M. J. Bastiaans and T. Alieva, "First-order optical systems with real eigenvalues," Opt. Commun. 272, 52-55 (2007).

K. B. Wolf, Geometric Optics on Phase Space (Springer, 2004).

S. C. Pei and J. J. Ding, "Eigenfunctions of linear canonical transform," IEEE Trans. Signal Process. 50, 11-26 (2002).

[CrossRef]

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

W. W. Lin, V. Mehrmann, and H. Xu, "Canonical forms for Hamiltonian and symplectic matrices and pencils," Linear Algebr. Appl. 302-303, 469-533 (1999).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993).

D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation: I," J. Opt. Soc. Am. A 10, 1875-1881 (1993).

H. M. Ozaktas and D. Mendlovic, "Fractional Fourier transforms and their optical implementation: II," J. Opt. Soc. Am. A 10, 2522-2531 (1993).

A. C. McBride and F. H. Kerr, "On Namias' fractional Fourier transforms," IMA J. Appl. Math. 39, 159-175 (1987).

V. Namias, "The fractional order Fourier transform and its applications to quantum mechanics," J. Inst. Math. Appl. 25, 241-265 (1980).

K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, 1979).

M. Moshinsky and C. Quesne, "Linear canonical transformations and their unitary representations," J. Math. Phys. 12, 1772-1780 (1971).

[CrossRef]

R. K. Luneburg, Mathematical Theory of Optics (U. of California Press, 1966).

A. Vander Lugt, "Operational notation for the analysis and synthesis of optical data-processing systems," Proc. IEEE 54, 1055-1063 (1966).

M. J. Bastiaans and T. Alieva, "First-order optical systems with real eigenvalues," Opt. Commun. 272, 52-55 (2007).

M. J. Bastiaans and T. Alieva, "First-order optical systems with unimodular eigenvalues," J. Opt. Soc. Am. A 23, 1875-1883 (2006).

T. Alieva and M. J. Bastiaans, "Alternative representation of the linear canonical integral transform," Opt. Lett. 30, 3302-3304 (2005).

[CrossRef]

M. J. Bastiaans and T. Alieva, "Generating function for Hermite-Gaussian modes propagating through first-order optical systems," J. Phys. A 38, L73-L78 (2005).

[CrossRef]

M. J. Bastiaans and T. Alieva, "First-order optical systems with real eigenvalues," Opt. Commun. 272, 52-55 (2007).

M. J. Bastiaans and T. Alieva, "First-order optical systems with unimodular eigenvalues," J. Opt. Soc. Am. A 23, 1875-1883 (2006).

T. Alieva and M. J. Bastiaans, "Alternative representation of the linear canonical integral transform," Opt. Lett. 30, 3302-3304 (2005).

[CrossRef]

M. J. Bastiaans and T. Alieva, "Generating function for Hermite-Gaussian modes propagating through first-order optical systems," J. Phys. A 38, L73-L78 (2005).

[CrossRef]

S. C. Pei and J. J. Ding, "Eigenfunctions of linear canonical transform," IEEE Trans. Signal Process. 50, 11-26 (2002).

[CrossRef]

F. R. Gantmacher, The Theory of Matrices (Chelsea, 1974-1977).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

A. C. McBride and F. H. Kerr, "On Namias' fractional Fourier transforms," IMA J. Appl. Math. 39, 159-175 (1987).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

W. W. Lin, V. Mehrmann, and H. Xu, "Canonical forms for Hamiltonian and symplectic matrices and pencils," Linear Algebr. Appl. 302-303, 469-533 (1999).

R. K. Luneburg, Mathematical Theory of Optics (U. of California Press, 1966).

A. C. McBride and F. H. Kerr, "On Namias' fractional Fourier transforms," IMA J. Appl. Math. 39, 159-175 (1987).

W. W. Lin, V. Mehrmann, and H. Xu, "Canonical forms for Hamiltonian and symplectic matrices and pencils," Linear Algebr. Appl. 302-303, 469-533 (1999).

