This material describes methods to concentrate diffuse light through the use of refraction alone and refraction combined with curvature. It is presented for review and consideration.
The most notable conclusion of this work is this: if it is possible to concentrate diffuse light, then it is possible to create a perpetual thermal gradient, or hotspot. This would exploit a loophole in the laws of thermodynamics through the process of energy borrowing, in which a static thermal gradient would form as the surroundings cool until equilibrium is achieved, with no net change in the energy of the entire system. An infrared diffuse-light concentrator would simply gather the energy which is continuously radiated by all matter in the form of blackbody radiation. In other words, to concentrate diffuse blackbody radiation would be to harvest the continuous, eternal, feeble output of individual atoms. The energy would then return to the individual atoms as it dissipates from the hotspot, thus creating a perpetual loop within a closed system. This hotspot could be used to drive a common heat-engine. The implications for energy and the environment are obvious.
The second conclusion resulting from the work described in the following material was this observation about transparent objects with optically smooth surfaces:
A sphere, which is circular in 3 dimensions, concentrates light towards a point (the center of the sphere), which has no dimension.
A cylinder, which is circular in 2 dimensions, concentrates light towards a line (the axis of the cylinder), which has one dimension.
Following this progression, one might conclude the following:
A plane is circular in 1 dimension, and concentrates light towards a plane, which has two dimensions.
Frankly, this conclusion doesn’t make much sense to me, except for the 1+2=3 part. Maybe it is possible for something to be circular in 1 dimension. Theories such as the various string theories and Richard C. Hoagland's theory of hyperdimensional physics (HDP explained) suggest the existence of extra dimensions. Perhaps a plane can be circular in 1 dimension according to those theories. If so, taking the progression further, what would be circular in 0 dimensions and concentrate (or, in this case, diffuse?) light in 3 dimensions? A point? Or following the progression in the upper direction, can something be circular in 4 dimensions? If so, will it concentrate light towards something that has -1 dimension? 4+(-1)=3. While we're on the subject, does anyone know exactly why refraction occurs as it does? Perhaps it has something to do with this relationship between photons, curves and dimensions. Read on and see if you can make sense of this.
Prototype concentrators have been constructed using materials transparent to visible light and IR light. Some functioned as expected, although the results in some cases were ambiguous, possibly due to inadequate facilities. Detailed descriptions follow. Much experimentation remains to be done. This material was first published on the web on 4-May-1999. It was updated on the following dates: 3-May-2000, 17-November-2003, April-2006, 14-March-2007, and 27-March-2007. Permission is granted to anyone wishing to reproduce any or all of the following material as long as the source is cited.
Incidentally, donations are gratefully accepted. A mono-crystalline KCl prototype costing approximately 10k US$ will be made when I can afford to buy it. It should produce a perpetual hotspot slightly above room temperature (1 degree Celsius?) through the process of energy borrowing in which the surrounding room cools imperceptibly and remains at the lower temperature as the hotspot remains warm. This, as we know, scoffs in the general direction of the laws of thermodynamics.
To concentrate diffuse light using flat windows, we utilize the phenomenon which occurs on the inside (the side of higher optical density) of a smooth transparent surface: sometimes the surface is a window and sometimes it is a mirror, depending on the angle at which outbound light strikes the surface. If outbound light from inside the region of higher optical density strikes the surface at an angle near 90 degrees of incidence, it passes through the surface and exits from the region of higher optical density. If the outbound light strikes the surface a glancing blow (close to parallel with the surface) it is reflected by the surface back into the region of higher optical density. Sometimes the surface is a window, sometimes it is a mirror for outbound light. The critical angle at which the surface changes from window to mirror is determined by the ratio of the different densities on each side of the surface.
Meanwhile, on the flip side of the surface, or the outside, the situation is entirely different. There is much less reflection. For a typical glass window 96% of the inbound light which strikes it passes through the surface into the region of higher density. The surface is far more likely to act as a window for inbound light than for outbound light.
The net result of a smooth, transparent surface is the concentration of about 96% of the inbound light into a tighter cone which flares outward into the region of greater density and the dilution of the fraction of outbound light that manages to escape the boundary (typically around 55% to 75% depending on the difference in optical density at the boundary) into a hemispherical fan radiating out into the region of lighter density. Light which has entered a denser medium is concentrated, or brighter. The trick is to make use of the concentrated light. This brings us to boundary refraction differential.
In a transparent medium with boundaries possessing different refraction characteristics there will be a greater probability of transmission across one of the boundaries.
A sheet of glass with a diffusing "opal" coating on one side is an example of a boundary-pair with a refraction differential. The smooth boundary between glass and air exhibits the index of refraction of the glass, approximately 1.5. The opposite boundary between clear glass and diffusing opal glass exhibits an effective index of refraction of 1.0 because any light entering the clear glass from the diffusing glass is scattered equally in all directions.
