Abstract:
A solar power plant ( 10 ) capable of generating electricity comprising a light pipe carrying highly concentrated solar light ( 19 ), a hot reservoir ( 24 ), a cold reservoir ( 20 ), and a plurality of large-scale solid-state nano-structured photonic crystals ( 12 ) that are capable of recycling out-of-band photons with transition energies associated with a photovoltaic cell ( 13 ) into photons with in-band energies associated with the same photovoltaic cell ( 13 ) when photon energy is subjected to propagation through a thermal temperature gradient that is held across a suitably nano-structured photonic crystal ( 12 ). The input thermal photons from the hot thermal reservoir ( 24 ) are shifted in energy to the optimal photovoltaic cell energy for electron-hole pair generation by work that is expanded by the heat engine to convert said input photons into phonons and then back to photons again at a new wavelength through a process of phonon rethermalization occurring inside the nano-structured photonic crystal ( 12 ).

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Not Applicable. 
     FEDERALLY SPONSORED RESEARCH 
     Not Applicable 
     SEQUENCE LISTING OR PROGRAM 
     Not Applicable 
     BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     The present invention relates the generation of electricity through a process that converts radiative heat energy into electricity through the use of photovoltaic cells, whereby photons are translated from out-of-band spectral regions of a photovoltaic cell to in-band spectral regions of the photovoltaic cell by means of intermediary phonons located in a nano-structured solid-state heat-engine, which is based on Photonic Crystals that can separate both photons and phonons spatially and energetically and apply the optimal energy photons to a photovoltaic cell to efficiently generate electricity. 
     2. Prior Art 
     Photovoltaic cells, also called solar cells, convert light into electricity by means of an electronic band-gap, which is typically formed as a pn-junction in a properly doped semiconductor such as Gallium Arsenide (GaAs) or Silicon (Si). The pn-junction has a built-in electric potential due to the space-charge depletion zone that is found in the vicinity of the transition from p-type material to n-type material. This electric potential is the cause of a corresponding built-in electric force field that can act on charges in the space-charge depletion zone to from a current in a closed loop electrical circuit that includes the photovoltaic cell. In particular, the process is initiated by an external photon that enters the space-charge depletion zone of the pn-junction and by its proximity causes the creation of an electron-hole pair if the incoming photon at least has the energy associated with the electronic band-gap of the pn-junction. If the photon has less energy than the electronic band-gap it may pass unobstructed through the device and if it has more energy than the electronic band-gap it may give up some of the energy to quanta of lattice vibrations, called phonons, while integer multiples of the electronic band-gap energy are converted into multiple electron-hole pairs. Any energy that is converted into phonons is typically lost as thermal heating of the photovoltaic cell. 
       FIG. 10  shows the Power Spectral Density (PSD)  107  of the sun versus the energy of the individual photons. The shape of the distribution is a strong function of the temperature of the sun and this depends on the fuel being fused and the strength of the gravitational field of the star. Note that energies for photons are always positive but  FIG. 10  also shows negative energies. These negative energies correspond to the bound states of electrons  100  in the valance band  108  of the semi-conductor of the solar photovoltaic cell. As can be seen an electron  100  that is deep in the valance band  108  can be excited from its current state to an excited state  101  in the conduction band  109 . The photon that excites this transition must have energy corresponding to the energy jump  102 . However, the energy  102  is greater than the band gap energy, which lies between the conduction band edge  105  and the valance band edge  106 . As a result phonons may be excited from the conduction band  104  and the valance band  103  with more energy than is needed to create an electron-hole pair. This energy is lost to the heating of the material. Also photons with energies that are smaller than the electronic band gap will not interact with the device and therefore are lost as radiation that passes through the solar cell or is reflected back from the solar cell depending on the particular composition and geometry of the device. Again this is wasted energy. 
     In the prior art most of the incident energy is lost to lattice vibrations and therefore not converted into electricity because the electronic band-gap of the photovoltaic is relatively narrow. This is typical of the traditional single junction solar cell. To improve on the efficiency of the solar cells prior art has been developed that seeks to exploit the use of different electronic band-gaps formed by different embodiments of the pn-junction. Thus multiple electronic band-gap structures have been developed with pn-junctions with different electronic band-gaps. These are pn-junctions stacked vertically or laterally. For example it has been reported at a National Center for Photovoltaic (NCPV) conference in Denver, Colo. in Apr. 16-19, 2000 that triple vertical junction GaInP2/Ga/As/Ge concentrator cells developed by the National Renewable Energy Lab (NREL) and Spectrolab have achieved 32.2% efficiency at 47 suns and 29% efficiency at 300 suns with an Air Mass of 1.5 at 25 degrees Celsius. As the number of layers of a stacked photovoltaic device increases the mutual interference between layers, caused by lattice mismatches, increases causing increased light absorption and reduced performance of the solar cell. 
