Polygon x-prism for imaging and display applications

A system, comprising:

• a first multi-faceted optical element that includes:
• K optical facets, wherein K is greater than or equal to six, and
• K-2 internal surfaces, each configured to reflect at least a portion of an optical beam that is incident thereupon, each internal surface including a coating designed to modify one or more of a spectral content, polarization, intensity or phase of the optical beam that is incident thereupon, wherein the first multifaceted optical element is configurable to either split an input light beam into four or more output light beams, or to combine four or more input light beams into a single output light beam, wherein:
• the system further includes at least a second multi-faceted optical element, wherein the first multi-faceted optical element is coupled to the at least second multi-faceted optical element to receive the single output light beam that is output from the first multi-faceted optical element and to split the received output light beam into four or more additional output light beams.

A polyhedron for use as an optical splitter, comprising:

• at least one input facet to receive an input light beam;
• at least five output facets;
• and
• at least four internal surfaces, each internal surface comprising a coating designed to modify one or more of a spectral content, a polarization, an intensity or a phase of light that is incident thereupon, wherein the internal surfaces are positioned to allow at least a portion of the input light beam to reach one of the output facets upon transmission through the polyhedron and at least a portion of the input light beam to reach one or more of the remaining output facets upon full or partial reflection from one or more of the internal facets, wherein the polyhedron has a hexagonal cross section, one input facet, six internal surfaces and seven output facets.

A polyhedron for use as an optical splitter, comprising:

• at least one input facet to receive an input light beam;
• at least five output facets;
• and
• at least four internal surfaces, each internal surface comprising a coating designed to modify one or more of a spectral content, a polarization, an intensity or a phase of light that is incident thereupon, wherein the internal surfaces are positioned to allow at least a portion of the input light beam to reach one of the output facets upon transmission through the polyhedron and at least a portion of the input light beam to reach one or more of the remaining output facets upon full or partial reflection from one or more of the internal facets, wherein the polyhedron has an octagonal cross section, one input facet, eight internal surfaces and nine output facets.