Approximately 96% of inbound light which strikes the clear boundary enters the glass (with 4% reflected) whereas only 50% of inbound light which strikes the opal boundary enters the glass (assuming that the opal glass scatters light with equal probability in all directions). Outbound light from inside the glass has a 50% chance of exiting via the opal boundary whereas it has less than a 50% chance of exiting via the clear boundary because of total internal reflection.
Thus, the opal boundary reflects more external light and transmits more internal light than does the clear boundary. Consequently, a piece of diffusing glass appears brighter on the opal side than on the clear side because of the imbalance. More light flows from the clear side to the opal side.
When constructing the prototype it was necessary to abrade the surface of the opal coating because it had been polished smooth which had the effect of creating a second clear boundary. After the polished surface had been removed from the opal coating the imbalance was apparent to the unaided eye. The rough opal surface was obviously brighter than the smooth glass surface under similar lighting.
The difference is more pronounced when viewed from an angle because the effects of refraction are more significant at higher angles. Furthermore, it is apparent that an anti-reflective coating on the smooth glass surface would contribute to an even greater imbalance (unless anti-reflective coatings function equally in both directions, a detail which is elusive and remains to be researched).
It is possible to create a measurable temperature differential using material which is transparent to room-temperature black-body infrared radiation. Two functioning prototypes have been constructed, one of sodium chloride (NaCl) and one of silicon (Si).
The NaCl prototype consisted of six monocrystalline disks each 80 mm in diameter by 10 mm thick, optically polished on one side and ground rough on the other. When placed in a stack each separated by 20 mm, polished-side down and all wrapped in a cylinder of paper, the disks produced a -0.2 to -0.3 degree C static temperature differential at the base of the stack with respect to the ambient temperature 50 mm adjacent to the stack. The differential remained as long as the prototype was assembled. The ambient black-body infrared radiation entered the polished surface easily but was partially reflected by the rough surface. Once inside the crystal the radiation had approximately equal probabilities of reflection off of both surfaces because of the total internal reflection of the polished side. It is possible that much of the radiation escaped around the circumference of each disk. The paper wrapping served as a sacrificial surface losing radiation to the smooth surface of the crystals which caused the paper to cool slightly. The air which was in contact with the paper cooled in turn and promptly cascaded downward and was detected by the sensor at the base of the stack.
The Si prototype consisted of 50 monocrystalline disks each 4 inches in diameter by 0.0188 inches thick, optically polished on one side and ground rough on the other. The rough side was then coated with a linseed-oil-based paint which is opaque to infrared light. When placed in a stack each separated by a paper o-ring spacer, polished-side up and wrapped in insulation, the disks produced a +0.1 to +0.2 degree C static temperature differential at both the base and the top of the stack with respect to readings taken at the base and the top of a control stack of 50 uncoated disks placed 1 inch to the side of the prototype. When the positions of the stacks were swapped, the sensors which had been cooler became warmer and vice-versa. When the positions of the stacks were maintained while the sensors were swapped, again the sensors which had been cooler became warmer and vice-versa. The ambient IR radiation entered the polished side, was absorbed by the opaque coating, and when re-radiated by the opaque coating had a high probability of being reflected back to the opaque coating by the total internal reflection of the polished side. Consequently, the temperature increased until the impeded rate of outgoing radiation reached equilibrium with the unimpeded rate of incoming radiation.
A particularly intriguing possibility is a sheet of ordinary glass bonded to a sheet of ordinary table salt. If the technical problems could be surmounted (sodium chloride is extremely brittle and may not bond to glass) the resulting sandwich would have excellent characteristics. Visible light would pass directly through both layers, but IR light would only pass through the salt. IR light would be absorbed and re-emitted by the glass which would have the effect of scattering the IR light as did the opal layer in the previous example. The sandwich would function as a boundary-pair with a refraction differential across the salt. The sandwich would look like a normal window but the glass would radiate heat and the salt would absorb heat.
The next approach to the concentration of diffuse light is the differential lens which utilizes curvature to increase the effects of refraction. Given equal radiant intensities of ambient light and the surface of a target, a differential lens will create a spontaneous net flow of light (a flow differential) towards the target. The target typically has a smaller area than does the lens which increases the efficiency of a differential lens when compared to a flat refraction differential concentrator of equal area. Some designs utilize refraction differential, some don't.
The objective of a differential lens is to converge parallel light from the most possible directions onto the smallest possible target. The optimum shape for a lens to concentrate light from many directions is circular and the optimum position for the target in a simple differential lens is at the radial center of the lens. A target placed in the center of a circular lens receives concentrated light from all directions. If the target is moved away from center it rapidly loses a significant portion of magnified directions which will only be beneficial if the conical window of incoming radiation is narrow. These designs can be implemented in two or three dimensions (cylindrical or spherical).
