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[CrossRef]

M. J. Bastiaans and T. Alieva, “Synthesis of an arbitrary ABCD system with fixed lens positions,” Opt. Lett 31, 2414–2416 (2006).

[CrossRef]

N. M. Atakishiyev, L. E. Vicent, and K. B. Wolf, “Continuous vs. discrete fractional Fourier transforms,” J. Comput. Appl. Math. 107, 73–95 (1999).

[CrossRef]

N. Mukunda, “Role of symmetry and group structure in optics,” Current Sci. 59, 1135–1151 (1990).

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Hamilton’s theory of turns generalized to Sp(2,R),” Phys. Rev. Lett. 62, 1331–1334 (1989).

[CrossRef]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “The theory of screws: a new geometric representation for the group SU(1,1),” J. Math. Phys. 30, 1000–1006 (1989).

[CrossRef]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).

[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).

[CrossRef]

K. B. Wolf, “Canonical transforms. I. Complex linear transforms,” J. Math. Phys. 15, 1295–1301 (1974).

[CrossRef]

Arvind, B. Dutta, N. Mukunda, and R. Simon, “The real symplectic groups in quantum mechanics and optics,” Pramana 45, 471–497 (1995).

[CrossRef]

N. M. Atakishiyev, L. E. Vicent, and K. B. Wolf, “Continuous vs. discrete fractional Fourier transforms,” J. Comput. Appl. Math. 107, 73–95 (1999).

[CrossRef]

S. Cornbleet, “Geometrical optics reviewed: a new light on an old subject,” Proc. IEEE 71, 471–502 (1983).

[CrossRef]

Arvind, B. Dutta, N. Mukunda, and R. Simon, “The real symplectic groups in quantum mechanics and optics,” Pramana 45, 471–497 (1995).

[CrossRef]

R. A. Horn and C. R. Johnson, “Canonical forms for similarity and triangular factorizations,” in Matrix Analysis (Cambridge University, 2013), pp. 163–224.

R. A. Horn and C. R. Johnson, “Canonical forms for similarity and triangular factorizations,” in Matrix Analysis (Cambridge University, 2013), pp. 163–224.

D. J. Ming and F. H. Yi, “New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems,” Chin. Phys. B 22, 060302 (2013).

[CrossRef]

Arvind, B. Dutta, N. Mukunda, and R. Simon, “The real symplectic groups in quantum mechanics and optics,” Pramana 45, 471–497 (1995).

[CrossRef]

N. Mukunda, “Role of symmetry and group structure in optics,” Current Sci. 59, 1135–1151 (1990).

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Hamilton’s theory of turns generalized to Sp(2,R),” Phys. Rev. Lett. 62, 1331–1334 (1989).

[CrossRef]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “The theory of screws: a new geometric representation for the group SU(1,1),” J. Math. Phys. 30, 1000–1006 (1989).

[CrossRef]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).

[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).

[CrossRef]

R. Simon and K. B. Wolf, “Structure of the set of paraxial optical systems,” J. Opt. Soc. Am. A 17, 342–355 (2000).

[CrossRef]

R. Simon and K. B. Wolf, “Fractional Fourier transforms in two dimensions,” J. Opt. Soc. Am. A 17, 2368–2381 (2000).

[CrossRef]

Arvind, B. Dutta, N. Mukunda, and R. Simon, “The real symplectic groups in quantum mechanics and optics,” Pramana 45, 471–497 (1995).

[CrossRef]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “The theory of screws: a new geometric representation for the group SU(1,1),” J. Math. Phys. 30, 1000–1006 (1989).

[CrossRef]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Hamilton’s theory of turns generalized to Sp(2,R),” Phys. Rev. Lett. 62, 1331–1334 (1989).

[CrossRef]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).

[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).

[CrossRef]

O. N. Stavroudis, “The lens group,” in The Optics of Rays, Wavefronts, and Caustics, H. S. W. Massey and K. A. Brueckner, eds. (Academic, 1972), pp. 281–297.

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Hamilton’s theory of turns generalized to Sp(2,R),” Phys. Rev. Lett. 62, 1331–1334 (1989).

[CrossRef]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “The theory of screws: a new geometric representation for the group SU(1,1),” J. Math. Phys. 30, 1000–1006 (1989).

[CrossRef]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).

[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).

[CrossRef]

N. M. Atakishiyev, L. E. Vicent, and K. B. Wolf, “Continuous vs. discrete fractional Fourier transforms,” J. Comput. Appl. Math. 107, 73–95 (1999).

