by Gerald Huth on February 12, 2011

In the last comment I noted an apparent similarity in the seemingly octagonal symmetry of solid state nano-pillars grown on silicon by a UC-Berkeley group with the octagonal motif seen in the biological retina of the eye. I think potentially important is their finding of  laser behavior in the nano-pillars that they have grown. I will remind the reader that perfect octagonal symmetry * is present on the retina of the eye at 7-8 degrees of eccentricity where statistically the density of rods is first sufficient to completely surround each of the diminishing number of cones. The following figure that illustrates this is taken from Plate 6 of  Pirenne’s VISION AND THE EYE  (Chapman and Hall, Ltd., 1967).

* As I have previously noted, these types of microscope drawings or electron micrographs represent views of non-living sections of tissue and thus present  necessarily distorted views deriving from excised, sliced, frozen, microtomed, etc. tissue samples.  Nano-antennas, however,  function in the exquisitely  fine spatial order of sub-micron (<10-6 meters) space. One must therefore be very careful in viewing these types of figures. In this case, with the ratio of dimensions of cones and rods approximating 1.8:1,  an octagonal symmetry must occur at this point where rods completely surround cones.

This proclivity for formation of complete octagonal symmetry deriving as it does from an overall statistical distribution of receptors has always seemed strange to me and must ultimately be explained.

In the nano-antenna explanation of light interaction, these individual octagonal sites uniquely provide the  geometrical definition of the precise middle of the visible band, i.e., 550 nanometers. The density of these sites peaks at a retinal eccentricity of 7-8 degrees forming  a radial band surrounding the central fovea. I have noted that this band represents the wavelength “fulcrum” * that Edwin Land  from his color vison experiments predicted must be present and that this evidently explains the phenomenon of the color constancy of vision. Biology makes use of spatial geometry as a wavelength reference – there is no need for an imagined ‘spectrometric’ function! * “…we have learned that the eye must have a fantastic mechanism for finding a balance point within a band of wavelengths”…Edwin Land It should be clear to the reader that this radial band extending from the edge of the fovea to ~20 degrees (peaking at 7-8 degrees) consists of  nano-antenna  light detection sites all of which have the same narrow wavelength response.  This is NOT the curve of spectral response that is seen in every text on the eye. Rather, this is the result of a geometrically determined constant spatial dimension. In antenna terminology it represents a narrowly tuned  “high Q” situation. This  is as far as I had proposed. The Berkeley result, however, introduces an additional (and exciting!) possibility . A finding that these nano-antenna sites harbor laser excitation would mean the presence of a further and fundamental wavelength narrowing beyond the high-Q description along with the implications of laser directionality at each site. There are both temporal and spatial considerations here. First, one must  keep in mind that the basic nano-antenna light interaction process with the receptor outer segment structure occurs in the femtosecond  (10-15 sec.) time domain (the retinal isomerization ‘signal producing’ event has long been known to occur in this time frame). This is in essence the “residence time” for light to interact with this micron length structure and one must consider only processes that occur in that time domain. The  Berkeley group proposes that helically propagating optical cavity modes (essentially a rotation of the light wave) underlie the laser emission that they report. They claim that this occurs within the 300 nanometer dimension of a single nano-pillar (my thoughts on this below).  It is the possibility of a similar rotational motion occurring in the biological nano-antenna structures of the retina that interest me. I will simply note that such a reflective helical motion in the micron length of a nano-pillar would have to occur in the very fast (femtosecond) time domain as discussed above. Spatially, I question that this helical reflection is occurring within the 300 nanometer dimension of  a single pillar  as the authors believe, i.e., within the near field of light wavelength. It seems to me that  such a finding would be at  issue with recent results of Mazur’s group at Harvard  (see the reference to this work in previous comment) where when a light guide (or cavity) is reduced to this dimension, light, via an evanescent wave phenomenon, travels outside of the light guide.  Further, the Mazur work shows that as the diameter is reduced more light energy flows around the body of the guide itself. What caught my attention initially in reading the news release of the Berkeley result (SCIENCE NEWS  Engineers Grow Nanolasers on Silicon, Pave Way for on-Chip Photonics ) was the presence of  an octagonal ‘surround’ or aura  of what I thought at that point was the actual laser emission. (it turned out in a subsequent reading of their paper that this figure was a simulation).