     In an alternative embodiment consisting of the lateral placement of different electronic band-gap photovoltaics there have been at least two approaches taken. The present author was part of the studies at NASA Jet Propulsion Laboratory (JPL) in the late 1990&#39;s that were focused on Solar Space Power (SSP). One of the efforts being developed at the time was a “Rainbow” approach that used optical components like prisms to spread out solar radiation into its component colors and then develop photovoltaics that were optimized to the specific color (energy) of the light. This proved to be difficult due to the large amount of hardware required, especially for spaceflight hardware, which is designed to be low mass. 
     Another prior art approach is given by U.S. Pat. No. 6,689,949, which is shown in prior art  FIG. 11  and describes a light containment system that has multiple single junction photovoltaic cells that are coated with reflective type filters. Each of the photovoltaic cells shown in this prior art have different band gaps. The generation of phonons  103  and  104 , as shown in  FIG. 10 , is avoided in  FIG. 11  by using multiple reflect type filters that are on the outer surface of the photovoltaic cells in order to reject out-of-band photons. The reflected and out-of-band radiation are recycled by making multiple reflections in the containment sphere. These reflections are essentially stochastic in nature and bounce around the inside of the sphere until the photon falls on a photovoltaic cell that is matched to its energy for conversion to electricity—or is parasitically absorbed. This approach still requires that multiple designs be developed for the photovoltaic cell. Additionally, the overall efficiency will still greatly depend on the number of bounces that that input photon uses before makes. Large numbers of bounces greatly increase the probability of absorption and dissipation as heat. Finally, and most importantly this prior art is unable to exploit temperature differences to generate electricity. The prior art of  FIG. 11  is restricted to light only. This precludes applications such as turning the heat energy generated by a nuclear reactor directly to electricity. 
     These disadvantages are overcome in the present invention. 
     OBJECTS AND ADVANTAGES 
     In accordance with the present invention, a photovoltatic converter (PVC) module is provided which can operate at a concentration range of 500-1000 suns or more and provide a scalable power output that may range between several kiloWatts to power levels on the order of 1 MegaWatt or more depending on the physical size of the embodiment used. The PVC must be run between a hot source and a cold source, such as—but not limited to—cold sea water, or snow pack, or deep space, or altitude and may draw its energy from one or more sources such as light from the sun, or the enthalpy of reaction from a combustion process, geothermal process, or from the heat generated by a nuclear reactor during a fission or fusion process. The disclosed PVC module is an enabling technology to reach very high solar-to-electric conversion efficiencies. More generally, the disclosed PVC is an enabling technology to reach very high solid-state heat-engine conversion efficiencies. Connecting a plurality of such modules together in a power plant permits the power plant to generate many hundreds of MegaWatts of electric power. Additionally, because of the extreme temperature present inside the PVC it is possible to have secondary processes present that take advantage of the environment. The two most notable examples of this are 1) the super heating of sea water for reducing the electricity required from the power plant to electrolyze the water and 2) the disassociation of Methane Hydrates by a process of pyrolysis into pure water, hydrogen, and pure carbon. Other secondary process are also possible. 
     The PVC module comprises:
         (a) an outer heat reservoir housing at one temperature polarity and containing an internal cavity of any closed shape inside said outer heat reservoir housing, the internal cavity having a unique surface area, and another surface either within said internal cavity or as a separate part of the outer heat reservoir housing that takes the opposite polarity temperature;   (b) a light absorber that captures an intense flux of solar photons and converts them into an intense flux of phonons and thus becomes the hot polarity thermal reservoir;   (c) at least one nano-structured photonic crystal that is fixed between a hot thermal reservoir and a cold thermal reservoir that controls energy flow of both photons and phonons in both energy and spatial direction so as to recycle out-of-band photons into in-band photons through the use of intermediary phonons, which spectrally shifts the unusable light energy into the usable band through the expenditure of thermal energy;   (d) a plurality of solar cells optimized for converting the narrow-band light that is output from said nano-structured photonic crystal structures into electricity.       