[CrossRef]

R. Simon and K. B. Wolf, “Fractional Fourier transforms in two dimensions,” J. Opt. Soc. Am. A 17, 2368–2381 (2000).

[CrossRef]

R. Simon and K. B. Wolf, “Structure of the set of paraxial optical systems,” J. Opt. Soc. Am. A 17, 342–355 (2000).

[CrossRef]

N. M. Atakishiyev, L. E. Vicent, and K. B. Wolf, “Continuous vs. discrete fractional Fourier transforms,” J. Comput. Appl. Math. 107, 73–95 (1999).

[CrossRef]

K. B. Wolf, “Canonical transforms. I. Complex linear transforms,” J. Math. Phys. 15, 1295–1301 (1974).

[CrossRef]

K. B. Wolf, “Canonical transformations,” in Geometric Optics on Phase Space (Springer, 2004), pp. 25–46.

K. B. Wolf, “Construction and properties of canonical transforms,” in Integral Transforms in Science and Engineering, A. Miele, ed. (Springer, 1979), pp. 381–416.

A. Yariv and P. Yeh, “Rays and optical beams,” in Photonics, A. S. Sedra, ed. (Oxford, 2007), pp. 66–109.

A. Yariv and P. Yeh, “Rays and optical beams,” in Photonics, A. S. Sedra, ed. (Oxford, 2007), pp. 66–109.

D. J. Ming and F. H. Yi, “New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems,” Chin. Phys. B 22, 060302 (2013).

[CrossRef]

H. H. Arsenault, “Generalization of the principal plane concept in matrix optics,” Am. J. Phys. 48, 397–399 (1980).

[CrossRef]

D. J. Ming and F. H. Yi, “New decomposition of the Fresnel operator corresponding to the optical transformation in ABCD-systems,” Chin. Phys. B 22, 060302 (2013).

[CrossRef]

N. Mukunda, “Role of symmetry and group structure in optics,” Current Sci. 59, 1135–1151 (1990).

N. M. Atakishiyev, L. E. Vicent, and K. B. Wolf, “Continuous vs. discrete fractional Fourier transforms,” J. Comput. Appl. Math. 107, 73–95 (1999).

[CrossRef]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “The theory of screws: a new geometric representation for the group SU(1,1),” J. Math. Phys. 30, 1000–1006 (1989).

[CrossRef]

K. B. Wolf, “Canonical transforms. I. Complex linear transforms,” J. Math. Phys. 15, 1295–1301 (1974).

[CrossRef]

R. Simon and K. B. Wolf, “Structure of the set of paraxial optical systems,” J. Opt. Soc. Am. A 17, 342–355 (2000).

[CrossRef]

M. J. Bastiaans and T. Alieva, “Classification of lossless first-order optical systems and the linear canonical transformation,” J. Opt. Soc. Am. A 24, 1053–1062 (2007).

[CrossRef]

T. Alieva and M. J. Bastiaans, “Properties of the linear canonical integral transformation,” J. Opt. Soc. Am. A 24, 3658–3665 (2007).

[CrossRef]

R. Simon and K. B. Wolf, “Fractional Fourier transforms in two dimensions,” J. Opt. Soc. Am. A 17, 2368–2381 (2000).

[CrossRef]

J. Shamir and N. Cohen, “Root and power transformations in optics,” J. Opt. Soc. Am. A 12, 2415–2423 (1995).

[CrossRef]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).

[CrossRef]

M. J. Bastiaans and T. Alieva, “Synthesis of an arbitrary ABCD system with fixed lens positions,” Opt. Lett 31, 2414–2416 (2006).

[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, “Generalized rays in first-order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984).

[CrossRef]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, “Hamilton’s theory of turns generalized to Sp(2,R),” Phys. Rev. Lett. 62, 1331–1334 (1989).

[CrossRef]

Arvind, B. Dutta, N. Mukunda, and R. Simon, “The real symplectic groups in quantum mechanics and optics,” Pramana 45, 471–497 (1995).

[CrossRef]

S. Cornbleet, “Geometrical optics reviewed: a new light on an old subject,” Proc. IEEE 71, 471–502 (1983).

[CrossRef]

R. A. Horn and C. R. Johnson, “Canonical forms for similarity and triangular factorizations,” in Matrix Analysis (Cambridge University, 2013), pp. 163–224.

O. N. Stavroudis, “The lens group,” in The Optics of Rays, Wavefronts, and Caustics, H. S. W. Massey and K. A. Brueckner, eds. (Academic, 1972), pp. 281–297.

K. B. Wolf, “Construction and properties of canonical transforms,” in Integral Transforms in Science and Engineering, A. Miele, ed. (Springer, 1979), pp. 381–416.

K. B. Wolf, “Canonical transformations,” in Geometric Optics on Phase Space (Springer, 2004), pp. 25–46.

A. Yariv and P. Yeh, “Rays and optical beams,” in Photonics, A. S. Sedra, ed. (Oxford, 2007), pp. 66–109.