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The group‐theoretical treatment of aberrating systems. II. Axis‐symmetric inhomogeneous systems and fiber optics in third aberration order
1.M. Navarro‐Saad and K. B. Wolf, “The group‐theoretical treatment of aberrating systems. I. Aligned lens systems in third aberration order,” J. Math. Phys. 27, 1449 (1986).
2.A. J. Dragt, Lectures on Nonlinear Orbit Dynamics A.I.P. Conference Proceedings, No. 87 (A.I.P., New York, 1982).
3.V. Guillemin and S. Sternberg, Symplectic Techniques in Physics (Cambridge U.P., Cambridge, 1984).
4.K. B. Wolf, “On time‐dependent quadratic quantum Hamiltonians,” SIAM J. Appl. Math. 40, 419 (1981).
5.Compare with A. J. Dragt and E. Forest, “Computation of nonlinear behavior of Hamiltonian systems using Lie algebraic methods,” J. Math. Phys. 24, 2734 (1983), Sec. 4, Eq. (4.7), we note that
5.Note in this regard the work by S. Steinberg, “Factored product expansions of solutions of nonlinear differential equations,” SIAM J. Math. Anal. 15, 108 (1984), which may be used for higher aberration orders.
6.Compare A. J. Dragt, “Lie algebraic theory of geometrical optics and optical aberrations,” J. Opt. Soc. Am. 72, 372 (1982), Eqs. (5.19)–(5.24).
7.K. B. Wolf, “Approximate canonical transformations and the treatment of aberrations. I. One‐dimensional simple N th‐order aberrations in optical systems,” Comunicaciones Técnicas IIMAS No. 352, 1983.
8.M. Navarro‐Saad and K. B. Wolf, “Factorization of the phase‐space transformation produced by an arbitrary refracting surface,” preprint CINVESTAV, March 1984.
9.K. B. Wolf, “A group‐theoretical model for Gaussian optics and third‐order aberrations,” in Proceedings of the XII Colloquium on Group‐theoretical Methods in Physics, Lecture Notes in Physics, Trieste, 1983 (Springer, Berlin, 1984).
10.I am indebted to Prof. Alex Dragt and Dr. Etienne Forest for pointing out an error in the original calculation.
11.M. Nazarathy and J. Shamir, “First‐order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356 (1982).
12.K. B. Wolf, “The Heisenberg‐Weyl ring in quantum mechanics,” in Group Theory and its Applications, edited by E. M. Loebl (Academic, New York, 1975), Vol. 3.
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