     Accordingly, several objects and advantages of the present invention are:
         1. to provide a solid-state electricity generator that can take concentrated sources of photons and convert them into electricity;   2. to provide a solid-state electricity generator that can take concentrated sources of phonons and convert them into electricity;   3. to provide a solid-state electric generator that has no large voids and therefore can withstand great pressures in the depths of the oceans without being crushed;   4. to provide a solid-state electric generator that can operate in deep space;   5. to provide a Photonic Crystal Structure that can separate photons by direction of propagation;   6. to provide a Photonic Crystal Structure that can separate photons by energy (color);   7. to provide a Photonic Crystal Structure that can translate photons of one energy to another energy by means of phonons in a heat engine;   8. to provide a means to rethermalize out-of-band light energy into in-band light energy for a photovoltaic cell;   9. to provide a means to only use single junction solar cells to capture most of the sun&#39;s radiation instead of multi junction multiple band solar cells;   10. to provide a means to generate electricity from light or alternately from other intense heat sources at the same time;       

     Further objects and advantages will become apparent from a consideration of the ensuing description and drawings in which like reference designations represent like features throughout the FIGURES. 
     SUMMARY 
     In accordance with the invention, an electric generator comprises a hot reservoir, a cold reservoir, and a solid-state nano-structured photonic crystal capable of recycling out-of-band photons into in-band photons of the photovoltaic cell when the photons are subjected to propagation through a thermal temperature gradient that is held across the photonic crystal while the thermal photons are still inside of the nano-structured Photonic Crystal. 
    
    
     
       DRAWINGS 
       Figures 
       The drawings referred to in this description should be understood as not being drawn to scale except if specifically noted. 
         FIG. 1  depicts a solid-state heat engine that is based on photonic crystal structures, which are heated by an input flux of intense solar radiation; 
         FIG. 2  depicts a different view of the photonic crystal heat engine as well as the core light absorber; 
         FIG. 3A  is a close up of a typical photonic crystal section that is used in the heat engine; 
         FIG. 3B  is another close up view of a typical photonic crystal section that is used in the heat engine; 
         FIG. 4  is a top plan view, in schematic, depicting the principles of voltage matching of photo-voltaic cells in different positions in the heat engine; 
         FIG. 5A  shows the flow of photon and phonon energy schematically in a nano-structured Photonic Crystal such that narrow-band photons emerge at right angles to the direction of conductive heat flow and are absorbed by a photovoltaic cell. 
         FIG. 5B  shows the flow of photon and phonon energy schematically in a nano-structured Photonic Crystal such that narrow-band photons emerge parallel to the direction of conductive heat flow and are absorbed by a photovoltaic cell; 
         FIG. 6A  shows an s-orbital of an atom transforming into a p-orbital of the atom in a process of stimulated absorption within the host material that makes up the nano-structured photonic crystal; 
         FIG. 6B  shows a p-orbital of an atom transforming into an s-orbital of the atom in a process of stimulated emission within the host material that makes up the nano-structured photonic crystal; 
         FIG. 6C  shows a p-orbital of an atom transforming into an s-orbital of the atom in a process of spontaneous emission within the host material that makes up the nano-structured photonic crystal; 
         FIG. 6D  shows an s-orbital of an atom transforming into a p-orbital of the atom in a process of spontaneous absorption within the host material that makes up the nano-structured photonic crystal, this process is shown for comparison purposes and has exceedingly small probability of occupance; 
         FIG. 7A  shows how a single stone thrown into a pond, or equivalently a point source for electromagnetic wave propagating in two dimensions, can manifest wave behavior; 
         FIG. 7B  shows how two stones thrown into a pond simultaneously, or equivalently two electromagnetic point disturbances, can interfere with each other to produce a null wave pattern along a particular direction; 
         FIG. 8A  shows a representative photonic crystal structure with its corresponding first Brillioun zone, additional principal crystallographic cut planes, and a light cone that is used to define the spectral radiant flux intensity; 
         FIG. 8B  shows the same photonic crystal structure from an alternative orientation; 
         FIG. 9  is a representative example of an alternative embodiment of the photonic crystal heat engine; 
         FIG. 10  shows on coordinates of Power Spectral Density versus wavelength both the output of the Sun and the electron band gap of a typical photovoltaic cell; 
         FIG. 11  is a schematic depiction of a prior art light containment electric generator from U.S. Pat. No. 6,689,949. 
     