M. Moshinsky and C. Quesne, "Linear canonical transformations and their unitary representations," J. Math. Phys. 12, 1772-1780 (1971).

[CrossRef]

V. Namias, "The fractional order Fourier transform and its applications to quantum mechanics," J. Inst. Math. Appl. 25, 241-265 (1980).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation: I," J. Opt. Soc. Am. A 10, 1875-1881 (1993).

H. M. Ozaktas and D. Mendlovic, "Fractional Fourier transforms and their optical implementation: II," J. Opt. Soc. Am. A 10, 2522-2531 (1993).

S. C. Pei and J. J. Ding, "Eigenfunctions of linear canonical transform," IEEE Trans. Signal Process. 50, 11-26 (2002).

[CrossRef]

M. Moshinsky and C. Quesne, "Linear canonical transformations and their unitary representations," J. Math. Phys. 12, 1772-1780 (1971).

[CrossRef]

A. Vander Lugt, "Operational notation for the analysis and synthesis of optical data-processing systems," Proc. IEEE 54, 1055-1063 (1966).

W. W. Lin, V. Mehrmann, and H. Xu, "Canonical forms for Hamiltonian and symplectic matrices and pencils," Linear Algebr. Appl. 302-303, 469-533 (1999).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

S. C. Pei and J. J. Ding, "Eigenfunctions of linear canonical transform," IEEE Trans. Signal Process. 50, 11-26 (2002).

[CrossRef]

A. C. McBride and F. H. Kerr, "On Namias' fractional Fourier transforms," IMA J. Appl. Math. 39, 159-175 (1987).

V. Namias, "The fractional order Fourier transform and its applications to quantum mechanics," J. Inst. Math. Appl. 25, 241-265 (1980).

M. Moshinsky and C. Quesne, "Linear canonical transformations and their unitary representations," J. Math. Phys. 12, 1772-1780 (1971).

[CrossRef]

H. J. Butterweck, "General theory of linear, coherent optical data-processing systems," J. Opt. Soc. Am. 67, 60-70 (1977).

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S. A. Collins, Jr., "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Am. 60, 1168-1177 (1970).

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

R. Simon and N. Mukunda, "Iwasawa decomposition in first-order optics: universal treatment of shape-invariant propagation for coherent and partially coherent beams," J. Opt. Soc. Am. A 15, 2146-2155 (1998).

M. J. Bastiaans and T. Alieva, "First-order optical systems with unimodular eigenvalues," J. Opt. Soc. Am. A 23, 1875-1883 (2006).

A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993).

D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation: I," J. Opt. Soc. Am. A 10, 1875-1881 (1993).

H. M. Ozaktas and D. Mendlovic, "Fractional Fourier transforms and their optical implementation: II," J. Opt. Soc. Am. A 10, 2522-2531 (1993).

M. J. Bastiaans and T. Alieva, "Generating function for Hermite-Gaussian modes propagating through first-order optical systems," J. Phys. A 38, L73-L78 (2005).

[CrossRef]

W. W. Lin, V. Mehrmann, and H. Xu, "Canonical forms for Hamiltonian and symplectic matrices and pencils," Linear Algebr. Appl. 302-303, 469-533 (1999).

M. J. Bastiaans and T. Alieva, "First-order optical systems with real eigenvalues," Opt. Commun. 272, 52-55 (2007).

A. Vander Lugt, "Operational notation for the analysis and synthesis of optical data-processing systems," Proc. IEEE 54, 1055-1063 (1966).

R. K. Luneburg, Mathematical Theory of Optics (U. of California Press, 1966).

K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, 1979).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

K. B. Wolf, Geometric Optics on Phase Space (Springer, 2004).

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

F. R. Gantmacher, The Theory of Matrices (Chelsea, 1974-1977).