In the paraxial regime of three-dimensional optics, two evolution Hamiltonians are equivalent when one can be transformed to the other modulo scale by similarity through an optical system. To determine the equivalence sets of paraxial optical Hamiltonians one requires the orbit analysis of the algebra sp(4, ℜ) of 4 × 4 real Hamiltonian matrices. Our strategy uses instead the isomorphic algebra so(3, 2) of 5 × 5 matrices with metric (+1, +1, +1, −1, −1) to find four orbit regions (strata), six isolated orbits at their boundaries, and six degenerate orbits at their common point. We thus resolve the degeneracies of the eigenvalue classification.

© 2002 Optical Society of America

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

Related Journal Articles

• Green dyadic calculations for inhomogeneous optical media (JOSAA)
• Frame-theory-based approach for determining the time–frequency distribution characterizing a dense group of reflecting objects (JOSAA)
• Analytical investigation of stratified isotropic media (JOSAA)
• Analytical investigation of one-dimensional magnetoelectric photonic crystals. The 2×2 matrix approach (JOSAA)
• Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complexcoordinate transforms and ray transfer matrices (JOSAA)

Related Conference Papers

• Topological decomposition of composite quantum state spaces
• Topological decomposition of composite quantum state spaces
• Noisy Grovers searching algorithm
• Noisy Grovers searching algorithm
• Information gain and entropy change in generalized quantum measurements
• Information gain and entropy change in generalized quantum measurements
• Additivity for some product channels
• Additivity for some product channels
• Topology Optimized Photonic Wire Splitters