Unit cell network design and operation

Abstract

In one embodiment, a signal transduction system includes an arrangement of interacting unit cells. Each unit cell can have one or more adjustable parameters that are adjustable to enable one or more adjustable impedance values of the unit cells at each of one or more operational frequencies. The interactions of the unit cells within the arrangement of the interacting unit cells can be describable with an interaction matrix that is approximately independent of the adjustable impedance values of the unit cells.

What is claimed is: 
     
         1 . (canceled) 
     
     
         2 . An apparatus for either or both transmitting and receiving signals comprising:
 a signal transduction system including an arrangement of interacting unit cells, wherein each unit cell has one or more adjustable parameters that are adjustable to enable one or more adjustable impedance values of the unit cells at each of one or more operational frequencies, wherein the interactions of the unit cells within the arrangement of the interacting unit cells are characterized by an interaction matrix that is approximated based on periodicity of the unit cells.   
     
     
         3 . The apparatus of  claim 2 , wherein each impedance value of the one or more adjustable impedance values corresponds to a frequency-domain mode of one or more modes for the each unit cell of the unit cells at one of the one or more operational frequencies. 
     
     
         4 . The apparatus of  claim 2 , wherein periodicity of the unit cells is characterized based on geometries of the unit cells. 
     
     
         5 . The apparatus of  claim 4 , wherein periodic unit cells of the unit cells are specific unit cells that have identical geometries. 
     
     
         6 . The apparatus of  claim 2 , wherein periodicity of the unit cells is characterized by positions of the unit cells in the arrangement of interacting unit cells. 
     
     
         7 . The apparatus of  claim 6 , wherein periodic unit cells of the unit cells are specific unit cells that are positioned within at least one interaction radius away from a unit cell that is not a periodic unit cell in the arrangement of interacting unit cells. 
     
     
         8 . The apparatus of  claim 7 , wherein the interaction radius is defined with respect to dimensions of one or more of the unit cells. 
     
     
         9 . The apparatus of  claim 6 , wherein periodic unit cells of the unit cells are specific unit cells that are positioned within at least one interaction radius away from a unit cell that is at an edge of the arrangement of interacting unit cells. 
     
     
         10 . The apparatus of  claim 2 , wherein the interaction matrix is approximated based on a subset of a total number of periodic unit cells of the unit cells. 
     
     
         11 . The apparatus of  claim 2 , wherein the interaction matrix is approximated by approximating diagonal elements of a matrix corresponding to periodic unit cells of the unit cells. 
     
     
         12 . The apparatus of  claim 11 , wherein the diagonal elements are approximated by simulating one unit cell of the periodic unit cells. 
     
     
         13 . The apparatus of  claim 12 , wherein the one unit cell is simulated by applying periodic boundary conditions to the one unit cell. 
     
     
         14 . The apparatus of  claim 11 , wherein the diagonal elements are approximated by simulating one or more periodically repeated groups of unit cells of the periodic unit cells. 
     
     
         15 . The apparatus of  claim 14 , wherein the one or more periodically repeated groups of unit cells are simulated by applying periodic boundary conditions to the one or more periodically repeated groups of unit cells. 
     
     
         16 . The apparatus of  claim 11 , wherein the diagonal elements are approximated by assuming the diagonal elements are equal to each other. 
     
     
         17 . A method of operating a signal transduction system for either or both transmitting and receiving signals comprising:
 identifying one or more target radiation patterns of the signal transduction system for the signals; and   adjusting one or more adjustable parameters of unit cells in an arrangement of interacting unit cells forming the signal transduction system according to the one or more target radiation patters and an interaction matrix, wherein the one or more adjustable parameters are adjustable to enable one or more adjustable impedance values of the unit cells at each of one or more operational frequencies, and the interactions of the unit cells within the arrangement of the interacting unit cells are characterized by the interaction matrix that is approximated based on periodicity of the unit cells.   
     
     
         18 . The method of  claim 17 , wherein each impedance value of the one or more adjustable impedance values corresponds to a frequency-domain mode of one or more modes for the unit cells at one of the one or more operational frequencies. 
     
     
         19 . The method of  claim 17 , wherein periodicity of the unit cells is characterized based on geometries of the unit cells. 
     
     
         20 . The method of  claim 19 , wherein periodic unit cells of the unit cells are specific unit cells that have identical geometries. 
     
     
         21 . The method of  claim 17 , wherein periodicity of the unit cells is characterized by positions of the unit cells in the arrangement of interacting unit cells. 
     
     
         22 . The method of  claim 21 , wherein periodic unit cells of the unit cells are specific unit cells that are positioned within at least one interaction radius away from a unit cell that is not a periodic unit cell in the arrangement of interacting unit cells. 
     
     
         23 . The method of  claim 22 , wherein the interaction radius is defined with respect to dimensions of one or more of the unit cells. 
     
     
         24 . The method of  claim 21 , wherein periodic unit cells of the unit cells are specific unit cells that are positioned within at least one interaction radius away from a unit cell that is at an edge of the arrangement of interacting unit cells. 
     
     
         25 . The method of  claim 17 , wherein the interaction matrix is approximated based on a subset of a total number of periodic unit cells of the unit cells. 
     
     
         26 . The method of  claim 17 , wherein the interaction matrix is approximated by approximating diagonal elements of a matrix corresponding to periodic unit cells of the unit cells. 
     
     
         27 . The method of  claim 26 , wherein the diagonal elements are approximated by simulating one unit cell of the periodic unit cells. 
     
     
         28 . The method of  claim 27 , wherein the one unit cell is simulated by applying periodic boundary conditions to the one unit cell. 
     
     
         29 . The method of  claim 26 , wherein the diagonal elements are approximated by simulating one or more periodically repeated groups of unit cells of the periodic unit cells. 
     
     
         30 . The method of  claim 29 , wherein the one or more periodically repeated groups of unit cells are simulated by applying periodic boundary conditions to the one or more periodically repeated groups of unit cells. 
     
     
         31 . The method of  claim 26 , wherein the diagonal elements are approximated by assuming the diagonal elements are equal to each other.