Finite-embedded coordinate designed transformation-optical devices

Abstract

The design method for complex electromagnetic materials is expanded from form-invariant coordinate transformations of Maxwell's equations to finite embedded coordinate transformations. Embedded transformations allow the transfer of electromagnetic field manipulations from the transformation-optical medium to another medium, thereby allowing the design of structures that are not exclusively invisible. A topological criterion for the reflectionless design of complex media is also disclosed and is illustrated in conjunction with the topological criterion to design a parallel beam shifter and a beam splitter with unconventional electromagnetic behavior.

We claim: 
     
         1 . A process of fabricating a transformation-optical/transformation-electromagnetic device comprising:
 computing a local form-invariant finite coordinate transformation for a transformation-optical device;   computing at least one form-invariant coordinate transformation for a region surrounding the device;   embedding the local form-invariant finite computed coordinate transformation into the region surrounding the device; and   fabricating the device based at least in part on the computed coordinate transformations.   
     
     
         2 . The process of  claim 1  wherein said transformation-optical/transformation-electromagnetic device comprises a metamaterial. 
     
     
         3 . The process of  claim 1  further comprising providing non-reversibly change to the properties of electromagnetic waves in said device. 
     
     
         4 . The process of  claim 2  further including transmitting the changed electromagnetic properties to free space. 
     
     
         5 . The process of  claim 2  further including transmitting the changed electromagnetic properties to a different medium. 
     
     
         6 . The process of  claim 1  further including enabling transference of electromagnetic field manipulations from said device to a further medium. 
     
     
         7 . A computer implemented method of designing transformation-optical/transformation-electromagnetic devices using embedded coordinate transformations of electromagnetic permittivity and permeability tensors, comprising:
 computing a local form-invariant coordinate transformation of Maxwell's Equations for a transformation-optical medium of an optical device;   computing form-invariant coordinate transformations for a region surrounding the transformation-optical medium of the device;   embedding the local form-invariant computed coordinate transformation into free space region or a second surrounding optical medium defining the device; and   providing the computed coordinate transformations to a metamaterial fabrication process equipment.   
     
     
         8 . A method of implementing effective permittivity and permeability transformation design for complex electromagnetic materials used in transformation-optical/transformation-electromagnetic devices, comprising:
 computing a local coordinate transformation for the transformation optical medium of a device;   computing a coordinate transformation for a region surrounding the transformation-optical medium of a device;   embedding the computed local coordinate transformation into computed coordinate transformation for the region surrounding the transformation-optical medium device;   wherein electromagnetic filed manipulations from a first transformation-optical medium can be transferred to a second medium or free space, and wherein continuity of the transformation design across a medium-to-medium interface is retained.   
     
     
         9 . A method of implementing effective permittivity and permeability transformation design for complex electromagnetic materials used in transformation-optical/transformation-electromagnetic devices, comprising:
 computing a local coordinate transformation for the transformation optical medium of a device;   computing a coordinate transformation for a region surrounding the transformation-optical medium of a device; and   embedding the computed local coordinate transformation into computed coordinate transformation for the region surrounding the transformation-optical medium device,   thereby enabling a transference of electromagnetic field manipulations from a first transformation-optical medium to a second medium.   
     
     
         10 . An electromagnetic/photonic beam-splitter, comprising:
 a metamaterial fabricated by computing a local coordinate transformation, computing a coordinate transformation for a region surrounding the metamaterial, embedding the computed local coordinate transformation into computed coordinate transformation for the region surrounding the metamaterial, and incorporating the metamaterial into the beam splitter; and   means for directing electromagnetic radiation to the metamaterial.   
     
     
         11 . A parallel beam shifter, comprising:
 a metamaterial fabricated by computing a local coordinate transformation, computing a coordinate transformation for a region surrounding the metamaterial, embedding the computed local coordinate transformation into computed coordinate transformation for the region surrounding the metamaterial, and incorporating the metamaterial into the beam shifter; and   means for directing electromagnetic radiation to the metamaterial.   
     
     
         12 . A process of fabricating a transformation-optical/transformation-electromagnetic device comprising:
 recording initial configurations of E-M fields in a medium on a Cartesian coordinate mesh;   distorting/changing the coordinate mesh to a predetermined configuration represented by a distorted coordinate mesh;   recording the distortions as a coordinate transformation between the Cartesian mesh and the distorted coordinate mesh;   computing scaled E-M field values in accordance with the coordinate transformations;   embedding the computed values into the coordinate space defining a transformation-optical device; and   fabricating the device based at least in part on said embedded computed values.   
     
     
         13 . The process of  claim 12  wherein computed E-M fields are represented by one or more of electric displacement field D, magnetic field intensity B, or Poynting vector S.