The optimum size of the target is that size which causes the target to appear to just fill the lens. This depends on the refraction of the lens medium. For common glass, the magnification at the center of a circular lens is approximately two to one. Thus, the target size for glass would be 1/2 the diameter of the lens. A target may be opaque or transparent.
A hollow cylinder with an internal diameter half that of the outside diameter is a simple example of a differential lens. Transparent material such as sodium chloride with an index of refraction of 1.5 will magnify the hollow center target of the cylinder. The target will appear to have approximately the same diameter as the lens. The surface of the target must be treated to allow the incoming light to cross the boundary between the medium and the air (in other words, to prevent total internal reflection). For example it could be made rough or it could be coated with an opaque material of sufficient density to absorb light even at oblique angles.
In this example the target will receive incoming IR radiation with greater intensity than ambient because of the magnification. However, it will radiate IR light at the normal rate for its temperature. An IR-sensitive camera viewing the target through the lens would perceive the target to be cooler than it actually is (specifically, the center will appear true and the apparent temperature will decrease toward the edges). Consequently, because of the increased rate of absorption the target will increase in temperature until the rate of emission has increased to compensate for the rate of absorption. At this point a static condition will exist in which the core is warmer than the surroundings.
A visible-light prototype for this method was constructed with a 6" diameter sphere containing a darkened temperature sensor placed at the center of the sphere. Because of the magnification, the sensor appeared to be approximately twice its size in all three dimensions. This implies a surface area four times greater than true. As a result, the sensor was highly sensitive to visible light. Even dim light in the room would immediately cause the temperature to climb. Only in complete darkness did the core temperature stabilize at room temperature.
The sphere creates some interesting optical illusions. For example, the tiny sensor had been placed in a short pipe for added surface area and because of the distortion caused by the spherical lens it is possible to look into both ends of the pipe simultaneously from any direction normal to the axis of the pipe. The ends appear to bend and follow the viewer around the room.
The sensitivity of the sensor to visible light was amplified by the greenhouse effect of the material of the sphere. Visible light passed through to the sensor but IR light could not radiate out because the sphere is opaque to IR radiation.
An infrared prototype was constructed using monocrystalline NaCl in the shape of a cylinder 80 mm in diameter by 60 mm in length with a hollow center approx. 40 mm in diameter. The hollow center was coated with a black enamel paint. There was no detectable change in the temperature of the core. If the lens was functioning as expected the heat may have been dissipated by conduction through the matrix of the NaCl crystal. Furthermore, the enamel paint may not have had sufficient density to absorb incoming IR light efficiently.
It may be necessary to compound the effect with multiple concentric rings in order to detect a temperature differential. The most efficient use of material may be multiple, wafer-thin, concentric rings with surface refraction differentials with respect to inner and outer surfaces.
A hemispheric IR lens with a flat target or with a hollow hemispheric target would absorb light from the curved side and radiate it towards the flat side. This has greater efficiency than does a flat boundary-pair design. This design could be miniaturized, mass produced and incorporated into cloth which would then actively contribute to heating or cooling. Some IR materials have higher refraction indices than does sodium chloride (such as 4.0 for germanium) which would allow for smaller targets and greater efficiency. Again, the target must be treated to prevent total internal reflection.
This "thumbtack" design is a variation on the previous hemispheric lenses. The target in this case is transparent which facilitates applications for visible light. Multiple miniature lenses arranged in a honeycomb pattern with the pointed conical targets projecting through holes cut in an opaque sheet would create a differential window. More light would enter the hemisphere than the cone.
This approach to the concentration of diffuse light does not require refraction differential. It applies standard principals utilized in conventional lens design.
The ultimate differential lens would be a theoretically perfect "universal" or multidirectional lens which would concentrate all light from all directions onto a single point. A multidirectional lens could function as a motionless solar tracker. Because of inherent limitations the following design of an imperfect universal lens cannot approach the efficiency of a perfect lens. Nonetheless it is more efficient than the previous methods and has the advantage of de-scattering the light, thus allowing the use of more familiar and mature lens technology. The target is not positioned in the center of the circular lens.
This particular design of a universal lens consists of multiple stages of multiple lenses. In other designs some components may be integrated to simplify the design but the fundamental steps remain the same. The three essential steps are 1) convergence of parallel light by a primary stage with high rotational symmetry, 2) normalization of the output of the primary along its focal arc and 3) redirection of the resulting concentrated light.
A non-integrated design for a universal lens requires at least 5 stages:
This design presents simple challenges such as the spherical aberration that is typical of circular lenses or the narrow 90º conical absorption window caused by the partial arc of the secondary. Even still, it is a simple matter to construct a lens that exceeds the efficiency of the simpler radial-center designs.
