Although biological cells are mostly transparent, they are phase objects that differ in shape and refractive index. Any image that is projected through layers of randomly oriented cells will normally be distorted by refraction, reflection, and scattering. Counterintuitively, the retina of the vertebrate eye is inverted with respect to its optical function and light must pass through several tissue layers before reaching the light-detecting photoreceptor cells. Here we report on the specific optical properties of glial cells present in the retina, which might contribute to optimize this apparently unfavorable situation. We investigated intact retinal tissue and individual Muller cells, which are radial glial cells spanning the entire retinal thickness. Muller cells have an extended funnel shape, a higher refractive index than their surrounding tissue, and are oriented along the direction of light propagation. Transmission and reflection confocal microscopy of retinal tissue in vitro and in vivo showed that these cells provide a low-scattering passage for light from the retinal surface to the photoreceptor cells. Using a modified dual-beam laser trap we could also demonstrate that individual Muller cells act as optical fibers. Furthermore, their parallel array in the retina is reminiscent of fiberoptic plates used for low-distortion image transfer. Thus, Muller cells seem to mediate the image transfer through the vertebrate retina with minimal distortion and low loss. This finding elucidates a fundamental feature of the inverted retina as an optical system and ascribes a new function to glial cells.

https://www.pnas.org/content/pnas/104/20/8287.full.pdf

Müller cells are living optical fibers in the vertebrate retina

Radial variation of pump and signal intensities in EDFA; accurate prediction by a novel approximation of the fundamental modal field

\n This paper reports simple but accurate analytical expressions of group delay and modal dispersion parameters for single-mode graded index fibers over a wide range of V numbers. The formulation employs power series expression for the fundamental modal field of graded index fiber derived by Chebyshev formalism. Choosing some typical step, parabolic and triangular index fibers as examples in our present study, we use the prescribed formulations to estimate group delay and modal dispersion parameters of those fibers both in presence and absence of Kerr nonlinearity. Iterative technique is applied for prediction of concerned propagation parameters in presence of Kerr nonlinearity. Our results show excellent agreement with the numerical exact ones both in absence and presence of Kerr nonlinearity. The exact results in case of Kerr nonlinearity are obtained using cumbersome finite element method. The execution of our accurate formalism involves little computation and is thus user friendly for technologists and researchers working in the field of nonlinear optical engineering.

Influence of Kerr nonlinearity on group delay and modal dispersion parameters of single-mode graded index fibers: evaluation by a simple but accurate method

In this paper, we approximate the fundamental mode in single mode step and graded index optical fiber by a single parameter Lorentzian function within scalar variational framework. We show that it works in a low V region, a region important for evanescent wave coupling, more accurately in terms of propagation constant in comparison to single parameter Gaussian for linear and nonlinear fibers. Furthermore, we show that the low V variations of normalized propagation constant b ( V ), group delay d ( V ), and waveguide dispersion g ( V ) with V based on Lorentzian approximation match more accurately with the results for linear optical fiber in comparison to Gaussian approximation in the low V region.

Lorentzian approximation of the fundamental mode in single mode linear and nonlinear fiber

Accurate knowledge of spot size, an important criterion in single-mode fiber optics, is obtained by two different optimization techniques, the well-known variational method and Marcuse formulation. The later is more accurate but cannot predict fiber parameters from given spot sizes. In this study, it is shown for the first time to the best of our knowledge that using simultaneously Marcuse relations of fiber spot sizes for single-mode graded index fibers and also variational formulation, we can more accurately and easily determine the fiber parameters for a particular normalized frequency. Then it is shown with typical example of fractional power in the core that in the case of such fibers, this synthesis of these two useful approaches can also more accurately estimate propagation characteristics of practical interest. This equivalence provides an easy and useful connection between two fundamental but disjoint approaches and should find wide use.

A simple and elegant technique connecting Marcuse spot size relations to variational formulations in single-mode fiber characterization

We propose a novel approximation of the fundamental modal field in single-mode graded-index fiber and present a variational analysis to investigate the propagation parameters of practical interest. Employ- ing the formulated fundamental modal field, we prescribe analytical ex- pressions for normalized Petermann I spot size, group delay, and modal dispersion parameter for single-mode graded-index fiber. With the ex- amples of step- and parabolic-index fibers, we show that these param- eters as evaluated by our formalism match excellently with the available exact ones over a wide range of V values. Particularly in the low V region, where the Gaussian approximation is not accurate, our results are found to predict the propagation characteristics accurately. Thus the validity of our formalism is justified. Much less computation is required than with previous methods. The approximation will be useful in the analysis of nonlinear and doped-fiber amplifiers. © 2002 Society of Photo-

Santanu Sanyal

Papers

Accurate prediction of the propagation characteristics of single-mode graded-index fibers by a novel approximation of the fundamental modal field