    
    
     DETAILED DESCRIPTION 
     FIGS.  1 ,  2 ,  3 A,  3 B, and  4 —Preferred Embodiment 
     A preferred embodiment of an electrical power generation plant  10  is illustrated in both  FIG. 1  and  FIG. 2 , which show views of the embodiment from different observation directions. The outer shell  20  is both a low temperature reservoir and a pressure vessel. The outer shell is constructed from a high thermal conductivity material  11  such as a metal stainless steel and may also have heat radiating fins (not shown) to assist in transferring unused heat energy out of the PVC module. Entering through the outer shell is a feed-through conduit  22  that passes light  18  from an external light conduit  19 , having a reflective surface  17 , through to light pipe  15  that is cut in a photonic crystal structure  16 . The solar radiation  18  is collected from a remote location (not shown). In the preferred embodiment a light conduit  19  may be wrapped in electrical conductors and electrically insulating material so that the electricity that is generated by an electric power generation plant  10  may run back along the same cable structure to conserve space (not shown). A input solar radiation  18  passes through a section of Photonic Crystal Structure (PCS)  16  with a built in light pipe  15  that exits as input light energy  21  into the core region that is a high temperature reservoir  24 . 
     The electric power generation plant  10  encloses multiple sections of nano-structured photonic crystal  12  that uses a physical cross-section that is geometrically consistent with filling the internal cavity of electric power generation plant  10 . In the present embodiment this is a truncated pyramid  12  with a hexagonal shape, pentagonal shapes are also present as can be seen in  FIG. 1 ,  FIG. 2 , and  FIG. 3 . The internal cavity may take any shape but the preferred embodiment has the form of a polyhedron such as a truncated icosahedron, which is almost spherical in three dimensions but has 32 locally flat surfaces to accommodate the flat photovoltaic cells  13 . In the present form the locally flat surfaces fit photovoltaic cells  13  with a hexagonal or pentagonal geometry. Between each solar cell is a small gap  14  that provides needed volume to fit the solar cells and provides some room for thermally induced length changes. The core volume  24  contains a material  25  that is preferably made from a strong solar absorber with a large specific thermal capacity such as, but not limited to, a hot liquid metal incased in a high temperature technical ceramic or a high temperature quartz glass doped with light absorbing ions. Turning to  FIG. 3B  and surface  27 , which is adjacent to the solar cells such as solar cell  30  in  FIG. 4 , passes the narrow-band light  54  that has been processed though the photonic crystal material  12 . Surface,  26  passes both solar light  51  or directly applied heat  52  as from, but not limited to, absorbed solar light that is now a conductive heat flow of phonons moving from hot surface  26  to cold surface  27 . Due to the temperature gradient that is across nano-structured photonic crystal  12  the photons and phonons internal to  12  interact with the nano-structured photonic crystal  12  to generate the desired narrow-band light in the direction of the photovoltaic cell, which is adjacent to surface  27 . The hot reservoir is located at surfaces like hot surface  26  at the apex of a pyramid and the cold reservoir is located at surfaces like cold surface  27 . The surface  27  thus passes the remaining heat  53  that must be radiated away to satisfy the second law of thermodynamics, which requires energy dispersal to occur whenever an energy transformation occurs. 
       FIG. 4  shows top level schematic of the solar cell power distribution network. The power bus  28  connects all of the sub circuits through connections  29 . The subcircuits consist typically of three elements in electrical series connection: a pentagonal solar cell array  32 , and two hexagonal arrays  31  and  30 . Other geometries may also be used. In the case of arrays with a fourth extra element  33  the fourth element may be attached in line with or connected in parallel to the core three elements to provide extra current. The electrical details of this parallel electrical connection are not indicated in the diagram. 
     Operation 
     FIGS.  1  to  10 —Preferred Embodiment 
     To describe how the PVC works it is necessary to first understand the way in which thermal photon radiation is generated and is coupled to phonons. Consider atoms that are embedded in a homogenous medium. In particular, consider  FIG. 6A . On the left is the outer s-orbital electron configuration  56   a  of an atom that is in the host material of the photonic crystal. Typically this material is a glass like quartz or pyrex. The s-orbital  56   a  intercepts a photon  58   a  and becomes excited into a p-orbital  57   a  through a process called stimulated absorbtion. The atom to which this p-orbital  57   a  is associated can now vibrate as part of the dielectric lattice, this vibration is also quantized and leads to a phonon (not shown) and this increases the temperature of the host material. Alternately, the atom can be hit by another photon of the exact same energy as shown in  FIG. 6B . Now note that an excited p-orbital  57   b  is sent into the s-orbital state  56   b  by the absorption of photon  58   b  in a process called stimulated emission. The result is that the material glows a bit more as light energy  59  is liberated. In  FIG. 6C  also note that from any of 4π steradians a quantum vacuum fluctuation  60   c  can cause the excited p-orbital  57   c  to radiate a photon  61  into an intrinsically unknowable direction, this is called spontaneous emission. The result is that a bit of radiant energy is sent into the homogenous dielectric in an intrinsically unknowable direction. Finally, in  FIG. 6D  it is noted that a process where vacuum fluctuations  60   d  excite the s-orbital of a host atom  56   d  to promote it to a p-orbital  57 . This is a process of spontaneous absorption and it does not appreciably occur throughout a large ensemble of atoms. That is, the energy state of the material can not spontaneously increase if the material has many atoms in it as this would be equivalent to energy becoming spontaneously and locally concentrated and not dispersed, as required by the second law of thermodynamics. Although not strictly disallowed, in the limit of large numbers of atoms, as is the case of the atoms of the photonic crystal, it is not expected that such processes will contribute in large numbers. Note, that other orbital configurations are possible and those of  FIGS. 6A-6D  are strictly representative. Therefore, based on  FIGS. 6A ,  6 B, and  6 C one that is skilled in the science and art of quantum mechanics and the thermodynamics of detailed balance can show that there exists a function that describes all these interactions, it is a well known function called the Planck&#39;s Black Body distribution. This function is influenced strongly by the assumption that spontaneous emission can occur in any of the 4π steradians. However, in a photonic crystal not all these modes are available. 