A crude prototype universal lens has been constructed with a 101.6 mm diameter acrylic sphere primary (73.3 mm focal length), 1 mm diameter secondaries (0.6 mm fl) and a 50.8 mm diameter fresnel tertiary/quaternary (33 mm fl). As expected, the spherical aberration is apparent. Nonetheless, a narrow test beam of laser light passing once through an arc of 40º is redirected by the lens such that it passes over the target in a rapid sweeping manner 50 times. The sweeping path could easily be shortened and the frequency increased by trimming the secondaries to fit more closely which would make the output more stationary and thus improve efficiency.
Experienced lens manufacturers could easily compensate for many of the simple challenges presented by this design. A properly constructed universal lens will illuminate the target with more intensity than ambient light. It should be easily detectable to the unaided eye. This type of lens is well-suited for coupling to fiber optics for use as one-way windows.
The primary stage could achieve a high rate of convergence if constructed of a material with a high index of refraction such as germanium and silicon or if constructed with a radial density gradient as described later. A high rate of convergence permits integrating the primary and the secondary while reducing the radius of the secondary. This creates a compact design with more room for tertiary/quaternary redirection within the width of the primary which would facilitate placing multiple lenses side by side. In this design the shape of the tiny secondaries would phase from half-moon at the equator to full moon at the south pole to match the profile of the primary. This design is potentially the most efficient of all with a 180º absorption window.
The secondary stage could be constructed of a solid arc of material with a
higher optical density than the primary. Placed before the focal arc of the
primary, the secondary would diverge the light which had been converged by the
front face of the primary. The output of the secondary would not be parallel
but it would fall within a narrower cone than the input light and it would be
intensified with respect to the input light. This design requires specific
relationships between the density of the primary, the density of the secondary,
and the thickness of the secondary.
Spherical aberration in the primary lens could be reduced by incorporating a
radial density gradient into the material of the lens with the highest density
at the center and the lowest density at the edge. A seamless gradient would be
ideal although distinct layers of graduated density may be easier to construct
and will still decrease the aberration.
Concentration of diffuse light is desirable for several reasons. A concentrator could serve as a motionless solar tracker, thereby increasing the effectiveness of solar power. Concentrators coupled to optical fiber could function as one-way windows to allow light into rooms through small apertures. Underground greenhouses utilizing natural light would be possible.
An infrared (IR) diffuse-light concentrator would create a spontaneous flow of heat from one side of the concentrator to the other. For example, an IR concentrator placed in the wall of a common picnic cooler would produce a static hot or cold condition inside the cooler. Clothing containing IR concentrators would heat or cool spontaneously.
This is possible because of blackbody radiation. At room temperature all matter radiates infrared light (heat) at an intensity on the order of 10 to 100 watts/m². If our eyes were sensitive to infrared light all objects would appear to be embers glowing like those at the base of a fire. We are bathed in infrared light. A diffuse-light concentrator would act as a check-valve through which light would flow in one direction with greater intensity than in the other direction.
Atoms produce blackbody radiation. To utilize blackbody radiation is to utilize power produced by individual atoms. Hypothetically, a diffuse-light concentrator could concentrate this power which could then be used to drive a heat engine. This appears to violate certain laws of thermodynamics, but there is a loophole. The concentrator would not create energy out of thin air, but it would gather IR energy passing through thin air. As heat increased at the concentrator it would decrease in the surrounding area resulting in no net change in the entire system. It would translate power from the atomic scale to power at a macro scale by combining the effects of the multitudes of individual atoms.
Perpetual motion on a scale between planetary and atomic is obstructed by the close proximity of matter which constantly collides and dissipates force vectors. Concentration of blackbody radiation is one way to coordinate the actions of individual atoms without dissipating the concentrated power through collisions.
If the process of diffuse-light concentration proves to be practical, some benefits may be available within two or three years. There will probably be four categories of products: heating/cooling components for climate control panels and clothing, one-way windows with fiber optics for illumination, heat engines for electrical power generation, and heat engines for transportation. Climate control and illumination may require less research and development than will heat engines. This would allow for the earliest introduction into the market of panels, clothing and windows. Because of the low power density of blackbody radiation all products will require large surface areas which, with respect to design time, favors climate control, illumination, and stationary power plants over transportable heat engines. Heat engines in automobiles, if practical, may not be ubiquitous for as many as 15 or 20 years because of R & D necessities.
Finally, should the process of diffuse-light concentration prove to be practical it is likely that there will be subsequent discoveries which further demonstrate the need to refine the current models of thermodynamics and physics. This may be the tip of the iceberg.
Ted Neville can be reached at tedneville@yahoo.com