modes and modecombinations are excited (Wijngaard, 1971). Interference effects can only be obtained when the phasevelocity of the modes is different, therefore the approximation 6 + 0 is not applicable to calculations of the phasevelocity. However, the difference in phasevelocitpbetween the modes of a plane polarized mode-combination is small enough to conserve the plane polarixation when the modes are guided along the outer segment.The author has discussed minor deviations from this result for frog rods (Wijngaard. 1971). The approximate conservance of the plane and the degree of polarization is characteristic for the relatively short fibres of small 6 in the retina. For the much longer fibres of, for example, Snitxer and Osterberg (1961) this may not be the case. These remarks should be considered in the designation of modes to patterns observed in retinal receptor outer segments.To obtain physiologically significant interference patterns the amplitudes of the modes should be calculated from the field incident on the retina. However, even for an incident plane wave this problem is complex owing to the influence of the inner segment. Therefore the field at the entrance of the outer segment was assumed to be a plane wave restricted to the outer segment with the electric field vector perpendicular to the plane of incidence. The propagation vector k of the p...