     Therefore, in this invention the assumptions that are made in the description of the black body are no longer valid because of the presence of the photonic crystal material.  FIGS. 7A and 7B  begin to describe what a photonic crystal is by making an analogy to stones thrown into a pond. In  FIG. 7A  the stone causes waves to be generated that spread out from the point of initial disturbance. If, instead, two stones into the pond simultaneously, as is indicated in  FIG. 7B , then there are two waves that are propagating and that overlap to give constructive and destructive interference. In some directions like the direction indicated by the line  62  there is destructive interference. In other directions there may be constructive interference. This analogy is directly applicable to electromagnetic waves as well. In particular, those familiar with the art of photonic crystals know that in three dimensions there exist crystal structures, like that schematically shown in  FIG. 8A , which will suppress the propagation of radiation in any direction—destructive wave cancellation in all directions. The photonic crystal has a periodically varying dielectric constant. The periodicity is applicable in three spatial dimensions and the varying dielectric constant acts as scattering centers, a kind of three dimensional pond, which will not allow the propagation of radiation in any direction even after a disturbance has occurred. This is a very special property that essentially makes an insulator for light just like rubber is considered an insulator for electrons. These materials are called photonic band gap materials and are a special case of photonic crystals. All the discussion up to this point is well known physics. However, this invention is based on a new appreciation of the physics of cancellation of electromagnetic waves generated thermally inside a photonic crystal, possessing strategically chosen photonic band gaps. Such a photonic crystal does not have a complete photonic band gap because that narrow-band part of the thermal radiation, which is also associated with the electronic band-gap transition of a photovoltaic cell, must be allowed to propagate to the photovoltaic cells. 
     The present author, while working for Caltech at NASA&#39;s Jet Propulsion Laboratory, developed the governing physical equations for photonic crystal structures that interact with both photons and phonons. These equations are highly coupled intero-differential equations that relate the spectral radiant intensity to the temperature, temperature gradients, nano-structure geometry, material thermal parameters, electromagnetic constitutive parameters, eigen solutions of Maxwell&#39;s Equations for a photonic crystal, thermal boundary conditions, light boundary conditions, the driving thermal sources, the driving light sources such as the sun, and the coordinate position inside the photonic crystal material. 
     In order to understand what is meant by radiant spectral intensity consider  FIG. 8A  and its alternate view  FIG. 8B . Consider a cone of photon energy carriers—this is a mathematical object called a light-cone  67 —embedded in a photonic crystal material. The light-cone carries photons with a narrow band of angular-frequencies dω centered at angular-frequency ω. Additionally, the energy of the photons is d 4 Q γ . These photons are propagating in the direction from the differential area  69   a  to the projected differential area dA ⊥  at  69   b , while the light-cone itself subtends a solid angle dΩ. The source area element dA  69   a  can be imagined to slide up the light-cone  67  until its perimeter intersects the cone. At this position create a differential volume element d 2 V in the form of a small differential cylinder  68 , this volume contains the photons under consideration and they have energy d 4 Q γ . If the differential area  69   a  was part of the surface of a black body then the total flux of radiant energy through the surface dA at  69   a  would be zero—because half of the energy would be propagating in the direction from  69   a  to  69   b  and the other half would be travelling in the opposite direction. However, under nonequilibrium conditions the total flux is non zero. It is desired to describe the light intensity under both equilibrium and nonequilibrium conditions in the photonic crystal. However, first note the periodic crystal structure  64  that is defined by lattice sites  65 . In this structure there are cut planes such as that shown at  63 . Atoms that radiate thermally on this plane will tend to destructively add with the radiation from the next plane if the plane spacing is half a wavelength of the light. Therefore, those directions that are defined by the normal directions to all such cut planes are can be thought of as potential band gap directions. These directions are easily visualized by the first Brillioun zone  66 , which shows the directions that are most easily formed into band gap directions where no radiation is allow to propagate. 
     From  FIG. 8A  define the Spectral Intensity I ω  in terms of the light cone  67  shown that is propagating through a medium. The medium may be a uniform medium or it may be a nano-structured medium  64  as shown in  FIG. 8A . In particular, it is defined as the photon energy per unit time dt, per unit projected area dA ⊥  at  69   b , per unit solid angle dΩ subtended by  67 , per unit radian frequency dω contained in  67 , so that 
     