However, in the figure itself, and in their following discussion, they seemingly want to visualize this emission as hexagonal although there are eight distinct elements present – and the surrounding octagonal aura. I might hazard a guess that the outer (yellow colored) sources of emission pertain to surrounding cells….but…? My specific question about the Berkeley result would be their proposal that  the source of  laser emission is within a single  300 nm nano-pillar.I certainly stand to be corrected but this seems to present a dilemma relative to the above noted experimental results of the Mazur group.

In the Berkeley experiments the light beam used to excite laser action is, as they note, of  approximately one micron in diameter. This area could encompass the excitation of  many nano-pillars and could support the teaching of the retina that light interaction occurs with nano-antenna   groupings of nano-pillars. It is difficult to tell from the Berkeley paper whether any spatial order of silicon nano-pillars exist in their growth method that wold support emission from nano-antenna groupings. This may be so, however, considering the single crystal nature of the underlying silicon growth substrate.  But…?

An additional dilemma – the “geometric nano-antenna rules” taught by light interaction with the biological retina would indicate that single wavelength (laser) emission should be the product of a grouping of nano-antennas all of the same diameter – in other words, an hexagonal motif.  ???  An octagonal motif  would mean that two discrete diameters of nano-antennas would be present ..and that the ratio of their diameters would be  approximately 2:1. This is not apparent or even likely in the silicon nano-pillar structure. Why then the indication of the octagonal motif?

We can now begin to wander around in the area of “intense speculation” – speculation uniquely made possible by the nano-antenna explanation for light interaction and the important Berkeley laser result. The laser emission that they propose essentially involves a helical ‘internal reflection’ around, or within, the hexagonal cavity that they visualize. Whether this reflection exists within the quantum realm of the atomic structure of a single pillar as they believe or within a larger spatial grouping or motif of pillars is not important here.  The point to consider is  the possible existence of  some form of  interaction between, in their visualization, hexagonal elements.

There may be reason to believe that a wave-guiding mechanism for such interaction occurs in the biological structure of the retinal motif. I had always assumed that the rhodopsin/retinal complexes contained within individual thylakoid disks of the outer segments diffuse as monomeric units in the fluid membrane structure. A recent finding The G protein-coupled receptor rhodopsin in the native membrane (Dimitrios Fotiadis et al) indicates that the complexes form spatially ordered dimer structures.

In native disk membranes, rhodopsin is a unidirectionally oriented transmembrane glycoprotein”

I would remind the reader again that even these indications of order represent sections of dead tissue and not the living state  where  nano-antenna mechanisms  function!

This order in the biological realm, in turn,  introduces a relevant paper Nanopillars Photonic Crystal Waveguides (D. N. Chigrin et al). The abstract of this paper:

AbstractWe present a novel type of a waveguide, which consists of several rows of periodically placed dielectric cylinders. In such a nanopillars photonic crystal waveguide, light confinement is due to the total internal reflection, while guided modes dispersion is strongly affected by waveguide periodicity. Nanopillars waveguide is multimode, where a number of modes is equal to the number of rows building the waveguide. We perform a detailed study of guided modes properties, focusing on possibilities to tune their frequencies and spectral separation. An approach towards the specific mode excitation is proposed and prospects of nanopillars waveguides application as a laser resonator are discussed”.

Might spatially oriented dimer arrays of rhodopsin complexes within the thylakoid disks of retinal receptors provide the directional connective interaction between individual receptors in the larger hexagonal or octagonal groupings to form a laser emission?

To this point I have considered the reason for the spatial (hexagonal or octagonal) nano-antenna structures might be to accept various angles of polarized light. This seemed to be consistent with behavior of the eye in this regard. The possibility of laser emission opens up many new areas of thought! Further,  the introduction of rotational motion (in the femtosecond time domain) might  lead to an explanation for  the association that I have made  of the  octagonal motif  with  a spatially symmetric  epitrochoidal figure.  As I have noted,  such a symmetric epitrochoid results from a ratio of dimensions of 1.8:1. that corresponds to the ratio of diameters of retinal cone and rod receptors.  Formation of an epitrochoid , however, requires the  rotation  of “something around something”  that I have not been able to imagine in this light interaction. May laser emission provide this answer? I will present again the epitrochoidal figure and its relationship to retinal topography:

GCH Oaji,CA 2.12.11


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