C. Pask

Spectral sensitivity of dipteran retinula cells

SummaryDipteran rhabdomeres are dielectric waveguides. Using dielectric waveguide theory an expression for the spectral sensitivity of retinula cells is derived. The spectral sensitivity of a retinula cell, S (A), depends strongly on the physical properties of the rhabdomere (diameter and refractive index) in addition to the spectral absorption of the photopigments. By correlating theory with existing experimental results we conclude that:1.The effect of containing photopigment within a rhabdom of small diameter is (a) to shift the visible absorption peak to lower wavelengths and (b) to increase the UV peak absorption relative to the visible peak. The smaller the diameter of the rhabdom the greater the effect (Fig. 8 and 9).2.The theoretical results (Fig. 10) for the spectral sensitivity,S (λ), of fly retinula cells are consistent with the single cell electrophysiology of Autrum and Burkhardt (1961) and Burkhardt (1962). The blue receptor type recorded by single cell electrophysiology is identified with rhabdomere number 7. The blue receptor is different from the green receptor type (rhabdomeres 1–6) because it has a smaller diameter not because of a different photopigment. The enormous measured UV sensitivity of the blue receptor type is due mainly to the waveguide effects caused by the small diameter of rhabdomere 7. Nevertheless, we conclude that in addition to a rhodopsin-like visible photopigment a separate UV photopigment is present in each rhabdomere. The spectral sensitivity of the photopigments consistent with these findings is shown as the dotted line in Fig. 10.3.Rhabdomere 7 acts like a UV colour filter for rhabdomere 8, since it is more distal and has a large UV absorption. Thus the yellow-green receptor type measured by single cell electrophysiology, which has a low UV sensitivity compared with the blue type, may be retinula cell 8.4.Spectral sensitivity curves inferred by optomotor reactions cannot be identified with retinula cells 1–6 in isolation of cells 7 and 8 and vice versa. Micro-spectrophotometric determination ofS (λ) is subject to methodological errors which render its reliability suspect. In the authors opinion, the intracellular recordings of Autrum and Burkhardt (1961) and Burkhardt (1962) represent the correctS (λ) curves for fly retinula cells.

Geometric optics approach to light acceptance and propagation in graded index fibres

The methods of geometric optics are applied to light acceptance and propagation in graded index fibres. The symmetry of the basic ray equations reveals ray path invariants. Rays are classified into bound, tunnelling and refracting rays. The role of source properties in exciting different ray types is analysed. Pulses are considered in terms of absolute widths, r.m.s. widths and complete shape detail. Optimization formulae are obtained. The incorporation of attenuation mechanisms is described and the effects of an absorbing core are analysed in detail.

Failure of geometric optics for analysis of circular optical fibers

In addition to rays that lose energy by undergoing refraction, there is a large class of weakly attenuated rays in circular optical fibers. These leaky rays are incorrectly predicted to be lossless by Fresnel’s laws. Thus, Fresnel’s laws fail for the analysis of long fibers. The significance and properties of leaky rays are discussed. A very simple attenuation coefficient is given, from which the loss of all rays is computed. This attenuation coefficient makes it possible to extend the use of ray tracing and Snell’s laws for analyzing circular optical fibers.

Light-acceptance property of an optical fiber

The amount of light power that is transmitted within a semi-infinite circular optical fiber when it is illuminated obliquely by a coherent beam of light is determined from an electromagnetic-theory analysis. The limit λ→0 is not classical geometric optics, i.e., not that found by tracing all rays along the fiber. Instead, the limit λ→0 corresponds to that of treating all rays as if they were meridional, i.e., as if they cross the fiber axis, ignoring rays skew to the axis. Thus, ray tracing is incorrect for fibers illuminated by coherent light. However, the acceptance property of an optical fiber illuminated by coherent light is very simply found from meridional ray tracing, if the dimensionless quantity 2πρ{n12−n22}1/2/λ is much greater than unity, where ρ is the fiber radius, λ the wavelength of light in vacuum, and n1, n2 the refractive indices of the fiber and its surround, respectively.

Incoherent illumination of an optical fiber

The power of the trapped modes on a semi-infinite optical fiber illuminated by an incoherent source is determined. All possible modes are excited, each with approximately the same power when V → ∞, V=2πρ{n12−n22}1/2/λ, where ρ is the fiber radius, λ the wavelength of light in vacuum, and n1, n2 are the refractive indices of the fiber and its surround, respectively. A ray-optical interpretation is given for the summed power of the modes. For V = ∞, the power corresponds to that found from classical geometric optics, treating all rays as if they are meridional. This result is independent of the degree of coherence of the source. The per cent error of meridional ray optics is 100/V when V is large. The total power within the fiber is the combined power of the trapped modes and the radiation field. In the limit V = ∞, the total power within the fiber at any position z along its axis is that given by classical geometric optics, i.e., that found by tracing all rays, skew and meridional. At the point z = ∞ for arbitrary V, the total power is that due to the trapped modes only.

Light Absorption in the Bee Photoreceptor

Photodetection by the individual rhabdomeres of the worker-bee photoreceptor (rhabdom) is analyzed by use of electromagnetic theory. The analysis takes full account of the rhabdom’s anisotropic absorption properties. We find, by coupled-mode theory, that only certain modes of a lossless symmetric rhabdom are stable on the lossy rhabdom. Furthermore, the fine structure of the rhabdom (a) enhances the detection of certain modes, whereas it discriminates against others, (b) acts as a polarization detection mechanism, and (c) provides information about the direction of incoming light.

Directional change of beams undergoing partial reflection

When a beam of finite width is partially reflected at a planar dielectric interface, there is in general a shift in the reflected beam direction away from that predicted by the simple application of the geometrical optics relfection law. We give a simple derivation of this shift, clarifying the underlying physical mechanism. The Gaussian beam is studied in detail.

Nondestructive index profile measurement of noncircular optical fibre preforms

Abstract We present quantitative results for the effect of noncircularity on a method recently proposed by Chu for the measurement of the refractive index profile of an optical fibre preform. Analytical studies show how Chus method can be applied to elliptical preforms.

Illumination of multimode optical fibresleaky ray analysis

The power transmitted within multimode circular optical fibres illuminated at one end by either coherent or incoherent light is determined. In general, a significant portion of this power is due to the radiation field even kilometres from the source. Thus an analysis in terms of bound modes alone is inadequate and so is geometric optics using Fresnels lawS. Instead, we use a modified form of geometric optics in which the rays are appropriately weighted to account for the leakage (radiation) from the fibre not included by Fresnels laws. Extensive numerical results are given.

Slowly varying optical fibers

The effects of slow variations in radius ρ and core-cladding refractive-index difference Δ along the length of optical fibers are determined by using the ray-path equations. Simple formulas in terms of the averaged properties of ρ and Δ show that, in power-law fibers, pulse dispersion is slightly increased and the magnitude of the induced power loss can be bounded. Results hold for general power-law fibers. Comparison with power-law fibers having exponent variations indicates that changes in profile shape cause larger pulse dispersion but less power loss than do ρ and Δ variations. In arbitrary fibers having the same amount of dopant used to form the profile in every core cross section, variations in ρ and Δ cause no power loss. The relationship between these results and the adiabatic invariant concept is outlined.