       
         
           
             
               
                 
                   
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     The present author has shown that a nano-structured photonic crystal structure can be described by two equations in two unknowns—the spectral intensity distribution and the temperature distribution. The first equation consists of a first order differential equation that has both a loss term and a forcing function. The loss term is proportional to the local spectral intensity in a given direction and the proportionality constant is the bulk absorptivity α ω  of the host material from which the photonic crystal is fabricated. As shall be seen, without a forcing function this is simply the classical Beers Law, which describes the exponential decrease in the spectral light intensity with penetration depth into a material. However, by the application of quantum mechanics and the principle of detailed balance it is possible to show that there must also be a forcing function term (right hand side of the following equation) that is very similar to the classical form of the Black Body law derived by Planck. The main difference is that in a photonic crystal the energy velocity υ ω  is given in terms of the photonic crystal intrinsic eigen energy velocities υ σ , which depend on the propagation quantum numbers σ. Additionally, the forcing function for the photonic crystal depends on a numerically determined function called the Photonic Crystal Thermal Total Density Of State (TDOS) function 
                   ρ   ~     TDOS     (   pc   )       ⁡     (   ω   )       ,         
which accounts for the overlap of the periodically varying dielectric function with the eigen field solutions from Maxwell&#39;s equations. The first governing equation is for atoms in the host material of the photonic crystal that have two level atomic transitions that couple to photons and phonons. In particular,
 
                     ⅆ     I   ω         ⅆ   s       ⁢     |     2   -   level       ⁢       +     α   ω       ⁢     I   ω         =         α   ω     ⁡     (         υ   ω     ·     m   ^         4   ⁢   π       )       ⁢       ℏω   ⁢         ρ   ~     TDOS     (   pc   )       ⁡     (   ω   )             ⅇ       ℏω   /     k   B       ⁢   T       -   1           ,         
where s is the path length along a direction of interest inside the photonic crystal material and {circumflex over (m)} is a local unit vector, which is tangent to s in the direction that one seeks to know the value of the spectral light intensity. If the temperature spatial distribution T=T(r) is known it is then possible to solve this equation directly to obtain T ω  along the path length s. However, T(r) is almost never known so that it is necessary to solve for both T and I ω  need then exists to use a second equation that is based on energy balance, the resulting equation is given by
 
                     C   p     ⁢   ρ   ⁢       ∂   T       ∂   t         -     ∇     ·     [       K   h     ·     ∇   T       ]         +       ∫     4   ⁢   π       ⁢       ∫   0   ∞     ⁢           ⅆ   I     ⁢           ⁢   ω       ⅆ   s       ⁢     ⅆ   ω     ⁢     ⅆ   Ω             =   q     ,         
where in general C p  is the heat capacity at constant pressure, ρ is the mass density, T is the absolute temperature, K h  is the tensor heat conductivity, and q is the energy per unit volume that is gained or lost inside the photonic crystal structure. These last two equations are differential equations that represent a boundary value problem. The boundary values of the intensity and the temperature (or the associated derivatives) must be specified to solve these equations.
 
