Universal Linear Components

Abstract

Universal linear components are provided. In general, a P input and Q output wave combiner is connected to a Q input and R output wave mode synthesizer via Q amplitude and/or phase modulators. The wave combiner and wave mode synthesizer are both linear, reciprocal and lossless. The wave combiner and wave mode synthesizer can be implemented using waveguide technology. This device can provide any desired linear transformation of spatial modes between its inputs and its outputs. This capability can be generalized to any linear transformation by using representation converters to convert other quantities to spatial mode patterns. The wave combiner and wave mode synthesizer are also useful separately, and can enable applications including self-adjusting mode coupling, optimal multi-mode communication, and add-drop capability in a multi-mode system. Control of the wave combiner and wave mode synthesizer can be implemented with single-variable optimizations.

1 . A component comprising:
 a wave combiner having P inputs and Q outputs configured such that a contribution of each of the P inputs to each of the Q outputs of the wave combiner is adjustable in at least one of amplitude and relative phase;   a wave mode synthesizer having R inputs and S outputs configured such that the contribution of each of the R inputs to the S outputs of the wave mode synthesizer is adjustable in at least one of amplitude and phase; and   T amplitude and/or phase modulators coupled between outputs of the wave combiner and inputs of the wave mode synthesizer;   wherein a configuration of at least one of the wave combiner, wave mode synthesizer and amplitude and/or phase modulators is determined using a singular value decomposition.   
     
     
         2 . The component of  claim 1 , wherein the T modulators include at least one of Mach-Zehnder modulators and phase modulators. 
     
     
         3 . The component of  claim 2 , wherein the T modulators include phase shifters to configure phase. 
     
     
         4 . The component of  claim 1 , wherein signals propagate sequentially from the wave combiner to the modulators, and then from the modulators to the wave mode synthesizer. 
     
     
         5 . The component of  claim 1 , wherein signals propagate sequentially from the wave mode synthesizer to the modulators, and then from the modulators to the wave combiner. 
     
     
         6 . The component of  claim 1 , wherein signals propagate bidirectionally between the wave combiner and the modulators and between the modulators and the wave mode synthesizer.