Part I of this series described a procedure for synthesizing birefringent networks having arbitrarily prescribed amplitude transmittance. The network resulting from that procedure consists of a series of identical cascaded birefringent crystals between an input and output polarizer. We refer to such a network as a “lossless birefringent network” since it contains no internal polarizers. The variables determined by the synthesis procedure of Part I are the angles to which the crystals and the output polarizer are rotated. This paperproves several general theorems concerned with lossless birefringent networks. These theorems deal with (1) uniqueness; (2) the effect upon the transmittance of changing the sign of the angles of the crystals and output polarizer; (3) the effect upon the transmittance of turning the network end for end; and (4) the symmetry relations which the crystal and polarizer angles must satisfy when certain restrictions are imposed upon the desired amplitude transmittance.
E. O. AMMANN, "Optical Network Synthesis Using Birefringent Crystals. III. Some General Properties of Lossless Birefringent Networks," J. Opt. Soc. Am. 56, 943-951 (1966)