     The very important point to understand from these equations is that by shining intense sunlight on a portion of a photonic crystal material we are specifying the mathematical boundary condition associated with the hot side of a heat engine. Also by specifying a cold temperature on another portion of the photonic crystal—perhaps due to a large thermal bath of sea water or snow—we are specifying the mathematical boundary condition associated with the cold side of the heat engine. The photonic crystal that lies between the hot side and the cold side of the heat engine then comes to a state of dynamic equilibrium, after an initial start up transient, and at that point a balance is achieved between the flux of phonons, associated with −∇·[K h ·∇T]; the flux of photons, associated with 
                 ∫     4   ⁢   π       ⁢       ∫   0   ∞     ⁢           ⅆ   I     ⁢           ⁢   ω       ⅆ   s       ⁢     ⅆ   ω     ⁢     ⅆ   Ω           ;         
any internal sources or sinks of energy q.
 
     By designing the photonic crystal to exhibit a PBG for a particular set of frequencies and a particular set of directions we can arrange for light energy to be converted into conductive heat energy and vice versa. In particular we can arrange for light energy that is out of the optimal band of operation of a photovoltaic cell to be converted to phonons and for some phonons to be converted into light at the optimal narrow band. This process does not come for free and energy must be expended for this to happen. This is the reason why a thermal gradient is needed—to provide the energy necessary to shift the frequencies of out-of-band photons into in-band photons. 
     We can understand the results of this process through a less mathematical description. Consider  FIG. 5A , which shows, in schematic, three differential pieces of photonic crystal. We shall describe the operation of the first differential piece  39  and the others then follow. The pieces of photonic crystal that are shown in  FIG. 5A  and  FIG. 5B  are assumed to be adjacent to each other spatially. The differential piece of material  39  has boundary temperatures depicted by a hot boundary on its immediate left  34  and a colder temperature boundary to the right  41 . This represents a temperature gradient and by establishing this gradient we force phonons to flow in the direct that is opposite to said gradient, that is in the direction from left to right in  FIG. 5A . That is, conductive heat energy flows from regions that are hot to regions that are cold and never in the reverse direction under natural and unforced circumstances. The phonons that are flowing into  39  from boundary  34  are described by the Planck-like phonon distribution  36  which shows, on coordinates of relative power spectral density versus wavelength, the power content of the phonons. Since the differential piece of nano-structured photonic crystal has an approximately uniform temperature we can think of it as radiating approximately according to the Planck Black Body distribution. However, as we shall discuss shortly, the thermal radiation from said differential piece of photonic crystal material  39  is not uniform in all directions. The choice of the detailed nano-structure of  39  will cause the thermal radiation to propagate in a particular direction while restricting the propagation of all other modes. In particular,  FIG. 5A  shows that this allowed mode is at right angles to the phonon flux. The phonon flux is indicated by  35  on the hot side of  39  and by  40  on the cold side of  39 . The photon flux, i.e. light flux, is indicated by  38 , which is seen to be at right angles to the phonon flux. In addition, the flux of thermal photons is not restricted to a particular direction but also to a particular energy or equivalently to a particular color of thermally generated light. In the preferred embodiment the structure of the differential piece of photonic crystal material  39  is chosen to only allow a narrow-band of photon energies to propagate in the orthogonal direction to the phonon flux. This narrow-band photon flux  38  corresponds to, and is matched with, the valance to conduction band energies of the photovoltaic cell as indicated in  FIG. 10  by  106  and  105 . In simple terms, we can say that the differential piece of material  39  glows radiantly with light from the intrinsic average temperature of the material but that the photons that are given off by the glowing process are restricted to propagate in a direction that is orthogonal to the conductive heat flow  35  and  40  and with an optimal energy (color) that will cause electron-hole pairs to be generated in a photovoltaic cell  42  with the greatest efficiency. The consequence of a small piece of the energy  37  of the lattice vibrations being removed is that that energy is free to propagate to the photovoltaic  42  through a photon propagation process  38  in the photonic crystal  39 . Note, that the temperature boundaries  34  and  41  have temperatures T and (T−ΔT), where the change in temperature ΔT is a positive quantity, this established the movement of phonons in the general direction from  34  to  41 . It also allows the lattice vibrations to rethermalize after the energy  37  is removed thus providing a new Planck-like power spectral distribution for the phonons but with diminished intensity relative to the previous phonon power spectral density  36  to the left of the next differential nano-structured photonic crystal section. After this process for each differential piece of photonic crystal  39  the remaining phonon flux  55  enters the coldest thermal reservoir  43 . Note that under perfect conditions the thermodynamic free energy content of the process will be transferred to the solar cell  42  so that the total efficiency of the system is the product of the Carnot efficiency and the solar efficiency for the narrow band of frequencies that is sent to the solar cell. This narrow-band efficiency is limited by the quantum efficiency of the electron-hole pair generation process and is often greater than 90% so that the maximum efficiency of the device is within about 10% of the Carnot efficiency. 
     Note, the photovoltaic cell  42  has a length that spans the photonic crystal material from  34  to  43 . This photovoltaic cell is bathed in optimally colored light to produce electricity. The light reaching  42  is most intense on the left side, which corresponds to the hottest part of the photonic crystal  34 , and is most diminished on at that part of the solar cell which corresponds to the coldest part of the photonic crystal  43 . This means that more electricity is generated from the solar cells on the left than on the right in  FIG. 5A . This is an asymmetry that can lead to inefficiency and it can be removed by changing the direction of the allowed photon modes relative to the direction of phonon flux. This is shown in the preferred embodiment of  FIG. 5B . 
     In  FIG. 5B  a different nano-structured photonic crystal  44  is used as the differential piece of material. In this case narrow-band photon energy  51  along with broad band phonon energy  52  is sent propagating in the same direction. Just as before, the photonic crystal operates on the thermally generated photons, but now the allowed propagation modes are in the same direction as the phonon flux, which is caused by the large temperature gradient between the hot reservoir  34  and the combined cold reservoir and photovoltaic cells located at  48 . With this particular geometry we can see that each differential piece of nano-structured photonic crystal allows a small amount of narrow-band photon energy to propagate forward. The first differential photonic crystal sends the photon energy corresponding to  45  forward, the second differential photonic crystal add to  45  so that the total amount of narrow-band energy is shown in  46 , continuing along in this way we get to the last differential photonic crystal and the total allowed energy that propagates towards the solar cell  48  is finally indicated by  47 . 
     Note that  FIGS. 5A and 5B  show two extremes of operation. It is also possible to have the narrow-band photons propagate at an arbitrary angle relative to the phonon flux. By showing the embodiments of  FIGS. 5A and 5B  the possibility of using other configurations is not precluded. 
     Once the solar energy has passed through the individual photonic crystal elements  12  of  FIG. 1  and  FIG. 2 , which have a thermal gradient on them, the resulting narrow-band light  54  is used to drive the photovoltaic cells such as  30 - 32 . The resulting electrical energy is then available for distribution. 
     DESCRIPTION 
     Alternative Embodiment and Operation 
     An alternative embodiment is shown in  FIG. 9 . This is not the only alternative but it provides a representative example of such systems. Solar light  95  enters at the top of the heat engine and is absorbed by the high emissivity surface  96 , this becomes the hot reservoir. The resulting phonons  94  propagate towards the cold reservoir at  89  by propagating through a photonic crystal  91 . The crystal is chosen to operate in accordance to  FIG. 5A  so that as the radiation propagates from  96  to  89  it is rethermalized along the path. This results in the creation of narrow band light in the radial direction  90 . This light impinges onto a photovoltaic array  92 , which is wrapped around the photonic crystal, and thus produces electricity. 
     CONCLUSION, RAMIFICATION, AND SCOPE 
     Accordingly the reader will see that the heat engine of this invention can be used to provide electrical power from a solid state system. Furthermore, this type of power plant has the additional advantages in that:
         1. it permits the production of electricity in any environment that can allow a temperature difference to be maintained;   2. it permits the secondary production of hydrogen and oxygen through the electrolysis of super heated water;   3. it permits the production of electricity even during time of low solar light levels or at night by including a separate large thermal reservoir, such as, but not limited to, water—which has a large heat capacity;   4. it can be made to wrap around the nuclear reactor of a submarine and directly create electricity for the submarine through the heat engine created between the nuclear reactor and the sea water;   5. it can be made to wrap around the nuclear reactor of a space satellite and directly create electricity for the satellite through the heat engine created between the nuclear reactor and the cold of sea of deep space;   6. it can be used, in conjunction with a solar collector, on a space-based satellite or platform to provide energy to said satellite or platform;   7. it can be used in groups or clusters to provide greater power output than just a single unit;       

     While the above description contains many specificities, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of this invention. For example, the enclosure and the photonic crystal components can have other shapes such as: ellipsoidal, toroididal, and various non symmetric shapes so long as a large temperature difference can be maintained between the hot and cold reservoirs of the heat engine. 
     Thus the scope of the invention should be determined by the appended claims and their legal equivalents, and not by the examples given.